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Changing Climate: Report of the Carbon Dioxide Assessment Committee (1983)

Chapter: FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS

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Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 88
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 89
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 90
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 91
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 92
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 93
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 94
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 95
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 96
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 97
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 98
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 99
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 100
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 101
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 102
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 103
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 104
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 105
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 106
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 107
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 108
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 109
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 110
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 111
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 112
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 113
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 114
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 115
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 116
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 117
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 118
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 119
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 120
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 121
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 122
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 123
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 124
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 125
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 126
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 127
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 128
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 129
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 130
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 131
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 132
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 133
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 134
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 135
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 136
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 137
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 138
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 139
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 140
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 141
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 142
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 143
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 144
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 145
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 146
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 147
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 148
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 149
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 150
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 151
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 152
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 153
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 154
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 155
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 156
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 157
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 158
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 159
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 160
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
×
Page 161
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 162
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 163
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 164
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 165
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 166
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 167
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 168
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 169
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 170
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 171
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 172
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 173
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 174
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 175
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 176
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 177
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 178
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 179
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 180
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 181
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 182
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 183
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 184
Suggested Citation:"FUTURE CARBON DIOXIDE EMISSIONS FROM FOSSIL FUELS." National Research Council. 1983. Changing Climate: Report of the Carbon Dioxide Assessment Committee. Washington, DC: The National Academies Press. doi: 10.17226/18714.
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Page 185

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Future Carbon Dioxide Emissions 2 from Fossil Fuels 2.1 FUTURE PATHS OF ENERGY AND CARBON DIOXIDE EMISSIONS William D. Nordhaus and Gary W. Yohe This section deals with the uncertainty about the buildup of CO2 in the atmosphere. It attempts to provide a simple model of CO2 emissions, identify the major uncertain variables or parameters influencing these emissions, and then estimate the best guess and inherent uncertainty about future CO2 emissions and concentrations. Section 2.l.l is a self-contained overview of the method, model, and results. Section 2.l.2 contains a detailed description of sources, methods, reservations, and results. 2.l.l Overview There is widespread agreement that anthropogenic carbon dioxide emissions have been rising steadily, primarily driven by the combustion of fossil fuels. There is, however, enormous uncertainty about the future emission rates and atmospheric concentrations beyond the year 2000; and even greater uncertainty exists about the extent of climatic change and the social and economic impacts of possible future trajec- tories of carbon dioxide. Yet, if the appropriate decisions are to be made, the balance of future risks and costs must be weighed, and producing best possible estimates of future emission trajectories is therefore imperative. Many of the early analyses of the carbon dioxide problem have produced estimates of future emissions and concentrations from extrapo- lative techniques (see Section 2.2, the accompanying survey by Ausubel and Nordhaus). For the purposes of understanding future outcomes and policy choices, these techniques leave important questions unanswered. First, they do not allow an assessment to be made about the degree of precision with which the forecast has been constructed. Moreover, little information is generated about the underlying structure that produced the reported trajectories. It is, therefore, hard to know how changing economic structures might alter the pattern of CO2 emissions. But information about precision and sensitivity are sometimes of criti- cal importance to policy makers. It is critical to know not only the 87

88 best scientific assessment of an event but also the extent to which that judgment is precisely or vaguely known. Particularly in cases where policy decisions are irreversible, for example, the best decision in the face of great uncertainty might be simply to gather more informa- tion. But that decision would be extremely difficult to reach without some notion of the extent of the uncertainty surrounding the projections. In an attempt to address uncertainties, a second generation of studies, employing scenario analysis, has arisen. These studies, notable among them Limits to Growth (Meadows et al., l972), CONAES (Modeling Resource Group, l978), and IIASA (l98l), have traced time paths for important variables with a well-defined model and specified sets of assumptions. The studies, which we call "nonprobabilistic scenario analysis," represent a marked improvement over earlier efforts. They still fall short of providing the policymaker with a precise notion of the likelihood that a particular combination of events might occur: Is the "high" scenario l in l0, l in l00, or what? In this section an effort is made to put more definite likelihoods on alternative views of the world. The technique, called probabilistic scenario analysis, extends the scenario approach to include modern developments in aggregate energy and economic modeling in a simple and transparent model of the global economy and carbon dioxide emissions. Particular care is given not only to assure that the energy and produc- tion sectors are integrated but also to respect the cost and avail- ability of fossil fuels. In addition, the analysis presented here attempts to recognize the intrinsic uncertainty about future economic, energy, and carbon cycle developments. This is done by specifying the most important uncertain parameters of the model, by examining current knowledge and disagreement about these parameters, and then by specifying a range of possible out- comes for each uncertain variable or parameter. The emphasis is not to resolve uncertainties but to represent current uncertainties as accu- rately as possible and integrate them into the structure in a consistent fashion. The result of the entire process is the generation of a range of paths and uncertainties for major economic, energy, and carbon dioxide variables—projections of not only a "best guess" of the future paths of important variables but also a set of alternative trajectories and associated probabilities that quantify the range of possible out- comes on the basis of the current state of knowledge about the under- lying uncertainty of the parameters. It is reasonable, even at this early stage, to ask why such an elaborate effort to quantify uncertainty should be undertaken. Cannot prudent policy be written on the basis of the "best-guess" trajectories of important variables? In general, the answer is "no." To limit analysis to the best-guess path is to limit one's options. Similarly, to consider some possible path with no assessment of its likelihood relative to other possible paths is a formula for frustration, leading to endless arguments about which path should be taken most seriously. But to consider a full range of possibilities, along with each one's likelihood, allows a balanced weighing of the important and the unimportant in whatever way seems appropriate.

89 Armed with probabilistic scenarios, in other words, the policymaker will be able to evaluate a new dimension of his problem. He can assess not only a policy along a most likely trajectory but also along other trajectories that cannot be ruled out with some degree of statistical significance. With some knowledge of the range of uncertainty, he might decide to ask for more information to narrow the range, particularly if a policy seems to be warranted only by a few selected outcomes. Alter- natively, he might choose to minimize the risk of proceeding along an undesirable set of possible paths. And finally, he might undertake a policy based simply on an expected value. Any one of these options might prove to be prudent, but none of them is possible without a quan- tified range of possibilities. It is toward providing such a range that this section is directed. The plan of the overview is this. We first sketch the model that is used to relate the different variables and project future carbon dioxide emissions. We then describe the data sources and some adjustments that we have made to the data. Finally, we describe the results. It should be noted that a full description of the methods is contained in Section 2.2. The economic and energy model is a highly aggregative model of the world economy and energy sector. It is based on the idea of a multi- input production function that represents the relationship between world Gross National Product (GNP) (the output), on the one hand, and labor, fossil fuels, and nonfossil fuels (the inputs), on the other. In addition, to reflect the likelihood that economic efficiency will continue to improve in the future, various technological parameters are included to describe the rate of growth of economic efficiency in general, as well as the extent to which that growth is more or less rapid in the energy sectors than in the nonenergy sectors. A further important feature is the explicit incorporation of both the extent to which it is relatively easy or difficult to substitute nonenergy inputs (insulation or radial tires) for energy inputs (heat- ing oil or gasoline) and the extent to which it is easy or difficult to substitute nonfossil energy (nuclear or solar-derived electricity or hydrogen) for fossil energy (coal-fired electricity or gasoline). The prices of different inputs play a central role in reflecting scarcity and driving the relative quantities of different inputs. We thus introduce a cost function for fossil fuels that relates their price to their degree of exhaustion or abundance. On the other side of the market we generate an economically consistent derived demand for energy from the structure of the production function as the response of eco- nomic agents to changes in relative prices of different fuels and other inputs. Thus, if fossil fuels are scarce and costly, the system will economize on this input and use relatively more nonfossil fuels and labor inputs. Finally, we recognize that there are a number of important uncer- tainties about the model and future trends. We thus incorporate l0 key uncertainties in the model. These relate to variables such as the rate of population growth, the availability and cost of fossil fuels, the

90 rate of growth of productivity, the extent to which productivity growth will be relatively more rapid in fossil fuels versus nonfossil fuels, or in energy versus nonenergy, and so forth. A complete list of the uncertainties, with their relative importance in determining the total uncertainty is presented later in this overview. The data are gathered from diverse sources and are of quite different levels of precision. In general, we have surveyed the recent literature on energy and economic modeling to determine what are commonly held views of such variables as future population growth or productivity growth. Other variables, such as the ease of substitution or differ- ential productivity growth, were ones that are not the subject of common discourse; for these, we examined recent trends or results generated by disaggregated studies. A much more difficult data problem arose from the need to estimate the uncertainty about key parameters or variables. Our starting assump- tion was to view the dispersion in results of published studies as a reflection of the underlying uncertainty about the variable studied. This starting point was modified in two respects. First, it is com- monly observed that even trained analysts tend to cluster together excessively—that is, they tend to underestimate the degree of uncer- tainty about their estimates. To account for this tendency to move toward the current consensus, we have spread out some of the distribu- tions of observations by slightly less than 50%. Second, we have also imposed our own judgments about the uncertainties in those cases where no external data or disagreement existed or where the disagreement was so small as to convince us that the predictions were not independent. He must emphasize that these judgments about the uncertainties in our understanding of the variables are only rough judgments; the methods of estimation are difficult, and they could be quite far from the estimates that would come from a more thorough study. On the other hand, however, several validation exercises revealed that our results were within the statistical realm of reason, i.e., they fell within reasonable bounds of uncertainty that could be deduced by other means on the basis of historical experience. Using the model and data just sketched, we investigated the range of outcomes for economic, energy, and carbon dioxide variables. There were ultimately l0 uncertain variables, each of which was discretized into high, medium, and low values in such a way that the variance of the discretized variable was equal to the variance of the continuous variable. We thus ended up with 3l0 (=59,049) different possible outcomes. Rather than do a complete description, we settled on sampling l00 or l000 of the different possible outcomes. The results reported below, then, should be interpreted as samples of the underlying dis- tributions (although the sampling errors are known to be quite low). He now turn to brief descriptions of the major results of this study, with the promise that a more complete description can be found in Section 2.l.2. The first set of results pertains to the central estimates and range of estimates of the central variables, carbon dioxide emissions and concentrations. Our central estimate here is

9l taken as the sample mean of l000 runs.* Carbon dioxide emissions are projected to rise modestly to the end of our time horizon, the year 2l00. We estimate that carbon dioxide emissions will grow at about l.6% annually to 2025, then slow to slightly under l% annually after 2025. Atmospheric concentrations in the average case are expected to hit the nominal doubling level (600 ppm) around the year 2070. These results show a considerably slower emissions rate and carbon dioxide buildup than many of the earlier studies (see Ausubel and Nordhaus, Section 2.2) for two major reasons. First, the expected growth of the global economy is now thought to be slower than had earlier been generally assumed; our work includes this new expectation. Perhaps more importantly, we also include the tendency to substitute nonfossil for fossil fuels as a result of the increasing relative prices of fossil fuels. This is an important effect that has frequently been ignored. The next result concerns our attention on the degree of uncertainty about future carbon dioxide emissions and concentrations. The range of uncertainty is shown in Figures 2.l to 2.4. Figures 2.l and 2.2 show l00 randomly chosen outcomes for carbon dioxide emissions and concentra- tions. These are shown mainly to give a visual impression of the range of outcomes. Figures 2.3 and 2.4 present the five runs that represent the 5th, 25th, 50th, 75th, and 95th percentiles of outcomes—where we measure the outcomes in terms of the cumulative carbon dioxide emissions by the year 2050. It should be emphasized that the percentiles are derived from the actual sampling distribution. They reflect, therefore, the distribution of outcomes derived from the interaction of expert opinion on the underlying random parameters and the economic model; they reflect judgment not an objectively derived distribution. Perhaps the most useful graph to study is Figure 2.4, which shows the percentiles of carbon dioxide concentrations. For a quarter or half century, the inertia built into the economy and the carbon cycle leave an impression of relative certainty about the outcomes. After the early part of the next century, however, the degree of uncertainty becomes extremely large. In terms of our conventional doubling time, note the time at which carbon dioxide concentrations are assumed to hit 600 ppm: Percentile Doubling Time 5 After 2l00 25 2l00 50 2065 75 2050 95 2035 *More precisely, if Xj were the value assumed by run j, whose underlying sample of the l0 random variables gave it a probability of l000 Pj, then the central estimate would be I pjxj-

92 100.0H 117.5 19.3 0.4 O.H 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.l Carbon dioxide emissions for l00 randomly drawn runs (billions of tons of carbon per year). Outcomes of l00 randomly chosen runs; the numbers on the right-hand side indicate the mean projected yearly emission for the year 2l00 and the extreme high and low outcomes.

93 2500.0 H 1250.0- 625.0- 312.5 2100 780 370 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.2 Atmospheric concentration of carbon dioxide (parts per million). Outcomes of l00 randomly selected runs; the numbers on the right-hand side indicate the mean concentration for the year 2l00 and the extreme high and low outcomes.

94 100.0 2 10.0 oc o 0.1 96th 54.9 1975 2000 2025 2050 YEAR 2075 2100 FIGURE 2.3 Carbon dioxide emissions (gigatons of carbon) from a sample of l00 randomly chosen runs. The 5th, 25th, 50th, 75th, and 95th percentile runs for yearly emissions, with emissions for years 2l00, 2025, 2050, and 2l00 indicated. From this result, we make the central conclusion: Given current knowledge, we find that the odds are even whether the doubling of carbon dioxide will occur in the period 2050-2l00 or outside that period. We further find that it is a l-in-4 possibility that CO2 doubling will occur before 2050, and a l-in-20 possibility that doubling will occur before 2035. The next issue addressed is the question of the relative importance of different uncertainties. We have computed by two different techniques the relative importance of the ten uncertain variables discussed above, and the results are shown in Table 2.l. This table calculates the contribution to the overall uncertainty that is made by each variable taken by itself. In one case, shown in column (2), the contribution is calculated as the uncertainty introduced when a variable takes its full range of uncertainty and all other variables are set equal to their most likely

95 2500.0H 2 1250.0 g 625.0- 312.5 95th 1440 910 770 580 540 6th 1975 2000 2025 YEAR 2050 2075 2100 FIGURE 2.4 Atmospheric concentration of carbon dioxide (5th, 25th, 50th, 75th, and 95th percentiles; parts per million). The indicated percentile runs for concentrations; the numbers on the right-hand side indicate concentrations in the year 2l00 for each run. values. In the first column, the uncertainty is calculated from the run in which the full panoply of uncertainties is deployed—that is, when all other nine uncertain variables are allowed to take their full ranges of outcomes. In both cases, we have created index numbers with the variable that induces the most uncertainty set equal to l00, and other variables are scaled by their ratio of uncertainty added to that of the variable with the largest contribution. The two indices are used because they convey different information. The variable in column (l) is more relevant to uncertainty reduction in the real world (because other variables do indeed have uncertainty); but the calculations in column (l) are dependent on the uncertainties assumed for the whole range of variables. The numbers in column (2) are, for that reason, more robust to misspecification in the uncertainty of other variables.

96 TABLE 2.l Indices of Sensitivity of Atmospheric Concentration in 2l00 to Uncertainty about Key Parameters (l00 = Level of Effect of Most Important Variable.3.) (l) (2) Marginal Marginal Variance Variance from from Most , Parameter- Full Sample- Likely Outcome- Ease of substitution between fossil and nonfossil fuels [l/(r - l)] l00 l00 General productivity growth [A(t)] 76 79 Ease of substitution between energy and labor [l/(q -l)] 56 70 Extraction costs for fossil fuels [gl] 50 56 Trends in real costs of producing energy [h^t)] 48 73 Airborne fraction for CO2 emission [AF(s)] 44 62 Fuel mix among fossil fuels [Z(t)j 3l 24 Population growth [L(t)l 22 36 Trends in relative costs of fossil and nonfossil fuels [h,(t)] _ (3)- 2l Total resources of fossil fuels [R] (50)— 5 .iValue of sensitivity is scaled at l00 for the variable that has the highest marginal variance. ^Notation in the square brackets refers to variable notation in the model presented formally in Section 2.2. —"Marginal variance" from full sample equals (l) the variance in the base case (i.e., with all variables varying according to their full range of uncertainty) minus (2) the variance with listed variable set at its most likely value (but all nine other variables varying according to their full uncertainty). Note that no resampling occurs. —"Marginal variance from most likely outcome" calculated as the variance when the listed variable assumes its full range of uncertainty and all nine other variables are set equal to their most likely value. ^Parentheses indicate that the marginal variance is negative. The ranking of the importance of uncertainties shown in Table 2.l contains several surprises. First, note that an unfamiliar production parameter ranks at the top of both columns—the ease of substitution between fossil and nonfossil fuels. While some studies have included substitution parameters in their model specifications (notably Edmonds and Reilly, l983), the sensitivity of concentration projections to assumptions about substitution has not been noted earlier. A second set of variables on the list include those that have been exhaustively discussed in the carbon dioxide literature—the world resources of

97 fossil fuels and the carbon cycle ("airborne fraction"). Our estimates indicate that these are of modest significance in the uncertainty about future carbon dioxide concentrations. Table 2.l is also extremely suggestive about research priorities in the carbon dioxide area. We cannot, it should be emphasized, move directly from the source of uncertainties to a budget allocation for research funds on carbon dioxide. It may be much easier, for example, to resolve uncertainties about the "depletion factor" for carbon fuels than about future "productivity growth." As a result research funds might therefore be more fruitfully deployed in the first prior area than in the second. On the other hand, the results suggest that considerably more atten- tion should be paid to some uncertainties that arise early in the logical chain from combustion to the carbon cycle, particularly better global modeling of energy and economy. It is striking, for example, to note that the United States supports considerable work on global carbon cycle and global general circulation (climate) models, but much less attention in the United States has been given to long-run global eco- nomic or energy modeling (see Section 2.2 for a further discussion. Finally, it is possible to explore more fully the ramifications of Figure 2.4—the figure that indicated 5th, 25th, 50th, 75th, and 95th percentile trajectories for atmospheric concentrations of carbon dioxide. One might ask, what parameters are most influential in determining whether the concentration path deviates from the median in either direction; Table 2.l provides the answer. If uncertainty in a parameter is significant in its effect on the overall variance of the outcome, then it follows that movement in that parameter away from its projected median would be significant in its effect on the outcome variable. Clearly, therefore, an increase (decrease) in the ease of substitution out of fossil fuel as it becomes more expensive would significantly increase the likelihood that the concentration trajectory would be lower (higher) than the 50th percentile. Similarly, slower (more rapid) productivity growth would cause slower growth in energy consumption and produce a significant lowering (raising) of the con- centration trajectory. As a final set of experiments, we have used our procedure to make extremely tentative estimates of the effect of energy-sector policies that are designed to reduce the burning of fossil fuels. The particular policy we investigate is the imposition of fossil fuel taxes, set, for illustrative purposes, at $l0 per ton of coal equivalent and at a more stringent level. Taxes were not chosen for any reason other than modeling ease. Any type of emissions restraint can be represented analytically by its equivalent tax. These runs use the most likely outcome as a base case. Figure 2.5 shows the trajectory of taxes that we have investigated, while Figures 2.6 and 2.7 show the effects of the different tax policies on the level of carbon dioxide emissions and on carbon dioxide concentrations. In general, the taxes lower emissions noticeably during the period in which the taxes are in place. The effect on concentrations at the end of the twenty-first century of the $l0 tax are quite modest. These examples are included here only to illustrate the nature of a problem that deserves much more attention.

98 They suggest, as does some other work in the literature (Edmonds and Reilly, l983), that the use of carbon taxes (or their regulatory equivalents) will have to be quite forceful to have a marked effect on carbon concentrations, even if they are imposed worldwide. Unilateral regulations would, of course, have to be substantially more restrictive. 90- 80- 1 70- 60- 3 50 - o -6 S = 40J X 30 J 20 - 10- 0 - TlME Pulse 1980 Pulse 2025 Stringent Permanent 1980 Permanent 2025 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.5 Taxation on carbon fuel price (l975 dollars per ton coal equivalent). The time tracks of a stringent tax and four alternative $l0 per ton of coal equivalent taxes; the temporary taxes peak at $20 to accommodate the model.

99 S 8 UJ CD tr Or -ir -2- -3- i -4- -6- -7- -8- -9- -10- Permanent Beginning in 1980 V Permanent Beginning in 2020 Temporary Beginning in 1980 Temporary Beginning in 2020 Pulse 1980 Permanent 1980 Stringent Pulse 2025 Permanent 2025 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.6 Plot of carbon emission versus time for taxed runs. Deviation in emissions from the base run for various taxes. 2.l.2 Detailed Description of the Model, Data, and Results The preceding section provided an overview of the paper—its motivation, its methodology, and its results. This section will provide a more complete description of the procedures. Throughout, an attempt will be made to refrain from using economic jargon and overly technical lan-

l00 0 -10- -20- -30- g -40J K -50- 8 -60- 8 O -70- -80- -90- -100 -110- -120 Temporary Beginning in 2020 Pulse 1980 Permanent 1980 Stringent PulBe 2025 Permanent 2025 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.7 Effect of carbon taxes on atmospheric concentration (parts per million per year) . Deviation of run from base run without carbon taxes . guage. Where this is impossible, definitions of terms will be given in footnotes. It is hoped that the reader who is unfamiliar with the terminology will be able to follow the reasoning of the paper by referring to these notes. 2.l.2.l The Model 2.l.2.l.l Methodological Summary Before we launch into a detailed description of the data and methods used in the present study, it may be useful to give a brief symbolic overview of the events to follow. We start by denoting the variables:

l0l xfc = endogenous variables (those determined within the system), as they unfold over time; zt = exogenous variables (those determined outside the system), as they unfold over time; k = parameters of the system, assumed to be constant over time; G = a functional relation, mapping the exogenous variables and parameters into the endogenous variables. The present study is concerned with the future evolution of CO2 emissions and concentrations as the endogenous variables—these are the xfc variables. The key exogenous variables (or zt) are economic "events," such as population growth or fossil fuel reserves. Parameters that relate the variables (the k's) are ones such as the airborne frac- tion or the emissions per unit energy produced. We thus write our system symbolically as xfc = G(zt, k). The pages that follow describe how we derive the relational function, G; how we estimate future trajectories of the exogenous variables, zt; and how we estimate the parameters, k. The central difficulty with studies of this kind is that the system is imperfectly known. We are not able to forecast the zt with accuracy; indeed, we may not know which are the important exogenous variables. The parameters, also, are imperfectly known. The technique that follows uses a procedure that we have denoted probabilistic scenario analysis. We start with a simple representation of the system (the function G). We then estimate future trajectories and subjective probability distributions [denoted by g(.) and h(.)] of the exogenous variables and parameters zt and k: g(zt), h(k) (judgmental probability distributions on zt, k). These then map through the G function to give us a conditional probability distribution—f(.)—on the variables of concern, the xt: G:[g(zt), h(k)] •> f(xt). All of this is, unfortunately, much more easily described than accom- plished. The major issues that arise are these: First, the G function is not known in advance and may be extremely complex. Second, neither the exogenous variables nor the parameters are well known. The scien- tific and economic literature can be used to illuminate the "best guess" about these variables or parameters, however. Third, the judgmental probability distributions are ignored in most of the applied scientific literature. Attempting to determine these distributions is the hardest part of our task. And finally, there is no established methodology for developing probabilistic scenarios. The text that follows outlines one attempt to overcome these difficulties.

l02 An aggregate world production function sets the stage.* We chose the simplest conventional form that would allow explicit parameters for both the share of GNP devoted to energy and the ease of substituting between fossil and nonfossil fuels t : X(t) = A(t)L(t)d(t)[bEC(t)r + (l - b)En(t)r] [l - *<, (l) where X(t) = world GNP at time t in constant l975 U.S. dollars; L(t) = world population at time t; A(t) » level of labor productivity at time t in U.S. dollars of output per capita; (l - d) - the proportion of GNP devoted to paying for energy; Ec(t) » consumption of fossil fuels at time t in metric tons of coal equivalent; En(t) = consumption of nonfossil fuel at time t in metric tons of coal equivalent; r « a parameter reflecting the ease of substitution between Ec(t) and En(t) ; and b = a parameter reflecting the relative levels of use of Ec(0) and En(0) . Equation (l) is not so mysterious as it might first appear. It assumes its peculiar form because of well-established techniques in micro- economics. They mandate that if a production process with certain conventional properties is to be represented mathematically, then the researcher is locked into an equation of the general type exhibited in (l) . A slightly simpler form exists (the straight Cobb-Douglas form) and could have been employed, but that would have restricted the degree of substitution between the two types of energy in an arbitrary and unacceptable manner. To preserve desired flexibility in the specifi- cation of the ease of substitution, Equation (l) is the simplest option available. Turning now to a brief discussion of some of those desirable properties, it is important to note, first, that Equation (l) displays constant returns to scale; i.e., doubling L(t) , Ec(t) , and En(t) from any level necessarily doubles output. As growth proceeds, this *A production function is a mathematical representation of a production process that employs a variety of inputs in a variety of combinations to manufacture some type of output. General production functions allow for substitution between any of the inputs in response to changes in input prices so that the manufacturer can maximize profits. tThe estimation of production functions is a well-developed field in economics. There have been numerous surveys, of which that by Johnston (l972) is perhaps the most comprehensive. Also see Nerlove (l965) for a careful study of the identification and estimation of the particular production function that we use, the "Cobb-Douglas" version.

l03 feature guarantees that payments to labor employed and for energy consumed exhaust output. It should be noted, at least in passing, that almost all production relationships that spring to mind easily, and almost all that are used in existing studies, display this constant returns-to-scale property. Imposing it on our production schedule did not drive us afield of conventional economic modeling. Note as well that Equation (l) aggregates the value of all nonenergy inputs into labor — the third factor of production. This aggregation produces a simplification that allows the model to isolate the potential substitution both between the two types of energy and between energy and other inputs without being unnecessarily cluttered by an index of what those inputs might be. No assumptions about constant capital-labor ratios are being made, and any increased productivity that might be created by this secondary substitution is captured in the A(t) param- eter. Nonetheless, the substitutions of critical importance in an energy-emissions model — substitution between the two major types of energy and substitution between energy and other inputs — are both identifiable and quantifiable. We will return to them shortly. Before doing so, however, it is convenient to discuss the derived demand for energy implicit in the functional form of Equation (l) as it stands. Since energy demand is derived entirely from production, Equation (l) imposes some unavoidable structure on the demand for energy. The share of X(t) devoted to paying for energy at any point in time is, first of all, fixed; i.e., letting Pn(t) represent the real price of Ec(t) at time t in l975 U.S. dollars and Pc(t) represent the real price of Ec(t) at time t, then the share devoted to energy can be expressed as Pn(t)En(t) + P°(t)Ec(t) » (l - d)X(t) (2a) for all t. Letting En(t) + Ec(t) = E(t) represent total energy demand and - P(t) represent the weighted aggregate price of energy, Equation (2a) can immediately be rewritten in the more convenient form: E(t) - (l - d)X(t)/P(t). (2b) It becomes clear, therefore, that Equation (l) imposes unitary price and income elasticities on the aggregate energy demand equation.* *The price elasticity of demand is a reflection of the responsive- ness of the quantity demanded to changes in the price. It is formally defined as the ratio between the percentage change in the quantity (continued overleaf)

l04 Additionally, the particular nested form of Equation (l) necessarily requires that the relative demand for Ec(t) and En(t) take the form EC(t) En(t) (l - b) P(t) l/r - l (3) Implicit in Equation (l), then, is the condition that a l% increase in the energy price ratio of fossil to nonfossil fuel must always generate a[(r - l)-l]% reduction in the ratio of fossil to nonfossil fuel use. Since the parameter r could be arbitrarily specified, however, Equation (3) is not nearly so restrictive as Equation (2b). Still, the point is this: by specifying the production function, we fully specify the underlying structure of demand for all three of our inputs—labor, fossil fuel, and nonfossil fuel. Quantification of the ability to substitute between the two types of energy and between labor and energy now follows straightforwardly from the derived demand schedules just noted. To that end, let d ln[EC(t)/En(t)] S **- d ln[PC(t)/Pn(t)] represent the notion of the "elasticity of substitution" between the two types of energy; i.e., let s represent a measure of how responsive the ratio of fossil to nonfossil fuel consumed worldwide is to changes in the relative prices of the two fuels. Logarithmic differentiation of Equation (3) then reveals that s = (r - l)"l. If r were to equal 0.5, therefore, s would equal -2.0, indicating that any l% increase in the relative price of carbon-based fuel would (continued from overleaf) demanded and the percentage change in the price that caused demand to change; i.e., (price elasticity) = d ln[E(t)]/d ln[P(t)]. Given Equation (2b), therefore, it is clear that the price elasticity of the derived demand for energy is (-l). The income elasticity of demand is similarly defined as the ratio between the percentage change in the quantity demanded and the percentage change in income. Since notationally the income elasticity of demand is d ln[E(t)]/d ln[X(t)], it is equally clear that this elasticity must also equal l for the schedule listed in Equation (2b). In conclusion, therefore, the structure of the production schedule recorded in Equation (l) implies that (i) a l% increase in the price of energy would always cause a l% reduction in the demand for energy, while (ii) a l% increase in world GNP would always cause a l% increase in the demand for energy.

l05 produce a 2% reduction in the carbon to noncarbon fuel consumption ratio. A similar computation meanwhile shows that the corresponding elasticity of substitution between either Ec(t) or En(t) and labor is unity. Thus, the unitary price and income elasticities of aggregate energy demand already noted from Equation (2b) were to be expected. The lack of flexibility in this last elasticity was a source of concern. We were not anxious to be boxed into a structure of unitary elasticities in the demand for energy, but we were bound by a well-known result of economic theory: in maintaining the simple production struc- ture that we felt was required to preserve the necessary transparency in the intertemporal model, we were forced to set the elasticity of substitution between energy and labor either to s = (r - l)"* or to unity. Rather than loosen this theoretical binding by resorting to a more complicated production function, we chose instead to provide the desired flexibility by keeping Equation (l) as our fundamental produc- tion relationship and adjusting the share of world GNP used to pay for energy over time. To see how this was accomplished, let i X(t) = A(t)[mL(t)q + (l - m)E(t)q] (l1) represent the next logical generalization of production. The parameter q here reflects the ease of substituting between energy and labor in the production process; it is the analog to the parameter r in Equation (l), and (q - l) is the corresponding elasticity between energy now aggregated into one factor and labor. The resulting derived demands for labor and energy could then be combined to form the analog of Equation (3) : E(t) (l - m) P(t) Mt) I m w(t) ' (4) where w(t) represents the unit price of labor. Multiplying both sides of Equation (4) by [P(t)/w(t)], a more convenient form emerges: q/(q - l) ,. d(t) w(t)L(t) where k = [ (l - nO/m]1/^ - l) and taking the approximation that w(t) = 1.* Notice that the first part of that equation simply states that the relative share of GNP devoted to paying for energy must equal the ratio of the energy bill of the world, P(t)E(t), and the global wage bill w(t)L(t). It makes the d(t) parameter defined here the precise ^Setting w(t) = l requires an approximation, as follows: The model assumes that if the relative price of energy to labor, [P(t)/w(t)l, is constant, then d (the share of labor) is constant. We are attempting to examine the effect of changes in P(t)/w(t) on d. (continued overleaf)

l06 analog of the d parameter recorded in Equation (l). Rearranging terms, then, the equation d(t) - [kP(t)q/(q - l) + l]"l (5) provides a means by which the share of world GNP paid to energy can be adjusted from period to period in a manner consistent with an elasticity of substitution between labor and energy equal to (q - l)"1. We were able, with this procedure, to approximate a more general schedule like Equation (l') with a series of simpler schedules of the type shown in Equation (l) by simply adjusting energy's share of GNP in a way that was consistent with the more complex structure that we needed. We are, in other words, out of our theoretical bind. With this final step completed, we are able to set both the elas- ticity of substitution between fossil and nonfossil fuels and the elasticity of substitution between energy and labor equal to whatever the data suggested were appropriate values without overburdening the model with unnecessary complication. To proceed from this point it is necessary to specify how A(t), L(t), and the prices of the two fuels are to be determined over time. Productivity and population are the easiest; they take the forms A(t) = and L(t) - where A0 - labor productivity at t = 0 (l975); a(t) » rate of growth of labor productivity at time t; Lg = world population at t = 0; and l(t) » rate of growth of population at time t; The last three are taken to be exogenous. (continued from overleaf) If we were instead to set w(t) equal to its model solution, then Equation (4') could be written as X(t) = ke (t)7 , (4") where X » (l - d)/d, 6 = P/w, 7= q/(l - q) . Thus the change in X from one path to another would be Aln X(t) = y[AlnP(t) -Alnw(t)]. For given L(t) and P(t), we can solve this for w(t), and A ln w(t) is an order of magnitude smaller than Aln P(t), because the share of E is about one tenth of the share of L. Our approximation thus misstates the change in d by about one tenth. Also note that the share of L changes only a little.

l07 Energy prices are divided into production and distribution cost components (roughly the difference between wholesale and retail prices), and production costs are presumed to be subject to technological change. The price of noncarbon-based fuel is, more specifically, given by Pn(t) =P^P;ethl(t) + Vt)lfc, (6.) where P, a distribution costs in l975 U.S. dollars per metric ton of coal equivalent; P" = initial production costs in l975 dollars per metric ton of coal; -h.(t) » rate of technological change in the energy industry at time t; and -h (t) = bias of technological change toward noncarbon energy at time t are all exogenous. The last two entries in the list may require a little explanation. The rate of technological change in the energy industry is the rate at which the efficiency in the industry is improv- ing; conversely, it can be viewed as the inverse of the rate of change in the real price of energy. If, for example, the price of energy were decreasing at a rate of l% per year, this would be consistent only with a rate of technological change of l% per year. The bias in the rate of technological change reflects the possibility that technical change and innovation will not proceed at the same rate in both energy sectors. If innovation were more rapid in the nonfossil fuel sector, for instance, then the bias would favor that sector, and h2(t) would be positive. The price equation for fossil fuel takes similar form. The only complicating element here is the implicit inclusion of a depletion factor—a reflection of the usual expectation that the price of fossil fuel should increase over time as the world's resources of fossil fuels are used up. We do not, here, necessarily include supply and demand effects.* The depletion factor represents, more accurately, the notion *The model has one theoretical flaw from the point of view of the economics of exhaustible resources. This is that there are no rents charged to scarce fossil fuels. The economics and some estimates of such scarcity rents are provided in Nordhaus (l979) for a model without uncertainty. There is a very great difficulty in the present model, however, in calculating the appropriate scarcity rents. This difficulty arises because the appropriate scarcity rents will be different in each of the 3^0 possible trajectories. And the actual rent at each point of time will depend on the way that the uncertainties are revealed over time. (continued overleaf)

l08 that the price of fossil fuel must increase as the cheaper wells are drilled or mines are exhausted and as more expensive sources come on line. Depletion is represented as follows: (t) t c c / I - \~"2 \ 1 P (t) » P]; + ( gn+ gn { R(t)/[R - R(t)]} )e + T(t - t) , (6b) where c P = distribution costs in l975 U.S. dollars per metric ton of coal equivalent; g0 = initial production costs in l975 dollars per metric ton of coal equivalent; R = a measure of the world's remaining carbon-based fuel reserves in metric tons of coal equivalent in l975; T(t - t) » a tax policy parameter used to reflect taxation of fossil fuels; R(t) - [Ec(0) + ... + Ec(t - l)] » total carbon-based fuel consumed since l975 in metric tons of coal equivalent; and g^(i = l,2) = depletion parameters. In this list, of course, all but R(t) are taken to be exogenous. At this point, then, only three parameters remain to be determined: b, A, and m. These are specified, given assumed values for s, r, q, d, L0, Ec(0), En(0), (PQ + P£), and (gQ + P°), so that the entire set of parameters satisfied Equations (l), (3), and (5) at time zero. No further data are necessary. Special mention needs to be made of the policy variable T(t - t). It is included to reflect any policy that might be designed to reduce carbon dioxide concentrations either directly by taxes or indirectly by discouraging the consumption of fossil fuels. Since either type of policy would make it more expensive to burn these fuels, either would be captured by the tax T(t - t) that increased the price of Ec(t). The parameter t simply denotes the lag between the imposition of a CO2 reduction policy and its effect on the day-to-day operations of fuel burners. The use of a tax to summarize even quantity-based restrictions is widespread in the economic literature and is supported by the following equivalence theorem: for any targeted quantity restriction on, for example, carbon-based fuels, there exists a tax to (continued from overleaf) After some thought about the best way to calculate the rents, we finally gave it up as hopelessly complicated. In reality, it seems that, except for oil and gas, the scarcity rents are likely to be quite small for most of the time. This conclusion is based on a reading of the estimates from Nordhaus (l979). However, it should be noted that omission of the scarcity rent leads to a downward bias in the market price of fossil fuels and consequently in an upward bias in the estimate of CO2 emissions and concentrations. We expect that this bias is likely to be on the order of 0 to 2% during the period under consideration.

l09 be added to the price of carbon-based fuels such that consumers, in their own best interest, will undertake actions to lower their consumption to the prescribed target level.* Either tool, properly computed, can therefore achieve any arbitrary policy objective, and the generality of the tax approach is assured. Some have noted that the two alternatives need not be equivalent, in terms of their efficiency, under uncertainty. A similar theorem exists, however, when the comparison is conducted between alternatives computed to generate the same expected result. Others have worried that the equivalent tax might, in practice, be difficult to compute. Whether that is true or not, of course, this purported difficulty does not damage the treatment in the present paper. Returning now to the model, Equations (l) and (6) complete a simple, economically consistent vehicle with which to project the driving force of industrial CO2 emissions. Only a link to the atmosphere is required; that link is represented by C(t) , where C(t) = emissions of carbon in gigatons per year; ZQ = the "emissions factor," equal to the initial ratio of carbon emissions to fossil fuel consumption in l975; and z(t) = the rate of growth of the emissions factor. The last two are, of course, exogenous. The ratio z(t) is, moreover, presumed to increase over time because of a supply-induced change in the fuel mix (i.e., toward coal and shales). Nonfossil fuels are presumed to provide energy without adding to carbon emissions. An airborne fraction approach to link emissions to atmospheric concentrations is finally employed to complete the model. Formally, M(t) - M(t - l) + AF(s)[0.47l C(t)] - sM(t - l), (7) where s = a seepage factor reflecting the slow absorption of airborne carbon dioxide into the deep oceans; AF(s) = the marginal airborne fraction of carbon dioxide; and M(t) = carbon mass in the atmosphere in period t measured in parts per million. *See Yohe (l979) for a survey of the literature on this point.

ll0 Equation (7) is a standard representation of the complex workings of the atmosphere , frequently used in the carbon cycle literature.* The coefficient 0.47l preceding C(t) simply converts gigatons of carbon into the appropriate atmospheric units of parts per million. The seepage factor is a subject of current debate among researchers (see Brewer, this volume, Chapter 3, Section 3.2); in separate work, we have shown that the maximum likelihood estimate of the airborne fraction is quite sensitive to the specification of s; thus, the AF(s) notation. In summary, then, the model operates with the demands for fossil and nonfossil fuel being derived entirely from a production function that, for any year, assumes the form X(t) = A(t)L(t)d(t)[bEC(t)r They emerge summarized by Pn(t)En(t) + Pc(t)Ec(t) = [ and (l - b) P(t) - b)En(t)r] - d(t)]X(t) l/r - l (l) (2a) (3) with d(t) - [kP(t)q/(q - l) + l]"l. (5) Furthermore, the neutral productivity growth factor and labor growth component of Equation (l) are given exogenously by A(t, and A0e T . L e a(t)t respectively. The supply conditions from fossil and nonfossil fuels are meanwhile determined by *See Bolin (l98l) for a complete discussion of the concentration model. Our modification of that work specifies a marginal airborne fraction—the fraction of period t emissions that remain in the atmosphere on the margin (i.e., in period t). Whenever the seepage factor is nonzero, the marginal fraction does not equal the average fraction that most of the previous studies have employed.

lll Pn(t) - Pn + sj e[hl(t) + h2(t)]t (6.) and PC(t) - P° + g + gR(t)/[R - R(t)]2 e + T(t - t) (6b) \ \ hi(t)t ]|92J e i with R(t) « Ec(0) + . . . + Ec(t - l). Emissions are then recorded according to C(t) - and atmospheric concentrations according to M(t) - M(t - l) + AF(s)[0.47l C(t)] - sM(t - l). (7) Figure 2.8 represents a geometric interpretation of this process. 2.l.2.2 The Data Two kinds of data are required. Initial conditions are, first of all, required. Table 2.2 records the estimates for world GNP, world popula- tion, and world fossil and nonfossil fuel in l975. Since these initial conditions are based on historical evidence, consensus is not difficult to achieve. Existing studies and comparison with published data are sufficient to generate consistent estimates for these parameters. Initial energy prices are a bit more problematical. We want aggregate prices based on the historical distribution of, for example, fossil fuels between coal, oil, and gas. Table 2.3 records both the necessary raw data and their sources. Table 2.4 produces the aggregates and illustrates the procedure that is employed in their construction. Table 2.5 registers the emissions ratios of the various types of fossil fuels from which the initial value for the aggregate emissions ratio is com- puted. Table 2.4 also records that aggregation procedure. Finally, an initial level of atmospheric carbon concentration is required; current measures set the l975 value at 33l parts per million (ppm) (see Keeling et al. in Clark, l982, Table l, page 378). Data are also required to set the long-term context of the study—a more difficult problem. Projections of various important parameters into the near and distant future were compared, but the uncertainties inherent in such projection made consensus impossible. Existing studies provide ranges for variables like world population growth, world produc- tivity growth, energy prices, and the emissions factor, but no generally accepted paths emerge. The observed ranges are, however, viewed as more than spurious disagreement among researchers. They are, instead, viewed as a reflection of the inherent uncertainty about the variables. A more precise description of the technique we use is the following: we assume that the published estimates for each of the random variables

ll2 O u 41 00 • d §

ll3 TABLE 2.2 Initial Conditions for Population, GNP, and Aggregate Fuel Consumption A. World Population in l975 IIASA (l98l, p. l33) 4 x l09 Ridker and Watson (l980, p. 45) 3.8 x l09 Keyfitz (l982) 3.98 x l09 Value employed: L(0) 4 x l09 B. world GNP in l975 IIASA (l98l, p. 457) $ 6.4 x l0l2 Ridker and Watson (l980, p. 45) $ 4.5 x l0l2 Report of the President (l980) $ 6.53 x l0l2 Value employed: X(0)a- $ 6.4 x l0l2 C. Fossil Fuel Consumption in l975 IIASA (l98l, p. l36) 8.l27 x 109 mtce Ridker and Watson (l980, p. l85) 8.ll4 x 109 mtce Value employed: Ec(0) 8.l x l09 mtce D. Nonfossil fuel Consumption in l975 IIASA (l98l, p. l36) 0.67 x l09 mtce Ridker and Watson (l980, p. l85) 0.69 x l09 mtce Value employed: En(0) 0.7 x l09 mtce iLThe Ridker and Watson estimate was ignored because it was built around an estimate of per capita income that appeared to be low relative to other published data. identified in our model is an unbiased, but not necessarily independent, estimate of that variable. We use the means and variances of those estimates as a basis for constructing judgmental probability distribu- tions for each variable. To obtain a manageable number of alternatives from which to sample, we assume that each judgmental probability dis- tribution is normally distributed. We then take high, middle, and low values (corresponding to 25, 50, and 25%, respectively) that maintain the same means and variances as the estimated normal distributions. To put it more intuitively, we have constructed discrete distribu- tions to mirror the level of uncertainty at present surrounding the various analysts' published projections. In deference to the tendency of individuals to underestimate uncertainty, however, the procedure for reflecting uncertainty does not stop there. Particularly when the estimated variances declined over time, future variances are expanded beyond their computed ranges to correct for systematic underestimation of uncertainty. Section 2.l.2.2.l is devoted to a thorough exploration of this second procedural phase; the remainder of this section will concentrate on applying the first phase to the critical parameters. In passing, though, it should be noted that our procedure produces more than a purely subjective view of the future paths of some com- plicated variables. It produces a "judgmental" view that weighs the expert opinions of many researchers as expressed in their published

ll4 TABLE 2.3 Energy Price and Disaggregate Consumption Data A. Consumption Patterns (l975)3. I. Fossil Fuel Coal 2.42 x l09 mtce 30% Oil 4.l0 x l09 mtce 50% Gas l.6l x l09 mtce 20% Total 8.l3 x l09 mtce l00% II. Non fossil Fuel Hydro 0.53 x l09 mtce 8l% Nuclear 0.l3 x l09 mtce l9% Total 0.66 x l09 mtce l00% B. Energy Prices (1975)& I. Primary£ Coal $ l5/mtce Oil $ 5 4 /mtce Gas $ l9/mtce Electricity II. Seconder y<l $ll8/mtce Coal $ 23/mtce Oil $ 98/mtce Gas $ 28/mtce Electricty $255/mtce C. Energy Prices (l98l)6. I. Primary£ Coal $ l5/mtce Oil $l08/mtce Gas $ 86/mtce Electricty $ll8/mtce II. Secondary*! Coal $ 23/mtce Oil $l7l/mtce Gas $ll6/mtce Electricty $255/mtce ^Source: IIASA (l98l), p. 47l. ^Measured in l975 United States dollars. Source: Reilly et al. (l98l). HThese are wholesale prices. -These are retail prices. ^Measured in l975 United States dollars. They are derived from the l975 prices to reflect the impact of the l979 Iran-Iraq war as follows. The June l0, l982, issue of Blue Chip Indicators provided an estimate for the l98l wholesale oil price of $34.00 (current dollars) per barrel. That translates into $22.50 per barrel in l975 dollars, or $l08/mtce. The btu equivalent price for gas was then computed to equal (0.8($l08/mtce)] = $86/mtce. Coal and electricity (generated from nonfossil fuels) were assumed to remain constant over the 6-year period. The secondary prices for oil and gas were then computed by adding the reported consensus differences between wholesale and retail prices: $l3/barrel or $63/mtce for oil and $30/mtce for oil. Thus, secondary prices of [$l08 + $63] = $l7l/mtce and [$86 + $30] = $ll6/mtce were recorded, respectively.

ll5 TABLE 2.4 Aggregate Prices and Emissions A. Energy Prices in l975£ I. Primary Fossil fuelfe $ 35/mtce Nonfossil fuel0- $ ll8/mtce II. Secondary Fossil fuel£ $ 62/mtce Nonfossil fuel0- $ 255/mtce B. Energy Prices in l9815. I. Primary Fossil fuelSL $ 76/mtce Nonfossil fuel0- $ ll8/mtce II. Secondary Fossil fuel^ $ ll6/mtce Nonfossil fuel0. $ 255/mtce C. Emissions Ratio in l9756-: Z(0) 580 g of C/mtce ^Measured in constant l975 dollars. ^Computed using the prices and weights recorded in Table 2.3. In l975, for example, coal amounted to 30% of the total fossil fuel consumed and cost $l5/mtce, oil amounted to 50% of the total and cost $54/mtce, and gas amounted to 20% at a cost of $l9/mtce. Thus, the aggregate price of fossil fuel in l975 was 0.3($l5) + 0.5($54) + 0.2($l9) - $35/mtce. —The price of nonfossil fuel was taken to be the price of electricity generated from nonfossil sources. -Computed using the weights and prices recorded in Table 2.3. The weights employed were the l975 numbers because it was unlikely that major substitutions could have occurred in the 6 years from l975 and l98l. This presumption is borne out by data published in the BP Statistical Review of the World Oil Industry, l980, p. l6. ^The ratio of grams of carbon emitted per mtce of fuel consumed. The l975 consumption weights of Table 2.3 were combined with the emission data of Table 2.5 to produce Z(0); i.e., Z(0) - 0.3(700) + 0.5(577) + 0.2(404) = 580 g of C/mtce. work. The data for obtaining parameter estimates are not, in other words, anonymous and private. They are public and thus presumably derived with the care that scientists use in producing work attached to their names. And they are judgmental views about nonelemental variables—not variables like GNP growth or energy growth that depend

ll6 TABLE 2.5 Carbon Emissions from Fossil Fuels! Fuel kg of C/l09 J kg of C/ratcek Petroleum l9.7 577 Gas l3.8 404 Coal 23.9 700 Shale oil£ 4l.8 l224 ^Source: Marland (l982). ^Conversion based on l mtce - 29.29 x l09 J; kg of C, kilograms of carbon. ^Includes carbon dioxide emissions due to shale oil mining and extraction. on a host of known and unknown effects, but variables like population growth and resource availability that depend on fewer things.* Beginning once again with population numbers, Table 2.6 shows that a variety of growth projections have been made for at least the next 50 years. Each assumes no major catastrophes; and while the general trend in each calls for a steady decline in the rate of growth, there is some disagreement. Differences are to be expected, of course, but it is interesting to note that these differences found their source in the assumptions made about the less-developed countries; the historical experience of the LDCs has been so widely varied that a common expecta- tion would, of course, have been surprising. The full effect of that disagreement is not reflected in the world projections, however, because the larger, more-developed countries have displayed low, stable growth rates over the past few decades. Of further interest was the marked reduction in the variance of pro- jections beyond the year 2025; most researchers predict that the world's population will stabilize sometime after the first third of the twenty- *Two technical points might be raised: First, are the estimates independent? It is likely that some of the figures depend on previous estimates—indeed, they might all go back to a single careful study. We have been unable to check for such an occurrence in every case, but in some we are confident that the outcomes are truly independent, even competitive. Second, are the underlying judgmental probability distributions independent? While some lingering correlations probably exist, we took care to construct our random variables so that the correlations were low—that is, the variables are intended to be orthogonal. Thus, the rate of productivity growth in energy is thought to be independent of the difference in productivity growth between fossil and nonfossil fuels.

ll7 TABLE 2.6 Projected Trends in the Growth Rates of World Population! Source of Estimate^ l975-2000 2000-2025 2025 and beyond OECD l.6% „ -- IIASA£ l.7% 0.9% d RFF (high) l.9% l.52% d RFF (low) l.4% 0.75% d Hudson Institute 2.0% l.4% _ Keyfitz0- l.6% 0.9% 0.3% Nean l.7% l.l% 0.3% Standard deviation 0.2% 0.36% n.a. Cell extremes l.4%; 2.0% 0.6%; l.6% n.a. ^Estimates of the l(t) parameters of population growth equation. ^Sources: OECD Interfutures Project (l979), IIASA (l98l), Ridker and Watson (l980), Kahn et al. (l976), and Keyfitz (l982). —The IIASA projections were based on an earlier set of estimates by Keyfitz. —The IIASA and RFF studies report the expectation of stable world population some time after the first third of the twenty-first century. first century. Sometimes they have reached that conclusion because they believe that by then the volatile LDC behavior will have evolved into the predictable model of the developed countries; sometimes their predicted stability was based on some other presumption. In either case, their behavioral hypothesis was as much of a guess about the unknown future as any other growth path, and it is hard to see why uncertainty should diminish as time goes forward. The observed reduc- tion in range of population growth projections beyond 2025 is thus a likely candidate for the adjustment discussed further in the next section. As troublesome as the later estimates might have been, however, the earlier ranges provided excellent arenas for illustrating the sum- marizing procedure for the observed variation. The various estimates, ranging from l.4% growth per year up to 2.0% for l975-2000 are, for example, assumed to be observations drawn from an underlying normal distribution of the true uncertainty. These observations (X^) are then used to compute estimates of the mean (yx) and variance (a2) of that distribution: M x n Xl + — + Xr and

ll8 where n represents the number of observations. To discretize the distribution defined by X and S2 into three cells of probabilities 0.25, 0.50, and 0.25, therefore, X is assigned a probability of 0.5 and (X + s /~2) probabilities of 0.25. In this way, mean and variance (s2-» 0.25(2s2) + 0.25(2s2)] are both preserved. For the l975-2000 range, therefore, l.7% is the "middle" estimate, while l.4% and 2.0% represent the extremes. Under this procedure, roughly 8% of the under- lying probability is left beyond the extremes on both sides. Similarly, l.0% is the middle estimate for the period 2000-2025, with 0.5% and l.5% catching the 0.25 probability tails. Estimates of growth in world productivity are recorded in Table 2.7. They are, for the most part, based on a somewhat surprising assumption about the growth of world trade over the next several decades. Each researcher found that the growth of the world economy will be bounded by growth in the largest markets—the developed countries. Many studies have identified productivity growth as a critical parameter for energy and carbon dioxide projections. The common presumption about the growth of world trade, ironically, has caused otherwise independent studies to project estimates of output growth that converge over time. Of particular note is the decline in the variance in projected growth rates beyond the year 2025. It may have been caused more by a dearth of estimates than anything else, but its range includes only the lower tail of the long-run historical experience of the United States, and it misses the Japanese experience completely. These ranges, too, are subject to revision later. TABLE 2.7 Projections of the Rate of Growth of World Productivity^ Source of Estimate^ l975-2000 2000-2025 2025 and beyond OECD (high) 3.4% - -M, OECD (mid) 2.8% — — . OECD (mid) l.9% — — OECD (low) 2.7% — — IIASA (high) 2.3% 0.9% — I I ASA (low) l.2% l.9% — Hudson 2.8% l.4% l.2% RFF (high) 2.4% 2.l% — RFF (low) l.6% l.8% — Hudson (low) ~ ~ 0.75% Mean 2.3% l.6% l.0% Standard deviation 0.7% 0.5% 0.3% Cell extremes l.2%; 3.4% 0.9%; 2.3% 0.5%; l.5% ^Estimates of the a(t) parameter in the productivity growth expression. —Sources: OECD Interfutures Project Watson (l980), and Kahn et al. (l976) expression. Sources: OECD Interfutures Project (l979), IIASA (l98l), Ridker and

ll9 TABLE 2.8 Projections of the Rate of Growth of Noncarbon Energy Prices^. Source of Estimate5- l975-2000 2000-2025 2025 and beyond IEA 0.0% 0.0% 0.0% RFF (DH NU)£ RFF (DHPl)0- RFF (DHP2)£ l.0% 0.7% l.0% 0.6% -0.l% -0.4% ~ Mean 0.6% 0.0% 0.0% Standard deviation 0.5% 0.4% n.a. Cell extremes -0.l%; l.3% -0.5%; 0.5% n.a. ^Estimates of the hl(t) and h2(t) parameters of the energy price (supply) equations. ^Sources: Reilly et al. (l98l), Ridker and Watson (l980). °JThe difference between these three scenarios is essentially a difference in the assumption about solar and nuclear development. The particulars are not so important, for our purpose, as the spread of uncertainty. Table 2.8 records projected future adjustments in the primary real price of noncarbon-based energy—electricity not derived from burning carbon-based fuel. These trends can, however, be interpreted as the inverse of the rate of technological change in the energy sector, i.e., in the notation of the previous section, hl(t). Since technological change can continue in the fossil fuel sector as well, these estimates are also used to frame the difference in the rate of advance between the two sectors [h2(t)]. These estimates, then, are clearly dependent not only on growth assumptions (and thus the need for new technology) but also about the future contributions of sources like nuclear, fusion, and solar-generating facilities. Despite the obvious uncertainties involved in projecting either factor into the twenty-first century, the estimates recorded in Table 2.8 again converge. The Reilly et al. (l982) view of constant real prices is therefore included as the middle case, and the ultimate variation around that case expanded. Estimates of the emissions factor are based both on the unit emis- sions for each source recorded in Table 2.5 and on projected mixes of carbon-based fuels in the future. For each case, the mix of oil, gas, coal, and shale oil is computed and used to weight the unit emissions in computing an aggregate. The procedure has already been illustrated in the calculation of Z(0) for Table 2.4. Results of the other computa- tions are noted in Table 2.9. The summarizing procedure is applied across the ranges of emissions for each period to produce high, medium, and low trends. Notice that the high trend includes a 3l% contribution from shales (as projected by RFF) by the year 2050. The lower two paths stabilized at l00% coal, or 700 g of C/mtce by 2075. The three pos- sibilities are illustrated in Figure 2.9.

l20 TABLE 2.9 Aggregate Carbon Emissions A. Fuel Proportions Proportions Carbon Emissions Year Source A Oil Gas Coal Shale l975 Table 2.3 0 .50 0 .20 0 .30 0 .00 580 2025 1 1 AS A (high) 0 .33 0 .29 0 .38 0 .00 580 1 1 AS A (low) 0 .34 0 .23 0 .43 0 .00 590 IEA 0 .28 0 .l8 0 .54 0 .00 6l2 RFF 0 .28 0 .23 0 .37 0 .06 607 2050 1 1 ASA (high) 0 .25 0 .l0 0 .65 0 .00 604 1 1 ASA (low) 0 .28 0 .l9 0 .53 0 .00 598 IEA 0 .26 0 .08 0 .66 0 .00 644 RFF 0 .02 0 .02 0 .65 0 .3l 854 B. Projected Growth in Emissions—Z(t) Emissions Growth Year Mean Std.Dev . Extremes Mean Extremes l995-2025 597 l5 582; 6l2 0 .05% 0 .0%; 0 .l% 2025-2050^ 627 25 602; 799 0 .2% 0 .l%; l .l% 2050-20752 n.a. n.a. 700; 700; 854 0 .4% 0 .6%; 0 .3% 2075-2l002 n.a. n.a. 700; 700; 854 0 .0% 0 .0%; 0 .0% ^Sources: IIASA (l98l), Reilly et al. (l982), Ridker and Watson (l980). —The mean and standard deviation reported here excludes the shale estimate to generate the low extreme and the middle growth paths. higher extreme includes the shale estimate in both computations. —The two lower runs exclude shale; the high extreme converges to a 30% shale share of carbon-based fuel. The Elasticities of substitution between energy and labor, on the one hand, and between the two types of energy, on the other, are estimated on the basis of the literature on price elasticities of demand. In the former case, for example, it is noted that many would put the overall price elasticity of demand for energy somewhere in the inelastic range, i.e., they would expect a l% price increase to reduce consumption by something less than l%. A range for s1 = (q - l) , the elasticity of substitution between E(t) and L(t), that select -0.4 and -l.2 for the 25% probability extremes and -0.7 for the mean is therefore employed. Similar reasoning puts the extremes for s = (r - l)-l, the elasticity between Ec(t) and En(t), at -0.5 and -2.0 around the middle run of -l.2.

l2l 875- 850- 825- I 800i 1D o 01 or CO o « UJ i oc 5 750^ 725- 700 J 650- 625- 600- 575- 550- (854) Low Middle High 1975 2000 2025 YEAR FIGURE 2.9 Carbon emissions ratio. 2050 2075 2100 There are by now a wide variety of studies of the elasticity of substitution between energy and nonenergy inputs. To a first approximation, this parameter is equal to the price elasticity of the derived demand for energy [this is shown in Nordhaus (1980a)]. Table 2.l0, drawn from Nordhaus (l980a), gives central estimates and ranges for the price elasticity of the demand for energy.

l22 TABLE 2.l0 Range of Estimated Final Demand Elasticities3. Sector Hog an Nordhaus Best Guess Implicit Elasticity for Primary Energy Residential -0.28 to -l. l0 -0.7l to -l.l4 -0 .9 -0 .3 Transport Industrial -0.22 -0.49 to to -l. 30 90 -0.36 -0.30 to to -l.28 -0.52 -0 -0 .8 .7 -0 -0 .2 .4 Aggregate -~ -0. -0.66 to -l.l5 -0 .8 -0 .3 ^Sources: The first column is from Hogan (l980); the second column, from Nordhaus (l977); the third column is Nordhaus's judgmental weighting of various studies. To obtain an estimate of the crude price elasticity in the fourth column, the final demand price elasticity in the third column is divided by the ratio of retail price to crude price. For use in the present study we lowered the elasticity to 0.7 because of some suggestion that price elasticities are lower in less- developed countries than in developed countries. In addition, note that, while the price elasticities may appear high, they are not for two reasons. First, they are long-run rather short-run elasticities. And, second, they relate to the elasticity for final energy demand, not for primary energy. As is shown in the last column of Table 2.l0, price elasticities for primary energy are considerably lower than the figures we use. The elasticity of substitution between carbon- and noncarbon-based fuels was derived as follows. We examined the effects of different CO2 taxes on the ratio of carbon to noncarbon fuels in the runs presented in Nordhaus (l979), Chapter 8. The logarithmic derivative of the ratio of the two fuels to the ratio of their prices was somewhat greater than l.5 in absolute value. We reduced the elasticity to l.2 to allow for the tendency of LP models to "overoptimize." The alter- natives were set above and below the important boundary elasticity of l. It must be noted that the empirical basis for this parameter is as weak as any we rely on. Turning now to the parameters in Equation (6b) , estimates for gj_, g2, and R are required. Estimates of world fossil fuel reserves vary widely according to the assumptions that are made about economic feas- ibility. Table 2.ll registers the variety from which our estimates were drawn. The low range includes only proven reserves that will certainly become economically feasible in the foreseeable future. The middle range captures a large increment of reserves that most researchers think will become feasible in that time span; it quadruples the low range by including difficult oil deposits and extensive use of cleansed coal. The upper range adds a small percentage of potential shale availability to the supply and puts world resources well beyond quantities that will be consumed over the span of our study—the next l25 years.

l23 TABLE 2.ll World Resources of Fossil Fuels3. A. Certain Economic Feasibility (low R)^ I IAS A 2.7 X l0 l2 mtce WAES 3.2 X l0 l2 mtce Value employed for low R 3 X l0 l2 mtce B. Probable Economic Feasibility (middle R) IIASA ll X l0 l2 mtce IEA (high) l2.2 X l0 l2 mtce IEA (low) l2.0 X l0 l2 mtce Value employed for middle R l2 X l0" mtce C. Including Shale Estimate (high ft) Total deposits — Duncan and Swanson l44 X l0 l2 mtce Value employed for high R (= middle R + 0.07 shale) 22 X l0 l2 mtce ^Sources: IIASA (l98l); Energy: Global Prospects, Workshop on Alternative Energy Strategies (WAES) (l977); Reilly et al. (l982); Duncan and Swanson (l965). —These numbers are consistent, component by component, with other incomplete data found in Moody and Geiger (l975), and World Energy Conference (l978). —The inclusion of shale allows for incredible availability of fossil fuel. The 7% utilization rate, chosen rather arbitrarily, generated a resource constraint that was always nonbinding through the year 2l00. The procedure for computing g± and g2 is more involved. For simplicity, first of all, g2 is set equal to l; manipulating gl provides more than enough flexibility. A range of prices for fossil fuel in some future time after an arbitrary Ri mtce of fossil fuel had been consumed, is then constructed. Denoting those prices by P and the various reserve estimates cited above by Rk, a collection o g^ values, now clearly dependent on both Pj and Rk, are computed according to 9Q + (8) where j and k index high, middle, and low values for Pj and R., respectively. Figure 2.l0 shows that this procedure generated three possible paths for each of the three Rk; i.e., nine separate specifications of the g^j,k) and thus nine specifications of Equation (6b). Table 2.l2 meanwhile records the prices estimated by several studies for Rl = ll00 x l09 mtce. It is a value chosen because of the availability of these price projections, and the table shows how the necessary aggregate prices are computed. Several other studies cited either prices without aggregation weights or consumption mixes without prices, so they were of little use. It is, nonetheless,

l24 121.5-d 121.0- 120.5- 120.0-= 119.5- 119.0- 118.5- 2 118.0J u. O ui O oc 117.5- & 117.0- 116.5- 116.0- Low Middle High 20 40 60 80 100 120 CUMULATIVE FOSSIL FUEL EXTRACTION 140 FIGURE 2.l0 Secondary (retail) price of fossil fuel as a function of cumulative fossil fuel extraction. Prices are l975 dollars per metric ton of coal equivalent. Cumulative extraction is measured from l975 in billion metric tons of coal equivalent. In the terms of this section, these are price paths for a given Rk and Pj for R. (Pl, PM, PH)

l25 TABLE 2.l2 Primary (Wholesale) Fossil Fuel Prices when Cumulative Extraction from l975 (R - ll00 x l09 mtce Source of Projection^ Oil* Gas^ Coal^ Aggregate Pric<£' S IIASA (high) $l30(0.33) $70(0.29) $25(0.39) $73/mtce IIASA (low) $l50(0.34) $65(0.23) $25(0.43) $76/mtce IEA (low) $l40(0.28) $65(0.l8) $25(0.54) $64/mtce IEA (high) $l40(0.34) $65(0.l8) $25(0.47) $7l/mtce RFF $l23(0.38) $75(0.27) $40(0.35) $8l/mtce Mean $73/mtce Standard deviation $5.7/mtce Cell extremes $65; $8l/mtce Sources: IIASA (l98l), Reilly et al. (l982). —The proportions of each source in the total consumption are given in the parentheses. —Aggregate prices are computed as weighted sums of the components, with the weights being the proportions noted in the parentheses. Thus, for IIASA (high) (0.33)($l30) + (0.29)($70) + (0.39)($25) = $73/mtce. ^Many studies did not provide a full range of necessary data. A compilation of 23 surveys of projected oil prices produced during the l98l Stanford International Energy Workshop did, however, provide a good sample of oil price expectations through the year 2000. Extrapo- lating those data through 2030 [the year when most studies see R(t) = ll00 x l09 mtce] using the range of weights listed here produced a much wider range extending from $43/mtce to $l06/mtce. These are rough estimates, of course, but lead to some widening later. interesting to note that interpolating between the estimated oil prices used in this study for 2025 (and contained in Table 2.l2) and the l98l oil prices provides us a benchmark for comparison. This benchmark fell in the third decile of 23 studies (i.e., lower end) compiled during the Stanford International Energy Workshop of l98l (Energy Modeling Forum, Stanford University). Even with these data collected, our work on the price equation for fossil fuel is not completed. Section 2.l.2.l outlines an approximation procedure that allowed both the simplicity of the nested production function recorded in Equation (l) and the flexibility of being able to vary the elasticity of substitution between energy and labor across time. It was an adjustment made necessary by a desire to incorporate a source of dynamic uncertainty into the model that could well loom large in the balance of this century. Much in the same spirit, we now need two similar adjustments in the fossil fuel equation. The first is designed to preserve the structure of Equation (3) even as the short- term effects of restricted oil supplies were recognized. The second gives society enough foresight to prepare for the imminent exhaustion of fossil fuel supplies.

l26 The need for the first adjustment can be seen by looking at the very recent past. The model, as presented above, allows instantaneous substitution into and out of aggregate energy and between its carbon and noncarbon components each year in response to changes in relative input prices. While this is a conventional assumption for long-range growth models in which people are presumed to predict price movements accurately and plan accordingly, it does not conform well to the uncer- tain world that has confronted energy consumers since l975. The dramatic disruption in world oil supplies caused by the advent of OPEC in l973, the events in Iran, the oil glut, and the decontrol of gas and oil prices in the United States are all examples of factors that have contributed to the uncertainty; and their net effect has been to increase the primary price of carbon-based fuel from $35/mtce in l975 to $76/mtce in l98l. Investment decisions taken in l975 were, however, made in response to l975 prices and l975 expectations. Much of the world's present capital stock was, in fact, put into place before the oil shocks of l973. The decisions that produced these investments were clearly not made with the type of accurate foresight required in the model. Nor can it be presumed that instantaneous substitution would have brought all the existing capital up to date relative to current energy prices. Thus, there exists a need to provide a longer reaction time at the beginning of the model to reflect the difficulty faced by most consumers in responding to such enormous price changes. One possible adjustment would involve making alterations in the production function, but that course is again rejected to avoid com- plexity. Rather than produce the complications of more complex intertemporal substitution, we modify the early fossil fuel prices against which consumption decisions would be made. For the first 25 years of each run, in particular, a linear combination of projected current fossil fuel prices (computed from l98l prices) and the lower l975 prices is employed to slow the rate of growth of fossil fuel prices; the result is a reduction in the reaction to higher fossil fuel prices mandated by Equation (3). After the year 2000, however, this delayed reaction is stopped and decisions are assumed to be made on the basis of prevailing fuel prices. More specifically, the l975 primary price of fossil fuel ($35/mtce) is used in conjunction with the price ranges computed for Rl » ll00 x l09 mtce to compute the appropriate gl coefficients. They are recorded here in Table 2.l3. This computation, with the Rl price range expanded to $43, $73, and $l03 per mtce to reflect the larger dispersion of the Stanford estimates of oil prices, is appropriate because the price estimates on which the range was based were made under l975 expections. Nonetheless, the primary price of fossil fuel did reach $76/mtce by l98l, and distribution costs did rise by $40/mtce from l975 through l98l. These figures, therefore, are used as initial conditions for the long-term supply equation; i.e., the equation PC(t) = 76 + gR(t)/IR - R(t)] exp[h(t)tJ + 40 (9) ]| 2)exp[hl fully specifies the long-term price equation for fossil fuel. Still, the point of this adjustment is that imposing these inflated prices in

l27 TABLE 2.l3 The g Parameters of Price at Rl— gl Probability 3200 x l09 mtce $43/mtce l3.8 0.06 3200 x l09 mtce $73/mtce 65 0.l3 3200 x l09 mtce $l03/mtce ll8 0.06 ll000 x l09 mtce $43/mtce 72 0.l3 ll000 x l09 mtce $73/mtce 342 0.24 ll000 x l09 mtce $l03/mtce 6l2 0.l3 2l000 x l09 mtce $43/mtce l45 0.06 2l000 x l09 mtce $73/mtce 687 0.l3 2l000 x l09 mtce $l03/mtce l230 0.06 ^Source: Tables 2.ll and 2.l4, Equation (6b), and the text of this section. l975 U.S. dollars. l98l would not have been consistent with the spontaneous flexibility of the production function. Since the relevant secondary price of fossil fuel in l975 is $62/mtce and not $ll6/mtce, the operative fossil fuel price for the first 25 years is adjusted linearly according to [P°(t)]' - [(25 - t)/25]62 + [t/25]PC(t). Notice, as illustrated in Figure 2.ll, that [PC(t)]' and P°(t) are therefore coincident only after the year 2000. The second adjustment is necessary to preclude the possibility that the world would unexpectedly exhaust all of its fossil fuel reserves. The notion here is that there exists a "backstop" technology (such as solar or fusion) that should become economically feasible before exhaustion and that entrepreneurs would provide that technology before the economic effects, perhaps collapse, that unexpected exhaustion would create. For our purposes, we model the backstop as a gradual contraction of reliance on fossil fuel once its price climbed to levels in excess of four times the price of nonfossil fuel. The multiple is selected to match current estimates of the cost of generating hydrogen from conventional sources; the subsequent rate of decline of fossil fuel consumption is assumed to be roughly 6% per year and is estimated from preliminary runs in which the supply of fossil fuel was exhausted in the absence of the backstop. Consideration of the airborne fraction is the final order of busi- ness. Estimates from a variety of experts are cited in Clark (l982) , but we found that they were mostly the products of statistically inefficient estimation procedures and highly sensitive to assumptions made about the contribution of carbon dioxide to the atmosphere from the biosphere. The latter sensitivity reflected misspecification of

l28 12( 115- 110- 105- £ 100- 41 T5 95 90- £ 85- ui o LL LL O UJ o DC CL 80- 75- 70- 65- 60- 55- 50- Pc(t) / [Pc(t>]' 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.ll Price of fossil fuel (l975 dollars per ton of coal equivalent). A comparison of Pc(t) and [Pc(t)]'—the adjustment required to accommodate the rapid increase in fossil fuel prices from l975 through l98l.

l29 the appropriate estimating equation and led us to our own study. At this point, we advance a maximum likelihood estimate of the marginal airborne fraction equal to 0.47, given an average seepage of 0.l% of ambient carbon dioxide into the oceans and an annual contribution from the biosphere of l Gt of C (the mean estimate). We differentiate between a marginal airborne fraction (the fraction of current emissions that remain in the atmosphere during their first year) and an average airborne fraction because of the seepage factor. The contribution of each year's emissions decays over time in our model, and that decay will have implications later when we turn to consider emission taxes as policies with which to address the carbon dioxide problem. The extreme cell estimates of the marginal fraction are also computed to discretize the usual normal distribution around a regression coefficient; 0.38 emerges as the low estimate, and 0.59 is the upper extreme. 2.l.2.2.l Adjustment of Subjective Uncertainty The inability of individuals, even those with statistical training, to deal efficiently with uncertainty about the future has come under increasing scrutiny. Studies in both the economic and psychological literature have argued, in particular, that individuals tend to underestimate the uncertainty about events.* For present purposes, two reasons for these systematic errors are relevant. First, when people look to previous studies in seeking guidance for their own views, they may place too much weight on the early studies. If one were then to view the range of resulting estimates as an indication of the true uncertainty, the computed variance would be too small. A simple illustration of this phenomenon, sometimes known as the wine-tasting problem, can make this point. Suppose that a sample of two independent observations, xl and X2, were taken from the same distribution, and let that distribution be normal with mean * and variance a2. Each x^ would therefore be independently, normally distributed with mean K and variance o 2. The sample mean, X » (xl + X2)/2 would then be an unbiased estimate of K, and S2 = (xl - x)2 + (X2 - x)2 would be an unbiased estimate of a2 (i.e., JE[S2] } = a2). If, however, the second scientist looks over the shoulder of the first, he might allow his judgment to be influenced. Say that the reports of observation X2 were weighted by xl so that reported values (y) are vl = xl and V2 = ax2 + d - a)xi. The reported variance would decline. The reason is that the y2 would display a variance a2(y0) = a2 a2 + (l - a)2 o 2= [l + 2 (a2 - a) ] a2 < a2, for 0 < a < l. *See Arrow (l982) for a summarizing review of both.

l30 So, the variance of the reported values is biased downward from a2. The infusion of judgment allows the first researcher's result to influence the second, and the observed variance is smaller than the underlying variance. Second, people seem reluctant to accept the true uncertainty inherent in small samples. Several studies report that individuals frequently base their expectations on one observation even when they are aware that historical experience has been widely varied.* The estimates for the more distant periods recorded in this section seem to suggest such a telescoping of uncertainty. In some cases, the range of estimates declined as the forecast period increased, even though the passage of time should have increased the uncertainties. It appears that, in the face of higher uncertainty, scientists may look to each other for guidance. To correct for the resulting tendencies to underestimate the degree of uncertainty, estimate ranges are expanded around the computed means; i.e., the ranges are adjusted either to keep the ranges from contract- ing over time or to make them consistent with historical experience. The adjustments are based on our judgment but are undertaken only if they could be justified by one of these two rationales. Table 2.l4 presents the results of this procedure. The population growth ranges after the year 2025 are, for example, expanded to main- tain the 0.5% deviation computed for the 2000-2025 period. The later productivity ranges are similarly expanded to match the uncertainty found in the first two periods. Energy price ranges are, finally, widened in response to the enormous political and economic uncertainties inherent in the world energy market. The survey of 23 projections for oil prices collected during the l98l Stanford International Energy Workshop (ranging from l0% reductions to l00% increases in the price of imported crude oil) provide some very rough guidance for our energy price uncertainty (Manne, l982). 2.l.2.3 Results 2.l.2.3.l Levels and Uncertainties of Major Variables Four types of experiments are conducted with the fully specified model. In the first, we investigate not only the most likely paths of emissions and concentrations but also the inherent uncertainty that surround those projections. This is accomplished by taking l000 random samples from the 3*° different trajectories. The results of a sample of l000 runs are recorded in Table 2.l5. Figures 2.l2 through 2.l6 plot the first l00 of those runs for some of the more important vari- ables. And Table 2.l6 records the annual growth rates of the most likely path for those variables. Notice that these rates of growth, particularly those for energy consumption and GNP, conform well with *See Arrow (l982) and the sources cited therein.

l3l TABLE 2.l4 Adjusted Ranges3- l975-2000 2000-2025 2025 and Beyond A. Population Growth High 2.0% l.6% 0.8% Middle l.7% l.l% 0.3% Low l.4% 0.6% -0.2% B. Productivity Growth High 3.4% 0.9% 0.l%(0.5%) Middle 2.3% l.6% l.0% Low l.2% 2.3% l.9%(l.5%) C. Nonfossil Fuel Price Growth High 2.0%(l.3%) l.0%(0.5%) l.0%(n.a.) Middle 0.5% 0.0% 0.0% Low -l.5%(-0.2%) -l.0%(-0.5%) -l.0%(n.a.) D. Aggregate Carbon Emissions—no change E. Fossil Fuel Prices for R± = ll00 x l09 mtce High $l03/mtce ($81/mtce) Middle $ 73/mtce Low $ 43/mtce ($65/mtce) F. Airborne Fraction—no change^ ^Source: Previous tables and the present text. Unadjusted figures are indicated in parentheses when adjustments to widen the ranges have been made. HThe uncertainties cited were measurement problems and were biometrically evaluated from the carbon dioxide literature; they were not subject to the types of underestimation cited here. the averages of the projections cited in Ausubel and Nordhaus (Section 2.2) through the year 2025. The 50-year averages predicted by the l000 runs are, in fact, 2.l% and 3.3% for energy and GNP; the averages for the previous studies are 2.4% and 3.4%, respectively. The results presented here should not, therefore, be considered to be the products of a model that embodies radically different expectations about economic growth than the consensus of professional opinion. The uncertainty surrounding the average path is, however, quite striking. The measured standard deviations of all variables expand over time, and that expansion is sometimes dramatic. For carbon emis- sions and concentrations, in particular, a fair amount of certainty through the year 2000 balloons to the point where, by 2l00, standard deviations of their projections equal 60% and 23% of their means, respectively. Put another way, the extreme values for concentrations run from 377 ppm to 58l ppm in the year 2025, and from 465 ppm to 22l2 ppm in the year 2l00! Those interested in the actual distributions of

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l33 1000.0 H > 100.0- = 10.0J 1.0- 0.1- 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.l2 Fossil fuel consumption for l00 randomly drawn runs (billion metric tons of coal equivalent per year).

l34 2500.CH a. s I UJ o 8 o E 1250.0- 625.0- 312.5- 2100 780 370 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.l3 Atmospheric concentration (parts per million) of carbon dioxide for l00 randomly drawn emission runs. The numbers on the right-hand side indicate the mean concentration for the year 2l00 and the extreme high and low outcomes. emissions and concentrations for critical years are referred to Figures 2.l7 and 2.l8. The model presented here finds that carbon dioxide emissions are likely to grow steadily over the next century or so, with an atmo- spheric concentration reaching 600 ppm, in our most likely case, shortly after 2065. If we call attainment of 600 ppm a "doubling," our

l35 896H 448- 224- 5 56- 28- 14- 7- 394 113 1975 2000 . i . - . - 2025 2050 2075 2100 YEAR FIGURE 2.l4 Gross world product for l00 randomly drawn runs (trillion l975 dollars). estimates indicate a doubling time longer than some earlier studies. This slower buildup arises primarily because we estimate a greater sensitivity of fossil fuel consumption to rising fossil fuel prices. But while this average result suggests a considerable time before a CO2 doubling, our analysis also shows a substantial probability that doubling will occur much more quickly. Looking at the distribution for the year 2050, in fact, our results show a 27% chance that doubling will already have occurred. Unless this uncertainty can be reduced by

l36 ISO- 80- 40- c S I § o E I K H1 Z 10 UJ 20- 1975 274 57.9 2000 2025 2050 2075 2100 YEAR FIGURE 2.l5 Energy consumption for l00 randomly drawn runs (billion metric tons of coal equivalent per year).

l37 500.00- 1 100.00 I I o iA I •J: 20.00- CO Z O o o m cr 4.00- 0.80- 0.16- 1975 2000 2025 2050 YEAR 209 31.1 2.3 2075 2100 FIGURE 2.l6 Nonfossil fuel consumption for l00 randomly drawn runs (billion metric tons of coal equivalent per year).

l38 TABLE 2.l6 Annual Growth Rates of Critical Variables (percent per annum) £ Variable l975- 2000- 2025- 2050- 2075- 2000 2025 2050 2075 2l00 GNP 3.7 2.9 l.5 l.5 l.5 Energy consumption l.4 2.7 l.2 l.l l.2 Fossil fuel consumption 0.6 2.5 0.9 0.5 0.4 Nonfossil fuel consumption 5.6 3.l l.8 2.0 2.0 Price of fossil fuel 2.8 0.3 l.2 2.9 l.l Price of nonfossil fuel 0.5 0.l 0.l 0.l 0.l C02 emissions 0.6 2.6 l.2 0.9 0.4 Concentrations 0.3 0.6 0.8 0.8 0.8 are calculated as the probability weighted means of the l00 random runs. further research, it would appear to be unwise to dismiss the possibil- ity that a C02 doubling may occur in the first half of the twenty- first century. Perhaps the best way to see this point is to refer back to Figure 2.4. There, only five paths are drawn, but it is clear that doubling occurs before the year 2050 along two of them, the 95th and 75th percentile paths. Finally, it is surprising that the backstop technology comes into play on ll% of the runs, with the earliest transition occurring in year 2054. Recall that a backstop technology is invoked when fossil fuels are almost completely exhausted. Exhaustion (and appearance of the backstop) usually requires a combination of variables that include low fossil fuel reserves, high productivity growth, high population growth, and small substitution possibilities out of carbon-based fuel. The share of GNP devoted to energy always rises sharply during the period immediately preceding transition to the backstop and thus conforms well to the notion that the conversion to a backstop technology will be expensive. Transition to the backstop then causes carbon emissions to fall to roughly 5% of their peak over the next 25 years. 2.l.2.3.2 Sources of Uncertainty A second experiment is designed to determine which of the l0 sources of uncertainty was most important in producing the ranges that have just been noted; it was conducted in two ways. In the first, each of the l0 random variables are, in turn, set equal to their two extreme values while all the others are fixed at their middle setting. In that way, the individual contributions of each source to the overall uncer- tainty of the projections is measured and compared. The second column of Table 2.l records an index of the individual standard deviations that emerged. The second method is, in effect, the converse of the

l39 first. Each random variable is, in turn, held at its most likely (or "middle") value while random samples are taken across the other nine; the resulting reduction in the uncertainty is then taken to be a reflec- tion of the marginal or incremental contribution of the fixed variable to overall uncertainty. The first column of Table 2.l records an index of this measure. Notice that both measures produce similar rankings. The ease of substitution between fossil fuels and nonfossil fuels rank first in both; this is an area that has thus far been almost ignored in prior study of the carbon dioxide problem. Second in both lists is the rate of productivity growth, but the importance of this variable is intui- tively clear and has been apparent for some time. Below these two, a second echelon grouping of four variables appears in both columns: ease of substitution between labor and energy, extraction costs of fossil fuels, technological change in the energy sector, and the airborne fraction. The last member of this list has been heavily studied over the past few years, but even our wide range of uncertainty only pushed it into the middle of the ranking according to either scale. The fuel mix and the rate of growth in the population form a third grouping. The bottom factors in terms of contribution to uncertainty are trends in relative energy costs and world fossil fuel resources. Holding these last two fixed actually produced higher variation in concentra- tions in 2l00. The cost variable effect is small and probably cannot be statistically distinguished from zero, but the resources effect is pronounced. It is, however, easily explained. The backstop technology is invoked only when world resources are set at their lowest value. And when the backstop is imposed, emissions fall quickly to zero and concentrations tend toward roughly the same number. Removing the back- stop as a possibility by removing the possibility that world fossil fuel resources might be quite small therefore removes circumstances that have a serious dampening effect on the range of possible atmo- spheric concentration. An expanded variance should therefore be expected. 2.l.2.3.3 Validation Our third area of experimentation poses the problem of validating our results. Validation is, of course, a major issue arising in the estimation and use of very-long-run economic and energy models where the time period over which the data are available is typically much too short to permit testing and validating by usual statistical techniques. Moreover, economic systems evolve and mutate over time, so even models that use classical statistical time series tests would be suspect. Our time frame—l25 years—clearly heightens concerns about these concerns. This raises the question of whether we have accurately estimated the uncertainty of future events by looking at each of the variables indi- vidually, imposing distributions on them and expanding those distribu- tions to account for the likelihood that scientists systematically overestimate the confidence in their results. Two types of tests are run to attempt to answer this question.

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l44 TABLE 2.l7 Alternative Estimates of the Uncertainty of Carbon Dioxide Emissions (Calculated as the Standard Deviation of the Logarithm of Emissions) Statistical (Calculated Time from Last Data (t) from Historical Data) Static3- Dynamic^ Model£ 0 0.005 0.06 0.04 25 0.l4 0.50 0.56 50 0.28 0.75 0.6l 75 0.42 0.76 0.67 l00 0.56 0.99 0.68 l25 0.70 n.a. 0.85 ^Calculated as t x se(g), where t is time in future and se(g) is the standard error of g in a regression log (emissions) = a + gt, over the sample period l960-l980. The equation was estimated assuming first-order autocorrelation of residuals. ^Calculated as the standard deviation of a forecast of log (emissions) t periods in the future or past. The number of nonoverlapping samples were l0 for t » 0, 9 for t = 25, 6 for t « 50, 4 for t = 75, and 2 for t = l00. -^Calculated as the standard deviation of log (emissions) for l00 randomly selected runs. We first use classical prediction theory to estimate the prediction errors that are consistent with the data over the period l960-l980 (see, for example, Johnston, l972; or Malinvaud, l980). Under this approach, we assume that there was a "true" growth rate of emissions, g, and that the data over the l960-l980 period are an unbiased sample of that true growth rate. The mean growth rate over this period is 3.67% per annum, and the standard deviation of the growth rate is 0.56l% per annum. Using this approach, we show in column 2 of Table 2.l7 the estimated standard errors of emissions that would be expected over forecast periods extending further and further into the future. In the second approach, the historical data are used to provide out-of-sample forecasts. (This technique has been used infrequently. For an example as well as further discussion, see Fair, l978.) Under this approach, we estimate a growth trend for each of five 2l-year periods (l860-l880, l880-l900, l900-l920, l920-l940, l940-l960). On the basis of the estimated trend functions, we then forecast into the future (unknown then but known now) through l980. Thus we obtain, respectively, l00, 80, 60, 40, and 20 years of out-of-sample forecasts. The same procedure is then used to "backcast," that is, to fit functions to recent data and then to project backward into time what emissions should have been. In the backcast exercises, for example, we fit a

l45 trend function to the data for l960-l980, then use that estimated relation to calculate emissions over the period l860-l960. Again, five 2l-year trends are estimated and five different sets of backcasts are constructed. From the l0 sets of forecasts and backcasts, we construct a set of out-of-sample errors, 0, 25, 50, 75, and l00 years away from the sample—future or past. The root-mean-squared errors are then cal- culated; they are labeled as "dynamic" statistical error forecasts and are shown in column 3 of Table 2.l7. The backcast procedure may at first appear bizarre. It is an implication of the model we are using, however, that estimates of the structure are equally valid forward and backward into time. This implication arises because the trend model has no explanatory variable but time, as well as because the trend model assumes that there is no change in the underlying economic structure. It should be emphasized, however, that use of this type of trend extrapolation model to forecast emissions in no way is an endorsement of such a technique for all purposes. We are employing it here only for validation purposes. The results of this validation test indicate that the error bounds for emissions estimated by the model, recorded in column 4 of Table 2.l7, are within the bounds generated by the two historical error estimation procedures. In general, the model produces error bounds greater than the classical statistical technique shown in column 2, but smaller than the dynamic estimates shown in column 3. If we were to choose between procedures for estimating errors, we would be inclined toward the dynamic rather than the static as a realistic estimate of forecasting uncertainty. The reason for this inclination is that the static estimate assumes that there is no change in the underlying structure of the economy, so that future growth rates are drawn from the probability distribution generated by the in-sample growth rates. The dynamic model, on the other hand, recognizes that there is evolution in the structure of the economy, so that the distri- bution from which we draw observations is likely to drift around over time. Assuming that the pace of economic structural change over the next l00 years will be about as rapid as that over the last l00 years, the dynamic estimates give a better estimate of the realistic error bounds for a forecast of the future. To the extent that careful struc- tural modeling allows us to improve on a naive extrapolation of trends— which is after all the major point of economic and energy models of the kind we introduce here—the error bounds of the model should be an improvement over the dynamic error bounds. And, finally, it should be noted that these exercises were conducted after the model had been constructed and estimated; no tuning of the model has been undertaken to bring it in line with either series recorded in Table 2.l7. 2.l.2.3.4 Policy Experiments Our final set of experiments considers the possibility that govern- ments will intervene to curtail CO2 emissions. There are clearly a wide variety of approaches to discouraging fossil fuel combustion and CO2 emissions. Some might take the form of taxes on production or

l46 consumption of carbon-based fuels; nonfossil sources might be encour- aged; countries that have large coal reserves might place export limitations or heavy taxes on coal exports. Government might agree to national CO2 emissions quotas and then enforce these in a wide variety of ways. At this point, we do not pass on the likelihood or desirability of these different policies—rather, we attempt to investigate their impacts. For purposes of analysis, it is convenient to convert all policies that discourage use of CO2 into the carbon-equivalent taxes. As an example, say that a 2x% tax on carbon fuels would always produce an x% reduction in their use. We would then use this hypothetical formula as a way of representing any quantitative restriction on carbon-based fuels. Whatever the set of policies, we can derive the tax rate on fossil fuels that would produce the same restraint on C02 emissions. This equivalent tax is the carbon-equivalent tax investigated here. We consider only the most likely run—the case in which all the random variables are set equal to their middle values. Because of the crude- ness of the policy, the results quoted below should be viewed as being extremely tentative. Five different taxes are imposed on the supply equation for fossil fuel. Two are taxes increasing from zero to $20 per mtce over the course of l0 years and then declining back to zero over the next decade; one pulse begins in the year l980, and the other begins in the year 2025. For a second set of runs, permanent taxes of $l0 per ton are introduced linearly over the first 20 years. One begins in the year l980, and the other begins in the year 2025. A final tax, modeled after the l00% control case presented in Nordhaus (l979) and called the "stringent tax," imposes a permanent tax that rose linearly beginning in the year 2000 from zero to $6 per mtce by the year 2020, then to $68 per mtce by the year 2040, and finally to $90 per mtce by the year 2060. These are all illustrated in Figure 2.l9. Table 2.l8 and Figures 2.20 and 2.2l show the results of the tax runs. Notice there that while the pulse taxes accomplish very little, the permanent tax initiated in 2025 is the most effective among the first four alternatives. This paradox is explained as follows: burning more fossil fuel early and postponing CO2 reductions lowers the even- tual C02 concentration because it allows the atmosphere to cleanse itself slowly. To see this, recall that our model allows for a slow seepage (l part per l000 per year) of ambient carbon dioxide into the deep oceans. Earlier emissions, therefore, gradually disperse into the deep oceans and produce end-of-period concentrations that are somewhat lower. The major conclusion concerns the extent to which concentrations appear to respond to taxes. As can be seen, a $l0 per ton tax accom- plishes only a modest reduction in CO2 concentrations. Should emissions restraint become desirable, it will take extremely forceful policies to make a big dent in the problem. Even the "stringent"

l47 _ 1 I 90 -I 80- 70- 60- :{S 50 - o •0 10 CTi r a 40- 30- 20- 10- 0 - TIME Pulse 1980 Pulse 2025 Stringent Permanent 1980 — Permanent 2025 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.l9 Taxation on carbon fuel price (l975 dollars per ton coal equivalent). The time tracks of a stringent tax and four alternative $l0 per ton of coal equivalent taxes; the temporary taxes peak at $20 to accommodate the model.

l48 TABLE 2.l8 Concentrations and Emissions along the Likelihood Path under Various Taxes on Carbon-Based Fuels l975 2000 2025 2050 2075 2l00 Concentrations Base 34l 368 428 5l6 633 780 l980 Permanent- 34l 367 423 506 6l7 759 l980 Peaked^ 34l 367 423 5l3 633 778 2025 Permanent— 34l 368 428 5l3 632 763 2025 Peaked^ 34l 368 428 52l 638 783 Stringent Taxes6- 34l 368 425 487 56l 66l Emissions Base 4.6l 5.54 l0.3 l3.3 l7.5 20.0 l980 Permanent3- 4.6l 5.06 9.5 l2.5 l6.7 l9.5 l980 Peaked^ 4.6l 5.3l l0.3 l4.0 l7.6 l9.4 2025 Permanent^. 4.6l 5.54 l0.3 l2.3 l6.5 l9.3 2025 Peaked! 4.6l 5.54 l0.3 l3.l l7.3 l9.9 Stringent Taxes6- 4.6l 5.54 8.4 7.9 l0.7 l3.9 §A permanent tax of $l0 per ton imposed linearly beginning in l980 and reaching its full value by the year 2000. =A pulse tax of 20 years' duration beginning in l980, climbing linearly to $20 per ton by l990 and then falling to zero by the year 2000; it averages $l0 per ton. £& permanent tax of $l0 per ton imposed linearly beginning in 2025 and reaching its full value by the year 2045. °A pulse tax of 20 years' duration beginning in 2025, climbing linearly to $20 per ton by 2035 and then falling to zero by the year 2045; it averages $l0 per ton. £& gradually increasing tax rising linearly from zero to $8 per ton between 2000 and 2020, from $8 to $68 per ton between 2020 and 2040, from $68 to $90 per ton between 2040 and 2060, and remaining at $90 per ton thereafter. This tax was drawn from Nordhaus (l979, Chapter 8). taxes, which would place 60% surcharges on the prices of fossil fuels, did not prevent doubling before 2l00 in our most likely case.* *Nordhaus (l979) presented an earlier estimate of the taxes needed to curtail the carbon dioxide buildup in an optimizing linear program- ming framework. In that calculation the potency of carbon taxes was very close to the estimates here. The estimate here is 0.46% reduction in 2l00 carbon dioxide concentration per $l of carbon tax, while in the earlier work the estimate was 0.36% reduction per $l. Note that comparison is not completely appropriate because these reactions are likely to be nonlinear.

l49 0- -1- -2- -3- » -4- i -5- UJ z -6 2 K -7- -8- -9- -10-3 Permanent Beginning in 2020 Temporary Beginning in 1980 Permanent Beginning in 1980 V Temporary Beg1nn1ng in 2020 Pulse 1980 Permanent 1980 Stringent Pulse 2025 Permanent 2025 1975 2000 2025 2050 2075 2100 YEAR FIGURE 2.20 Plot of carbon emission versus time for taxed runs. Deviation in emissions from the base run for various taxes. It should be emphasized that this conclusion about the potency of CC>2 taxes (or their regulatory equivalents) is extremely tentative. It is based on a model for which many of the parameters are known imperfectly. On the other hand, the model's conclusions appear to confirm results of a completely independent model, as reported in the last footnote and those of Edmonds and Reilly (l983).

l50 0- -10- -20- -30- E a -40- < (5 -50- -60- O -70- K Si -80- -100- -110- -120- Temporary Beginning in 2020 Temporary Beginning in 1980 Permanent Beginning in 2020 Permanent Beginning in 1980 Pulse 1960 Permanent 1980 Stringent Pulse 2025 Permanent 2025 1975 2000 2025 YEAR 2050 2075 2100 FIGURE 2.2l Effect of carbon taxes on atmospheric concentration (parts per million per year). Deviation of run from base run without carbon taxes. Nevertheless, the conclusions about the potency of policy are sobering. They suggest that a significant reduction in the concen- tration of C02 will require very stringent policies, such as hefty taxes on fossil fuels. Global taxes of around $60 per ton of coal equivalent (approximately $l0 per barrel of oil equivalent) reduce the concentrations of CO2 at the end of our period by only l5% from the base run. Moreover, these taxes must be global; it is presumed that a tax imposed by only a fraction of the countries would have an effect roughly proportional to those countries' share of carbon emissions.

l5l To the extent that such an approach can offer guidance, therefore, it suggests that there are unlikely to be easy ways to prevent the buildup of atmospheric CO2. The strategies suggested later by Schelling (Chapter 9)—climate modification or simply adaptation to a high CO2 and high temperature world—are likely to be more economical ways of adjusting to the potential for a large buildup of CO2 and other greenhouse gases. Whether the imponderable side effects on society—on coastlines and agriculture, on life in high latitudes, on human health, and simply the unforeseen—will in the end prove more costly than a stringent abatement of greenhouse gases, we do not now know. References Arrow, K. J. (l982). Risk perceptions in psychology and economics. Economic Inquiry 20:l-9. Bolin, B. ed. (l98l). Carbon Cycle Modelling. SCOPE l6. Wiley, New York. Brainard, W. C. (l967). Uncertainty and the effectiveness of policy. Am. Econ. Rev. 57(2) . Clark, W., ed. (l982). The Carbon Dioxide Review: l982. Oxford U. Press, New York. Council on Environmental Quality (l98l). Global Energy Futures and the Carbon Dioxide Problem. Washington, D.C. Duncan, D. C., and V. E. Swanson (l965). Organic Rich Shale of the United States and World Land Areas. U.S. Geological Survey Circ. 523. Edmonds, J., and J. Reilly (l983). A long-term global energy economic model of carbon dioxide release from fossil use. Energy Econ. 1:74-88. Fair, R. C. (l980). Estimating the expected predictive accuracy of econometric models. Int. Econ. Rev. 2l(2). Hogan, W. W. (l980). Dimensions of energy demand. In H. H. Landsberg, ed., Selected Studies on Energy; Background Papers for Energy: The Next Twenty Years. Ballinger, Cambridge, Mass., p. l4. International Institute for Applied Systems Analysis (IIASA) (l98l). Energy in a Finite World: Paths to a Sustainable Future. Report of the Energy Systems Group of IIASA, W. Ha'fele, Program Leader. Ballinger, Cambridge, Mass. Johnston, J. (l972). Econometric Methods. McGraw-Hill, New York. Kahn, H., W. Brown, and L. Martel (l976). The Next 200 Years. Hudson Institute Report, Morrow, New York. Keeling, C. D. (l973). The carbon dioxide cycle. In Chemistry of the Lower Atmosphere, N. Rasool, ed. Plenum, New York. Keyfitz, N. (l982). Population projections, l975-2075. In Clark (l982), pp. 460-463. Machta, L. (l972). The role of the oceans and biosphere in the carbon dioxide cycle. In 0. Oyrssen and D. Jagnes, eds., The Changing Chemistry of the Oceans. Wiley-Interscience, New York, pp. l2l-l45. Machta, L., and G. Telegades (l974). Climate forecasting. In Weather and Climate Modification, W. N. Hess, ed. Wiley, New York.

l52 Malinvaud, E. (l980). Statistical Methods of Econometrics. North-Holland, Amsterdam. Manne, A. S. (l974). Waiting for the Breeder. Research Report RR-74-5. International Institute for Applied Systems Analysis (IIASA), Laxenburg, Austria. Manne, A. S., ed. (l982). Summary Report of the International Energy Workshop, l98l. Stanford University Institute for Energy Studies, Stanford, Calif. Marland, G. (l982). The impact of synthetic fuels on global carbon dioxide emissions. In Clark (l982), pp. 406-4l0. Meadows, D. H., D. L. Meadows, J. Randers, and W. W. Behrens (l972). The Limits to Growth: A Report for the Club of Rome's Project on the Predicament of Mankind. Universe Books, New York. Modeling Resource Group (MRG) (l978). Energy Modeling for an Uncertain Future. Supporting Paper 2, Committee on Nuclear and Alternative Energy Systems (CONAES), chaired by T. C. Koopmans. National Research Council, Washington, D.C. Moody, J. D., and R. E. Geiger (l975). Petroleum resources: how much oil and where? Technol. Rev. 77:38-45. National Research Council (l979). Energy in Transition l985-20l0. Final Report of the Committee on Nuclear and Alternative Energy Systems (CONAES). National Academy of Sciences, Washington D.C. Nelson, R. R., and S. G. Winter (l964). A case study in the economics of information and coordination: 'the weather forecasting system," Q. J. Econ. 78(3) . Nerlove, M. (l965). Estimation and Identification of Cobb-Douglas Production Functions. North-Holland, Amsterdam. Nordhaus, W. D. (l977). The demand for energy: an international perspective. In W. D. Nordhaus, ed., International Studies of the Demand for Energy. North-Holland, Amsterdam, p. 273. Nordhaus, W. D. (l979). Efficient Use of Energy Resources. Yale U. Press, New Haven, Conn. Nordhaus, W. D. (l980a). Oil and economic performance in industrial countries. Brooking3 Papers on Economic Activity 2:34l-388. Brookings, Washington, D.C. Nordhaus, W. D. (l980b). Thinking about Carbon Dioxide: Theoretical and Empirical Aspects of Optimal Control Strategies. Discussion Paper No. 565. Cowles Foundation, Yale University, New Haven, Conn. OECD Interfutures Project (l979) . Facing the Future. Organization for Economic Cooperation and Development, Paris. Raiffa, H. (l968). Decision Analysis: Introductory Lectures on Choices under Uncertainty. Addison-Wesley, Reading, Mass. Reilly, J., R. Dougher, and J. Edmonds (l982). Determinants of Global Energy Supply to the Year 2050. Contribution 82-6 to the Carbon Dioxide Assessment Program. Institute for Energy Analysis, Oak Ridge Associated Universities, Oak Ridge, Tenn. Ridker, R. G., and W. D. Watson (l980). To Choose A Future; Resource and Environmental Consequences of Alternative Growth Paths. Johns Hopkins U. Press, Baltimore, Md. Tversky, A., and D. Kahneman (l974). Judgement under uncertainty. Science l85:ll24-ll3l.

l53 Tversky, A., and D. Kahneman (l98l). The framing of decisions and the psychology of choice. Science 2ll:453-458. Uzawa, H. (l962). Production functions with constant elasticities of substitution. Rev. Boon. Studies 29:29l-299. Varian, H. (l980). Microeconomic Analysis. Norton, New York. Workshop on Alternative Energy Strategies (WAES) (l977). Energy: Global Prospects l985-2000. Report of the Workshop on Alternative Energy Strategies, McGraw-Hill, New York. Yohe, G. W. (l979). Comparisons of price and quantity controls—a survey. J. Comp. Econ. 3:2l3-234. 2.2 A REVIEW OF ESTIMATES OF FUTURE CARBON DIOXIDE EMISSIONS Jesse H. Ausubel and William D. Nordhaus 2.2.l Introduction In analyzing prospects and policies concerning future carbon dioxide buildup, it is necessary to begin with projections of levels of CO2 emissions. Because of the long residence time in the atmosphere of CO2 emissions, along with the potential for large and durable societal impacts of higher CO2 concentrations, there is great interest in long-term projections—those extending a half-century or more. While it is clearly necessary to make global long-term projections in this area, the projections are intrinsically uncertain, and the uncertainty compounds over time. This section reviews methods involved in making projections of carbon dioxide emissions, describes the major projections, and offers some comparisons and comments. It is intended to serve three purposes. First, it should help to acquaint the reader with the state of the art in CO2 forecasting and the range of previous forecasts. Second, this review may help to identify shortcomings of current efforts and point to directions for new research. Third, it should establish the context of the forecasts developed by Nordhaus and Yohe (Section 2.l) for this report. Projections of future trajectories of CO2 emissions can be roughly divided into three categories: (A) projections that are no more than extrapolations and that are primarily intended to be used to initiate studies of the carbon cycle or the climate system; (B) those based on relatively detailed examination of global energy supply and demand in which CO2 emissions are largely incidental; (C) projections deriving from analysis of the energy system in which changing levels of CO2 are themselves taken into account. Leading examples of category A, in which CO2 emissions are projected with little more than passing reference to energy modeling, are Keeling and Bacastow (l977) and Siegenthaler and Oeschger (l978). These papers extrapolate emissions

l54 in order to predict future atmospheric CO2 levels. Such efforts also appear in numerous reports and papers concentrating on calculating climatic change, for example, JASON (l979) and Hansen et al. (l98l). The projections consist of little more than extrapolating rates of fossil fuel emissions growth from recent decades out a century and more into the future. These extrapolations can be regarded as simplifica- tions or summarizations of more complete projections; they are useful for studies of the sensitivity of the carbon cycle and climate system but unpersuasive as elements of a comprehensive CO2 assessment. The projections based on relatively detailed analysis of an uncon- trolled global energy-climate system, (B), which are the most important for purposes of this section, differ greatly in their design, in the extent to which formal models are employed, and in detail with respect to fuels, geography, and other factors. Leading examples include those made by H. Perry and H. H. Landsberg (l977) for the NRC Geophysics Study Committee, the several projections by Rotty and by Edmonds and Reilly of the Institute for Energy Analysis (IEA) of Oak Ridge Associated Universities (Rotty, l977; Rotty and Marland, l980; Edmonds and Reilly, l983a), the projections of Nordhaus (l977) and (l979), and those made for the Energy Systems Program of the International Institute for Applied Systems Analysis (IIASA) (Niehaus and Williams, l979; IIASA, l98l). Category (C) projections, which require the basic analysis of category (B) as input, seek additionally to take into account the changing level of atmospheric CO2 (or the costs of climatic change) in the calculations. That is, C02 is included as a possible eventual constraint on the energy system. Projections incorporating this per- spective are found in Nordhaus (l979, l980), Council on Environmental Quality (CEQ) (l980), A. M. Perry (l982), Perry et al. (l982) , and Edmonds and Reilly (l983a). Almost all of the scenarios applied to studies of CO2 that are based on reasonably in-depth analysis of the energy situation project a continued growth of energy demand (or consumption) to between about 20 and 40 terawatt (TW) years per year (yr/yr) over the next 40 or 50 years, an increase of two and a half to five times the recent level.* These include scenarios developed for studies by the National Research Council (NRC), the International Institute for Applied Systems Analysis (IIASA), and the Institute for Energy Analysis (IEA) of Oak Ridge Associated Universities and by Nordhaus (l979). Several other energy scenarios, like those of the Interfutures Project (l979), the Hudson Institute (Kahn et al., l976), the World Energy Conference (l978), and Stewart (l98l) are in the same range. Whenever such scenarios do not project a large share of nonfossil energy, they lead to relatively serious concerns about climatic change in the next 50 to l00 years.t *Estimated global primary energy supply in l975 was roughly 8 TW yr/yr (IIASA, l98l). tThe market share of nonfossil energy sources (including noncom- mercial energy) is about l5% at present. The prominent scenarios (continued on facing page)

l55 Most of the estimates of CO2 emissions from fossil fuels in the year 2030 lie in a range between about l0 and 30 gigatons of carbon (Gt of C). Thus, based on a review of past projections, it appears that the range of estimates of energy consumption 50 years hence is a factor of 2 or more, and consequent (X>2 emissions show a range of a factor of 3 or more. It should become clear that the range of estimates is wider than the range of approaches. The large differences in the estimates are trace- able in almost all cases to the sensitivity of the models to differences in estimates of the variables or parameters. Most prominent are assump- tions about rates of population growth, economic growth, the ratio of energy demand to economic activity, and the mix of supply sources that will meet energy demand. Brief descriptions of the major projections in the three categories follow. 2.2.2 Projections Based on Extrapolations The extrapolative (A) models are essentially one-equation global models. There are no nations, no economic sectors, no GNP or population projec- tions. In these models, an idealized resource depletion function is customarily used to project the evolution of annual releases through future centuries. There are usually three key variables in the func- tion. One is the total resource of carbon-based fuels. The second is the initial growth rate. The third is a parameter that embodies judg- ments about the future pattern of exploitation of the resource. It can be set such that peak exploitation occurs when the resource is, for example, 20% depleted, with the possible intention of reflecting a con- sumer response to rising prices. Or, it can be set to draw different patterns of exploitation, for example, short and intensive, or gradual. In the very long run (past 2l00), the key variable determining CO2 buildup in this approach is the total carbon resource. The studies have typically taken a number in the vicinity of 5000 Gt of C for the total carbon resource. Such a figure is not out of line with estimates of ultimately available resources, although it is a factor of l0 larger than today's proved recoverable reserves (see World Energy Conference, l980). In the medium run (up to 2l00), the central variable determining the CO2 buildup in simple extrapolation models is the initial growth rate. It has been common in the literature to base this variable on work of Rotty (l977), who estimated from historical data that CO2 emissions from fossil fuel burning (with a trivial addition for cement manufacture) increased 4.3% per year if one excludes the periods of the two world wars and the global economic depression of the early l930s. This figure of 4.3% has been extremely influential and has been widely used to project future levels of atmospheric CO2. Many papers and mentioned above generally foresee either an unchanged share for nonfossil sources or a moderate expansion of nonfossil sources, to about 20-35% over the next 50 years.

l56 reports on CO2-induced climatic change written in the past few years mention it prominently. For example, a JASON report (l979) opens with the statement, "If the current growth rate in the use of fossil fuels continues at 4.3% per year, then the CO2 concentration in the atmo- sphere can be expected to double by about 2035. ..." While the 4.3% figure is the one most mentioned in the climate literature, increasing debate has grown around it (e.g., World Climate Programme, l98l). One reason for the recent skepticism is that energy growth has slowed considerably—to an average of little more than 2% annually—since l973. Projections reviewed below range from that of Lovins (l980; Lovins et al., l982), who suggests there might be a global decrease in use of energy and fossil fuels, to the 50 TW yr/yr case proposed by Niehaus and Williams (l979), in which energy demand grows at an average of about 4% in coming decades and all of this high projected energy demand is covered by fossil fuels. It is worth noting that the highest projections of CO2 emissions have generally come from the simple extrapolative models and rarely from studies that incorporate explicit supply and demand models for energy. To illustrate, the Keeling and Bacastow (l977) "preferred scenario" projects emissions somewhat larger than the high coal scenario developed by Niehaus (l979) as an upper limit scenario from the energy perspective, and the Siegenthaler and Oeschger (l978) "upper-limit" scenario generates emissions at about twice the rate of the Niehaus high scenario. The extrapolations might be best characterized as "gedanken experi- ments" devised for study of the carbon cycle: "suppose x thousand tons of carbon exist as fossil fuels and all will be used at a certain rate. ..." While extrapolative models have been successful in drawing attention to the CO2 issue, they are of limited interest in projecting likely outcomes for CO2 emissions and concentrations. The main virtue of the approach is simplicity, for a constant growth or logistic curve has great transparency, particularly relative to the enormously com- plicated energy models. On the other hand, these models do not respect fundamental aspects of economic and energy sector behavior, such as conservation based on rising energy prices. It is not surprising that these models will, therefore, lack realism during periods (after l973, for example) when changes in economic and political structures have been profound. 2.2.3 Energy System Projections The major class of forecasts of C02 emissions arises from formal or informal energy modeling. Most of this work dates from the l973 "energy crisis" and is only recently published. In general, it forms the most reliable basis on which to draw for projections. Note that only global studies are sufficient for projecting CO2 emissions; the numerous national and regional energy studies may provide a consistency check on global studies, but they cannot be used independently to project C02 emissions.

l57 2.2.3.l Perry-Landsberg (MAS) Perry and Landsberg (l977) assembled projections of world energy con- sumption and emissions to the year 2025 for the HAS report, Energy and Climate. The projections are for ll geographic regions, which are sometimes large nations and sometimes groups of nations. Regional demand for energy is derived from projections of population, GNP, and the relationship of GNP per capita and energy consumption. A "high- population/low-economic-growth" situation is postulated for developing countries and a "low-population/low-economic-growth" situation for developed countries. Global population in 2025 is at 9.3 billion, about 20% higher than IIASA and Rotty. The net result is a total energy demand forecasted to reach about 39 TW yr/yr in 2025. Emissions are calculated for two situations chosen to stress the contrast between a strategy based on "renewables" (i.e., noncarbon- based, abundant energy sources) and one based on coal. In the first case, if regional demand exceeds regional production, an estimate is made assuming the new noncarbon-based energy resource is available to meet the deficiency of nonrenewable resources. In the second case, an estimate is made for the situation for which regional deficiency would be met by coal. Based on these assumptions, annual world CO2 emissions in 2025 would be between l3 and l4 Gt of C in the first case and about 27 Gt of C in the second, or about 2.5 to 5 times current levels. The Perry-Landsberg study forms a careful baseline for comparison. It is comprehensible and plausible. A major shortcoming is that it omits any explicit role for prices to play in driving demand toward or away from energy in general or individual fuels in particular. In addi- tion, while the total demand for energy grows out of a well-specified model, the fuel mix is based on arbitrary assumptions. 2.2.3.2 IIASA 2.2.3.2.l Niehaus and Williams The IIASA Energy Systems Program analyzed several hypothetical energy strategies for the period up to the year 2l00 for their implications for atmospheric CO2 (Niehaus and Williams, l979; IIASA, l98l). As such, it could not directly employ the so-called "IIASA energy models," which were run only to the year 2030. Rather, distri- bution of energy supply among coal, oil, gas, solar, and nuclear is derived from a very-long-term energy model developed by Voss (l977). The Voss model employs principles similar to that of the Forrester- Meadows (system dynamics) school and is structured into six sectors: population, energy, resources, industrial production, capital, and the environment. It is global; there is no geographic disaggregation. Among the strategies explored (Niehaus and Williams, l979) are four in which global demand levels out to either 30 TW yr/yr or 50 TW yr/yr in the mid-twenty-first century and remains at that level to 2l00. In both the lower- and higher-demand cases there is an analysis in which

l58 nuclear and solar energy play an important role and in which they do not. Table 2.l9 shows the reserves of fossil fuels used in each strategy. The relation between total coal use and C02 emissions is characteristic of projections leading to high or low C02 emissions. The scenarios with reliance on nuclear and solar energy lead to peak annual CO2 emissions of about 8 to l0 Gt of C around the year 2000, while the scenarios with reliance on fossil fuels lead to emissions of about 22 and 30 Gt of C in 2030, increasing somewhat thereafter. While consideration is given to available fossil resources at the global level, there is no study of regional or national implications. The Niehaus-Williams projections are based fundamentally on judgments external to economic analysis or modeling. Once the energy growth path and fuel mix are set, the outcome for CO2 emissions is determined— the use of the system model plays but a small role in the outcome. The most important issue is whether the ex cathedra judgments as to the ultimate levels of global energy demand (the 30 and 50 TW yr/yr levels discussed above) are reasonable. While such figures are conventional, and indeed so often used that they become comfortable assumptions, they have no grounding in a physical or economic con- straint or in the outcome of an energy model. The notion of "satura- tion" at these levels is a popular idea that has no particular basis, other than the hope that human society will pass through a transition to a stable plateau over the next couple of generations. Thus, while the critical assumptions of energy demand and fuel mix in these studies do not appear implausible, their grounding is weak. 2.2.3.2.2 The IIASA Energy Models IIASA used a set of extremely detailed models to delineate two scenarios, a "high" and a "low" case culminating in 2030 with world energy consumption at 35 and 22 TW yr/yr, respectively. The models are oriented toward engineering and technical considerations for specific demand sectors and global consistency of supply among the seven regions TABLE 2.l9 Reserves of Fossil Fuels Used in Different Outcomes (l975-2l00)1 Coal Oil Gas Strategy (Gt of C) (Gt of C) (Gt of C) 30 TW with solar and nuclear l70 l70 ll0 50 TW with solar and nuclear 230 2l0 l30 30-TW fossil fuel l980 l90 l20 50-TW fossil fuel 3020 230 l40 5After Niehaus and Williams (l979).

l59 into which the world is disaggregated. The distribution of supply sources in the actual IIASA scenarios is quite different from Niehaus and Williams, even though the Niehaus and Williams runs were originally chosen to be broadly consistent with the global energy demand pattern. Both the high and low IIASA scenarios are hybrids, with expanded use of many supply sources, so that in 2030 ll TW yr/yr are coming from non- fossil fuel sources in the high case and 7 TW yr/yr in the low case. In the high case emissions are above l6 Gt of C in 2030, and in the low case they are nearing l0 Gt of C. The IIASA models have probably been the closest existing approach to an appropriate disaggregated technique for forecasting CO2 emissions. In principle, they are grounded in engineering and economic relations, with attention to feasibility and response of supply and demand to price. In practice, because of the need to accommodate differing views, world energy consumption was adjusted judgmentally to be "reasonable," as well as on the basis of the formal methods. In this respect, the outcome shares the problems outlined in the last paragraph of the dis- cussion of the Niehaus-Williams approach. Another issue raised by the IIASA model is whether a high degree of disaggregation is appropriate. Such an approach allows considerations such as those involving trade and national policies; however, it also makes the models difficult to comprehend, manipulate, change, and verify independently. 2.2.3.3 Rotty et al. For several years, Rotty and co-workers at the Institute for Energy Analysis of Oak Ridge Associated Universities emphasized extrapolation of the 4.3% estimate of historic annual increase in CO2 emissions and figures tapering off from this (Rotty, l977, l978, l979a,b; Marland and Rotty, l979). Based on demand and fuel-share projections made for six world regions, an annual fossil fuel release of CO2 containing 23-26 Gt of C from energy use of 36-40 TW yr/yr in the year 2025 is calcu- lated. The work is partly based on a more formal analysis by Allen et al. (l98l) developed for the year 2000. In extension of the projections to 2025 Rotty assumes supply will meet demand without examination of balancing economic factors such as prices. For projections of emissions beyond 2025, a different extrapolative technique involving application of arbitrary global fossil resource depletion rates is employed (see Section 2.2.3.2 above). A more recent paper (Rotty and Marland, l980) includes some discus- sion of constraints on fossil fuel use. Three kinds of constraints are examined: resource, environmental, and fuel demand. With respect to resource supplies, Rotty and Marland conclude that "the fraction of total resources used up to the present is so small that physical quan- tities cannot yet be perceived as presenting a real constraint." However, it is mentioned that unequal geographic distribution of the resources probably will continue to be a source of international stress. Climatic change as an environmental issue is dismissed as a constraint to fossil fuel use.

l60 In contrast, Rotty and Marland (l980) discuss at some length the likelihood that slower growth in fuel demand dictated by social and economic factors will limit fossil fuel use. Reduced rates of economic growth are projected as a result of very recent trends and anticipated problems with capital and escalating costs and shifts toward conserva- tion and less energy intensive industries. No formal modeling is offered to substantiate the position. Regardless of the precise causes, summing up estimates for about a dozen countries and half a dozen com- posite regions leads Rotty and Marland to project C02 emissions in 2025 of about l4 Gt of C in a 26 TW yr/yr global energy scenario—an annual growth rate of 2% per year from today. Thus, the range of Rotty emission projections are quite similar to those of IIASA and Perry and Landsberg. The strengths and weaknesses of the Rotty approach are partly those of the extrapolative models and partly those of the Perry-Landsberg approach. The repeated adjustment of assumptions is evidence of the uncomfortably arbitrary nature of the endeavor. 2.2.3.4 Nordhaus Nordhaus (l977, l979) estimated the uncontrolled path of CO, emissions in a modification of a model developed for studies of efficient alloca- tion of energy resources (or of a competitive market for energy). Nordhaus's approach was fundamentally based on economic modeling and assumptions—with interaction of forces of supply and demand leading to a path of prices and energy consumption over time. By comparison, prices play a lesser role in the IIASA and Perry and Landsberg approaches and virtually no role in Rotty's projections. Nordhaus employs a medium-sized linear programming model, with basic components being an objective function (based on demand functions for energy) and a supply function centered on geological considerations and technology. The outcome is calculated by finding the lowest cost way of meeting the demand function, using a linear programming (LP) algo- rithm. The demand function (technically, the objective function) for the LP is drawn from data on market behavior. It is built up from four energy sectors (electricity, industry, residential, and transportation), with demand in each sector a function of population, per capita income, and relative prices. The technology or constraint set is derived from engineering and geological data on resource availability and costs of extraction, transportation, and conversion. The model incorporates constraints on new technologies, adaptation of demands, and upper bounds on rates of growth. Running the model involves balancing supply and demand over time, with prices playing the central role of equilibration. Results are given in terms of both activity levels (for example, production of coal or oil in a given period) and prices. The calculation provides for six different fuels used in the four energy sectors, for two different regions (United States and rest of world), for ten time periods of 20 years each. The macroeconomic assumptions are that rapid growth in GNP per capita will continue in both regions, but at a diminishing rate

l6l after 2000, and that population will also slow to reach a world level of l0 billion in 2050. Nordhaus calculates that the uncontrolled path leads to large changes in the level of atmospheric CO2. In the uncontrolled case, annual emissions are at l8 Gt of C in 2020 and steeply increasing, so they reach 40 Gt of C in 2040. Global energy demand is about 40 TW yr/yr in 2030. A key in these high projections is high initial GNP growth rates; for l975-l990 the assumed growth per year is 3.7% in the United States and 6.5% in the rest of the world. The results of the Nordhaus analysis exhibit the strengths and weak- nesses of pure (nonjudgment-based) economic modeling. On the one hand, the outcome is based on objective data (such as market prices and resource availability) and is thus reproducible and can be easily modified over time. On the other hand, results are very sensitive to assumptions about future price and growth trends. The actual model runs were based on an assumption of rapid future economic growth and low fuel prices—leading thereby to rapid estimated growth of CO2 emissions and atmospheric concentrations. 2.2.3.5 Edmonds and Reilly Rotty's work is now being followed at IEA by a more formal CO2 emissions model developed by Edmonds and Reilly. The model takes as inputs key economic, resource availability, and demographic variables such as income, energy costs, resource constraints, labor force, and population. From these it calculates consistent energy-use paths. Consistency is defined as a balancing of supply and demand in the face of resource constraints, with energy prices adjusting to assure an equilibrium solution. Energy use is disaggregated into nine world regions and all major possible fuel types, including oil, gas, coal, coal liquefaction, and shale oil. The model is intended to be applicable out about l00 years, with calculations feasible at intervals that the user selects, for example, l0 or 20 years. The model is extensively documented (Edmonds et al., l98l; Reilly et al., l98l; Edmonds and Reilly, l983c), and a base case is now being developed (Edmonds and Reilly, l983a,b). Initial results show a quite steady increase in energy demand of about 2.5% per year from now to 2050, so that demand has reached about 29 TW yr/yr in 2025 and 50 TW yr/yr in 2050. CO2 emissions increase by l.5% per year from now to 2000, and by 2.3% per year between 2000 and 2025, reaching l2 Gt. Because of increasing reliance on coal, oil shale, and synthetic fuels, emissions then rise quite steeply, by more than 3% per year, and reach an annual rate of 26 Gt of C by 2050. The Edmonds-Reilly model has the potential of being an extremely useful follow-up to earlier detailed studies, such as that of IIASA. It contains sufficient regional and sectoral disaggregation that experts in individual areas (such as analysts specializing only in the U. S. economy or a particular fuel source) can evaluate the detailed forecasts and assumptions. It also appears to be flexibly designed, so that results of different assumptions can be examined easily.

l62 At the same time, the current effort contains some of the problems that have plagued earlier large-scale energy models. Perhaps the most important is the decoupling of energy demand from output. The current model has energy demand sensitive to prices and incomes, but incomes and outputs are not directly related to energy, labor, and other inputs. (Technically, energy is not treated as a derived demand, that is, derived from a production function relating inputs to output.) A second problematic feature is the extensive use of logistic curves that are not sensitive to prices for determining supply. It should also be noted that the Edmonds-Reilly model is quite large and somewhat forbidding for a casual user. The benefit from techno- logical and regional detail is partially vitiated by the difficulty of understanding the structure and workings of the model. As in many large-scale models, the size makes identification of critical parameters or assumptions a formidable task. Notwithstanding these reservations, the Edmonds-Reilly work stands out today as the only carefully documented long-run global energy model operating in the United States. 2.2.3.6 Other Projections Marchetti (l980) has made a forecast of the amount of CO2 that will be emitted to the year 2050 based on a logistic substitution model of energy systems (Marchetti and Nakicenovic, l979). This model treats energy sources as technologies competing for a market and applies a form of market penetration analysis. A logistic function is used for describing the evolution of energy sources and is fitted to historical statistical data. The driving force for change in this model appears to be the geographical density of energy consumption, and the mechanisms leading to the switch from one source to another are the different tech- nical characteristics associated with each energy source. For example, in the Marchetti view oil succeeded coal primarily because of the advan- tages achievable by a system operating on fluids. With data on energy consumption back to l860 and including both com- mercial and noncommercial (wood, farm waste, hay) energy sources, the slope of the fitted curve of energy demand implies an annual growth of 2.3%. [This contrasts strongly with Rotty (l979b), who emphasizes that commercial energy supply, excluding times of world conflicts and depres- sion, has grown at a rate of about 5.3% since l860.] Applying a future growth rate of 3% per year, Marchetti calculates energy consumption for the various sources for the period l975-2050 based on the logistic equa- tions. The model predicts a relatively rapid phaseout of coal, a dominant role for natural gas, rapid growth of nuclear power, and a negligible role for new sources other than nuclear over the next 50 years. The model implies an increase in annual C02 emissions to about l4 Gt of C in 2030, an amount close to the lower estimates of Perry and Landsberg, IIASA, and IEA, and a cumulative emission of carbon to the atmosphere between the years l975 and 2050 of about 400 Gt of C [to somewhat less than 450 ppm(v)]. Perhaps more important, it predicts a gradual reduction in emissions and atmospheric CO2 thereafter, rather than continuing increase.

l63 While Marchetti's projection of fuel shares is singular, his analysis of the long-term pattern of energy demand is not. Stewart (l98l) also uses an empirical approach leaning on application of logistic growth curves, chosen to fit historical data extending back to l850. Stewart argues additionally that energy growth is likely to evolve in surges or cycles rather than monotonically. Stewart identifies historical "cycles" in energy use with periods of around 50 years (perhaps a manifestation of the frequently cited Kondratieff cycle of economic activity) and notes that deviations of plus or minus 20% around a long-term logistic growth curve were experienced. On the basis of an assumed stable cyclical structure, Stewart pro- jects world energy consumption to the year 2025. For the period l975-2000 a 40% growth is indicated; this breaks down into zero energy growth in the United States and a 60% growth for the world outside the United States. This overall projection for 2000 is lower than most. However, Stewart's projection for 2025 is close to other high values. After the relatively depressed period between l975 and 2000, world energy growth between 2000 and 2025 is projected at a rate of about 4%, increasing from about l3 TW yr/yr to almost 36 TW yr/yr. Legasov and Kuz'min of the Atomic Energy Institute of the USSR have also made a projection employing a logistic approach. The key variable in their function is one that describes the level of stabilization of per capita energy consumption (Legasov and Kuz'min, l98l; Report of the US/USSR Workshop, l982). Legasov and Kuz'min explore two cases, one in which global average annual per capita energy consumption by 2l00 reaches l0 kW (roughly the level in the United States today) and one in which it reaches 20 kW. Population, meanwhile, stabilizes at a level of l2 billion people. Under these assumptions global energy use in 2020 is either 50 or 60 TW yr/yr, with a population of 8.8 billion. Legasov and Kuz'min project coal and nuclear power as the principal energy sources for the coming decades, with nuclear power gradually becoming dominant. Under these assumptions, CO2 emissions in 2020 are about l5 Gt in the lower case and l8 Gt in the upper case and roughly stable for several subsequent decades. The three approaches described above are more sophisticated than the extrapolation approach (see Section 2.2.3.2), but the underlying method- ology is similar. All assume that there is a stable underlying dynamic (exponential, logistic, or logistic-cum-sinusoidal) and forecast off that base. These approaches allow for no structural relation between exogenous variables like population and resources and endogenous vari- ables like energy consumption. Such autoregressive or inertial models do relatively well at prediction in the short run, but their level of aggregation is so high that for most purposes one must still turn to the more structural models. A final source is Lovins (Lovins, l980; Lovins et al., l982), who projects very low CO2 emissions because of a shift to conservation and renewable (nonfossil) sources. With a 4.6-fold increase in global economic activity during l975-2080 and a doubling of world population, total energy needs will, according to Lovins, be below the l975 level, indeed dropping over the next century to less than half the present level. A projected increase in energy efficiency in end uses along

l64 with renewable sources for energy production might, according to Lovins, largely or wholly eliminate the global use of fossil fuels. A case study of the Federal Republic of Germany, a diverse heavily industrial- ized economy in a rigorous climate, is used as an "existence proof" (basis for extrapolation) for the efficiency and renewables strategy. Lovins*s results appear to be wishful with respect both to rapid development and diffusion of solar technologies and to lifestyle changes involving energy conservation. He does not present a formal model or develop the implications of the analysis for capital and labor needs. In addition, some of the trends identified, such as increasing efficien- cy of end-use devices, may raise the demand for energy, an outcome not accounted for. While Lovins may turn out to be correct, the analytical basis for his views remains elusive and characterized by strong cultural bias. 2.2.4 Projections with C02 Feedback to the Energy System The energy projections reviewed in Section 2.2.3 share a potential deficiency when used to generate long-term CO2 emission trajectories. Calculation of the ejected C02 is largely incidental. An energy path is plotted for a variety of reasons, and C02 is merely the outcome of the chosen path. There are two ways in which such an approach may be deficient. First, by focusing on C02 directly, it may be possible to get more accurate C02 forecasts, as secondary issues (such as coal versus oil) can be ignored. Second, if a C02 buildup takes place and leads to serious social consequences, there may be some impact on the economy directly (through output) or indirectly (through policy reactions). Put differently, models that allow very high CO2 but do not allow feedback from environmental change to energy policy must be regarded with caution; they mask significant assumptions about the behavior of people and governments (Stahl and Ausubel, l98l). Projections that include increased CO2 levels as a possible eventual constraint on CO2 emissions include Nordhaus (l979, l980) , Edmonds and Reilly (l983a,b), CEQ (l980), and Perry (l98l; Perry et al., l982). These projections generally require that some threshold concentration of CO2 (or similar constraint) be set, presumably by political intervention. Trajectories are then calculated that keep ambient levels from exceeding this threshold. Thus, in these approaches, rather than begin from high- and low-energy scenarios, the approach is to work backward from a desired or specified terminal condition to defining energy demand and fuel mix patterns that satisfy it. 2.2.4.l Nordhaus Along with estimating the uncontrolled path described earlier, Nordhaus (l977, l979) also estimates time paths of emissions given particular carbon dioxide constraints. Efficient allocation of energy resources

l65 is calculated using the model described earlier under the assumption that it would be necessary to prevent atmospheric CO2 from exceeding either l.5, 2, or 3 times the preindustrial level [about 450, 600, or 900 ppm(v)]. The optimal path does not differ from the uncontrolled path for the first period (up to l990). Abatement measures become necessary only in the second period (l990-20l0) for the stringent control (450 ppm) and in the third period (20l0-2030) for the milder control programs. To illustrate, in 2020 emissions for the uncontrolled case and the trip- ling are identical at l8 Gt of C, and the doubling case is only mar- ginally lower at l6 Gt of C, but the 50% increase limit requires emissions of only 4 Gt of C. In 2040 the stringent-case emissions have trailed off to barely more than 2 Gt of C, the doubling case leaves carbon emission steady at l6 Gt of C, while the tripling and uncon- trolled case have both reached the vicinity of 40 Gt of C per year. This technique allows estimates of the costs of controlling CO2 emissions as well as the "carbon taxes" necessary to induce such responses. Nordhaus (l980, l982) also develops an optimal control framework, which seeks to identify the most economical way to balance the exploita- tion of both carbon fuels and climatic resources. The analysis is at a highly aggregate, global level; implications for sectors or for regional or national policies are not explored. Nordhaus weighs CO2 control strategies according to two criteria: their effects on the paths of consumption that are generated by the control strategy and maximization of the discounted value of consumption streams, where the discount rate combines both a temporal and a growth factor. The framework consists of four simple equations. These are a description of the carbon cycle and climatic effects of COo eleva- tion, estimates of the costs of reducing or abating CO2 emissions, an equation that incorporates estimates of economic impacts of CO2 buildup, and an equation that represents intertemporal choice between consumption paths. Since there is great uncertainty about the economic and social impact of elevation of CO2 concentration, Nordhaus tests the sensitivity of the model to different sets of costs. These are described by a "loss parameter," which indicates the fractional loss of consumption per doubling of CO2. By varying this and other parameters, a set of emissions trajectories is calculated. The outcome of the model was considered at best illustrative given the uncertainty surrounding key parameters (such as the economic impact of climate change). A major result, however, was that the best degree of CO2 control was extremely sensitive to important uncertain parameters, that is, no obvious control strategy stood out. 2.2.4.2 Edmonds and Reilly Edmonds and Reilly (l983a,b) have also begun to explore the effect of taxation policies of various kinds on CO2 buildup. One question asked is what consequences a substantial CO2 tax in the United States would

l66 have on the level of atmospheric CO2. They find that global carbon emissions are reduced by much less than the U.S. reduction owing to the fact that decreased U.S. energy demand resulting from the CO2 tax lowers world energy prices, which in turn spurs energy consumption in other regions. In contrast, when a global tax is combined with a U.S. embargo on coal exports, there are substantial reductions in U.S. and non-U.S. CO2 emissions. While all the studies on taxation of CO2 are still quite tentative, the three sets of tax experiments that we have reviewed—the Nordhaus results discussed in Section 2.2.4.l, the Nordhaus-Yohe results in Section 2.l, and the Edmonds-Reilly results—appear broadly consistent. This finding is striking, given that the three approaches are very different. 2.2.4.3 CEQ The CEQ study (l98l) derives several curves to yield a buildup of atmospheric CO2 equal to l.5, 2.0, and 3.0 times the preindustrial level (slightly less than 450, 600, and 900 ppm, respectively). It employs a simple, two-equation global model consisting of a differ- ential equation to explain buildup of atmospheric CO2 and a logistic equation to forecast CO2 emissions. The major unknown parameter is the initial growth rate of fossil fuel combustion. The model is run backward to calculate global fossil fuel releases that would produce the assumed buildups of carbon dioxide. Curves preferred for further analysis correspond in 2030 to fossil fuel energy production of about 8, l3, and l7 TW yr/yr and emissions of 6, l0, and l3 Gt of C, respectively. The controlled curves are compared with two overall energy projec- tions. The high global energy demand scenario is for a world whose population has leveled off at l0 billion by the year 2l00 and an aver- age per capita energy use equal to two thirds the present U.S. level. Energy use in 2030 is about 35 TW yr/yr (similar to the IIASA high scenario) and rises to about 75 TW yr/yr by 2l00, a ninefold increase over current levels, with about one fourth accounted for by population growth. A lower world energy use scenario represents a world whose population has leveled off at about 8.5 billion by 2l00 at an average per capita level of one third present U.S. consumption. In 2030 energy use is about 20 TW yr/yr (similar to the IIASA low scenario) and reaches a plateau well before 2l00 of about 30 TW yr/yr, about a fourfold increase over current consumption in which one half the growth is attributable to population increase. The CEQ study evaluates the significance of the gap between overall energy demand and the three assumed CO2 limits. For example, to avoid exceeding a 50% increase in global CO2 concentration and to meet the low-energy-demand scenario (a low growth, environmentally cautious world), nonfossil fuel sources would be required to increase from about l TW yr/yr today to more than 4 TW yr/yr by the year 2000, or about a 9% growth per year. By 2020 nonfossil fuel sources would have to contribute about l0 TW yr/yr, with their growth averaging 4%

l67 between 2000-2020. The l0 TW yr/yr are more than the current total global annual energy use, and more than the nonfossil (solar and nuclear) supply estimated for 2020 in the IIASA high scenario. The CEQ study estimates that together hydropower and nuclear power could probably provide between 2 and 3 TW yr/yr (fuel equivalent) by the year 2000. Thus, with low-energy growth but also a low ceiling on CO2 levels, a contribution of about l to 2 TW yr/yr would be needed by 2000 from other renewables, with rapid increases thereafter as hydropower potential is exhausted. 2.2.4.4 A. M. Perry et al. Perry and colleagues (l982; Perry et al., l982) begin by adopting global energy projections from IIASA, the World Coal Study (l980), and others as reference scenarios. The novel parameter in their analysis is the date when global fossil energy use must begin to deviate from the reference scenarios in order to meet various atmospheric CO2 limits. This date is referred to as the action initiation time (AIT). All the analyses so far are at the global level; that is, they refer to when a global policy (national policies summing to a global policy) would need to begin to be followed. The approach built around action initiation times stresses that the rate of change of energy strategies is extremely important. If some CO2 limit were approached along the kinds of curves normally drawn, the limit would certainly be passed, because of the inertia or momentum of the energy system. If the ceiling were not to be exceeded, CO2 production would have to fall abruptly to zero, a virtual impossibility. Thus, Perry (l982) proposes anticipatory scenarios, which involve a gradual slowing of growth of fossil fuel use, followed by an eventual slow decline. With a high initial growth rate or a late AIT, the transition required in order to remain below a given CO2 target may be too rapid and the subsequent decline too steep—the required transition may be infeasible. According to arbitrary feasibility criteria relating to historic evolution and behavior of energy systems, several scenarios are drawn that should allow sufficient time for the necessary changes in energy demand patterns and supply technologies. Table 2.20 lists some AITs thought to be of intermediate difficulty. In the Perry study, as well as the CEQ study, it is apparent that by fixing only a few parameters, principally energy growth, CO2 limits, and a few characteristic times like market penetration, the overall trends of fossil and nonfossil energy use become approximately deter- mined. With further work it may be possible to judge more reliably whether the different patterns of energy use designed to limit CO2 concentrations would be easy or difficult to attain. Without such information, it seems premature to employ these models for prescriptive purposes.

l68 TABLE 2.20 Required Action Initiation Times for Various CO2 Ceilings3-'^ CO2 Limit Initial Growth Rate of Annual Carbon Emissions (ppm) l.5%/yr 2.5%/yr 3%/yr 500 2005 l995 l990 600 2025 20l0 2000 700 2040 2025 20l0 800 2035 2020 ^Source: Perry (l982). —For example, if a global limit for CO2 in the atmosphere of 500 ppm is to be met, and emissions are growing at the outset by l.5%/year, actions to reduce the share of fossil fuels would need to begin in the year 2005. If emissions are growing by 3% in the coming decade and we wish to meet a limit of 500 ppm, policies to discourage use of fossil fuels might need to become effective as early as l990. These action initiation times are for transitions away from fossil fuels judged by Perry to be of intermediate difficulty. 2.2.4.5 General Comments Studies that attempt to include feedback from CO2 concentrations to energy policy are in their infancy. A particular problem is the con- fusion and combination of "positive" and "normative" approaches. In a "positive" model, the attempt is to describe how a system will behave under given boundary conditions. In a normative approach, one sets up a policy goal or objective function and then asks how the system ought to behave in order to optimize the objective function. While the dis- tinction is seldom clearly delineated in global energy models (see particularly the comment on Lovins above), potential confusion is most likely to arise concerning the class of models discussed in this section. For the most part, the best interpretation would seem to be the following: the energy systems are based on a positive description, and CO2 constraints are viewed as alternative normative policy constraints. However, assumptions of inaction (or absence of feedback) at very high levels of CO2 emissions are also in a sense normative. A second issue concerns the actual limits imposed. While the limitation of a doubling of C02 is the policy most often analyzed, it does not arise from a well-developed line of reasoning. An ideal (or even a "good") set of C02 policies will depend on the costs and benefits of climate change and C02 controls; costs and benefits are so poorly understood that no clear line of policy stands out as appropriate (see Schelling, Chapter 9). In terms of conclusions, the Nordhaus, CEQ, and Perry studies seem to be largely consistent in their projections of what emission trajec-

l69 tories would look like under particular CO2-induced constraints. As long as fossil fuel growth rates continue at the low level of the past few years and concentrations of 400-450 ppm are judged acceptable, there is little urgency for significant reductions in CO2 emissions below an uncontrolled path before l990. Emissions would need to be reduced below an uncontrolled path around 2000 if a limit in the vicinity of 450-500 ppm is desirable. To limit concentrations to 600 ppm (a doub- ling from preindustrial levels) would require that serious reductions be initiated in the 20l0 to 2030 period. These long lead times before CO2 reductions are necessary may be misleading, however. To effect a significant reduction of CO2 emissions in an orderly and efficient way probably requires planning and policy measures decades in advance, for the infrastructure and capital stock associated with fossil fuels cannot quickly be scrapped and replaced without high economic cost. Also, it is probably necessary to consider policies with regard to climatic change on the basis of possible combined effects of CO2 and other greenhouse gases. 2.2.5 A Note on the Biosphere In the past the biosphere may have been a cumulative source of CO2 as a result of human activities within a factor of 2 as great as burning of fossil fuels (Clark et al., l982; Woodwell, this volume, Chapter 3, Section 3.3). However, it appears that in projecting future CO2 emissions resulting from human activities the role of the biosphere is swamped by the potential contribution of fossil fuel combustion.* An estimate for the maximum possible future addition from all biospheric sources is 240 Gt of C (Revelle and Munk, l977). Baumgartner (l979) estimates that clearing of all tropical forests might contribute about l40 Gt of C. The total carbon content of the Amazon forest is estimated at about l20 Gt of C (Sioli, l973). Chan et al. (l980) develop a high deforestation scenario in which total additional transfer of carbon from the biosphere to the atmosphere by the year 2l00 is about l00 Gt of C. The World Climate Programme (l98l) group of experts adopted a range of 50 to l50 Gt of C for biospheric emissions in the l980-2025 period. Machta (this volume, Chapter 3, Section 3.5) estimates that massive oxidation of the biota might increase atmospheric CO2 by 75 ppm by A.D. 2l00. Projections of future atmospheric CO2 concentrations embracing both burning of fossil fuels and terrestrial sources have all been dominated by growth rates in fossil fuel emissions, except in cases where fossil fuel emissions are extremely low or in cases like that described by Woodwell (Chapter 3, Section 3.6), where all the world's forests are entirely destroyed in a few decades. While annual bio- *While the role of the biosphere may be marginal in projecting future emissions, it is, of course, important in calculating how the emissions are distributed among ultimate reservoirs.

l70 spheric emissions from human activities may average as high as l to 3 Gt of C per year in future decades, fossil fuel emissions are typically projected to be an order of magnitude larger. From a different per- spective, Schelling (Section 9.2.4) estimates that massive destruction or plantation of forests might accelerate or retard the growth of atmospheric CO2 to a particular level by a decade or so during the second half of the next century. 2.2.6 Projections of Non-CC^ Trace Gases Changes in atmospheric concentrations of several infrared absorbing gases besides CO2 may result from human activities (see Machta, Chapter 4, Section 4.3). These activities include the following: (a) Stratospheric flight. Increasing supersonic air traffic may lead to changes in the 03 and H2O content of the stratosphere. (b) Use of nitrogen fertilizers. Denitrification of fertilizers in the soil releases nitrous oxide (N;>0) to the atmosphere. Less sig- nificant increases in NH3 and HN03 may also result. (c) Use of chlorofluorocarbons (CFCs)—CCl2F2 and CCl3F—as refrigerants and propellants in aerosol spray cans, for example. (d) Extraction and burning of fossil fuels. Methane (CH4) may be released as a result of mining of coal and extraction of oil and gas. CH4 is also a conversion product of CO, and its presence is thus correlated with burning of fossil fuels. (e) Agricultural and livestock production. Increasing methane emissions may be associated with large livestock herds and expansion and intensification of rice production. Projections of future emissions of these non-CO2 trace gases are generally at a more primitive stage than are C02 projections.* Researchers studying biogeochemical cycles and the atmosphere typically have used simple assumptions of linear increase or exponential growth based on a short segment of recent years (see Flohn, l980, pp. 22-23). Wang et al. (l976), in a widely cited article, assumed that by 2020 stratospheric H2O, N^, and CH4 would all double and that the CFCs would increase by a factor of 20. Alternatively, projections may be extrapolated from more detailed studies, like the Climatic Impact Assessment Program (CIAP, l975), which developed scenarios of strato- spheric flight. The time horizons of the studies of stratospheric flight, agricultural production, industrial use of chemicals, and other activities vary, and the macroeconomic assumptions employed vary as well. There is a lack of studies of the combined greenhouse effect that use assumptions consistently in generating both C02 emissions *In addition to the references given in the text of this section, see Hameed et al. (l980), Lacis et al. (l98l), Logan et al. (l978), Ramanathan (l980), and Rowland and Molina (l975).

l7l and emissions of other infrared-absorbing trace gases. Given the very large inertia and modest rate of technological change in energy systems, projection of CO2 emissions over periods of 50 years and longer has large but manageable error bounds. In human activities—like use of CFCs or stratospheric flight—where more rapid technological change is occurring, and where less inertia is imposed by a large and expensive capital stock, projections extending many decades are much more hazardous. 2.2.7 Findings 2.2.7.l The State of the Art 2.2.7.l.l Recent Progress Few serious attempts at global long-range energy perspectives were undertaken before the l970s. There has been rapid methodological progress in methods of making energy and CO2 projections over the last decade. Much important work is a spinoff from energy analysis spurred by the l973 oil shock. With some exceptions, methods developed independent of CO2 studies in energy modeling, statistics, and econometrics should be adequate for the task of projecting future anthropogenic CO2 emissions, when brought together with knowledge from geology, engineering, and other relevant fields. 2.2.7.l.2 Nature of Modeling Exercises Modeling is a way of organizing thinking about a problem, one that should allow improved scrutiny of data, assumptions, and relationships. There is unlikely to be one "correct" approach to energy modeling for c°2 applications. The systems involved are too complex, too uncer- tain; questions we ask may differ; methodological improvements occur frequently. Moreover, there are cultural factors that influence forecasting. It is obvious to even a casual observer of the energy scene that there are deeply held and diverse views about energy futures, which are, after all, views of the character and relationship of man, nature, and society. Even if all could agree on a single model to use, we would certainly disagree on values for many variables. This is not merely a question of uncertainty; it is a question of coexisting contradictory certainties, points about which different groups and individuals hold highly assured but also highly different views. Historical fashions in forecasting may be equally significant. It would be myopic to think that the current set of projections is free of today's implicit assumptions or biases. One cannot help but notice the tendency in energy forecasting to extrapolate the most recent past, whether one of relatively rapid or slow growth, far into the future. When the price of electricity was going down in the l950s, people spoke of nuclear electricity becoming too cheap to meter; when the price of oil increased in the l970s, people spoke of a barrel rising to a price

l72 of $l00 or $200. The tendency of many forecasters to move in parallel (so that when one makes an upward or downward turn, all do) is also noteworthy. How historical trends and trendlines in forecasts should affect both choice of method and our interpretation of contemporary forecasts and the spread of forecasts remains to be explored further. Probabilistic approaches, like that of Nordhaus and Yohe (Section 2.l), are one natural response. However, in view of the fickleness of forecasts, it is clearly useful to encourage a variety of approaches: large and small; formal and informal; stochastic and deterministic. A pervasive question in research in CO2 and energy is how much disaggregation is useful for accurate predictions of future CO2 emissions. (A similar question arises, indeed, in climate modeling, where the question of the optimal level of refinement of spatial grid and time steps also occurs.) It is often assumed that more disaggrega- tion is better. Careful investigation of the issue shows, however, that no general result holds. The potential improvement from disag- gregation depends on the purposes of the study, the structure of microrelations, and the quality of the microdata. (See Grunfeld and Griliches, l960.) There are at least two possible reasons why disaggregation in CO2 projections might not produce more reliable estimates. First, disag- gregated data may be less reliable than aggregated data. This problem can lead to errors in variables and biased statistical estimates of microrelations. For example, we might have a good estimate of global energy production and, therefore, consumption but not of the distribu- tion of global consumption. Second, there may be interdependence across regions that would be taken into account in aggregate models but not in disaggregated models. An example is the constraint that the balance of trade of the world be zero (or the net oil imports of the world be zero). A pasting together of studies of individual countries would generally not respect the constraint. In both cases, it is possible that aggregate models could provide superior prediction to disaggregated models. 2.2.7.l.3 Assessment of Current Efforts The current modeling and knowledge of future C02 emissions appears marginally adequate today; we have a general idea of likely future trends and the range of uncertainty. It may be that further effort could increase the accuracy of our forecasts substantially. Given the large uncertainty that future energy growth and energy projections are contributing to the C02 issue, this area may well merit more research attention and support than it has received in the past. Future research efforts might be designed with four points in mind. l. In general, the most detailed and theoretically based projections of C02 have been a spillover from work in other areas, particularly energy studies. This fact suggests that continued support of energy modeling efforts will be of importance in further pushing out the frontier of knowledge about future CO2 emissions, as well as the interaction between possible CO2 controls and the economy.

l73 2. We have identified a serious deficiency in the support of long- run economic and energy models in the United States. There is not one U.S. long-range global energy or economic model that is being developed and constantly maintained, updated with documentation, and usable by a wide variety of groups. This shortcoming is in stark contrast to cli- mate or carbon cycle models, where several models receive long-term support, are periodically updated, and can be used by outside groups. Another striking contrast is with short-run economic models, which are too plentiful to enumerate. 3. The bulk of CO2 projections have been primitive from a method- ological point of view. Work on projecting CC^ emissions has not drawn sufficiently on existing work in statistics, econometrics, or decision theory. There has been little attention to uncertainties and probabilities. Also, considerable confusion of normative and positive approaches exists in modeling of CO2 emissions. 4. Application of models for analysis of policies where there are, for example, feedbacks to the economy from climatic change or CO2 control strategies is just beginning. Efforts to evaluate the effec- tiveness for CO2 control of energy policies of particular nations or groups of nations in a globally consistent framework have been lacking. 2.2.7.2 Likely Future Outcomes It is possible to synthesize past work to obtain a likely range of future CO2 emissions. Before doing so, it is important to reiterate the inhomogeneous character of the projections surveyed. Some studies, like those of Rotty, Perry and Landsberg, and Marchetti, seek to be best guesses or forecasts of future energy demand; others, like IIASA, posit scenarios, seek to fill out the descriptions, and avoid making claims about probability. Not only do the studies vary in intent, they are also of limited comparability in structure. The studies differ widely in levels of detail, time horizon, data base, and geographical aggregation. While projections of CO2 emissions may extend to the year 2l00, few energy studies offer detailed analysis beyond the year 2000, and fewer still offer detail past 2025 or 2030. The relative reliance on economic, engineering, and ecological logic varies. In addition, the studies are not independent. For example, researchers who participated in the IIASA work also participated in IEA and Interfutures research; both Lovins and IIASA rely on Keyfitz's population projections. 2.2.7.2.l Energy Growth Figure 2.22 summarizes the energy consumption forecasts to the year 2030. Projections of CO2 emissions are basically products of projections of energy demand and fuel mix. Projections of growth in energy use involve, more or less explicitly, assumptions or estimates concerning population growth, changes in per capita production of goods and ser- vices, and changes in the primary energy input required per unit of

l74 60 1 ^f Edmonds and Reilly (1983) / it Exxon (1980) / l l BO 0 NASA (1981) 1 A Nordhaus (1977) 1 • OECD-lncerfucures (1979) 1 ffl Perry and Landsberg (1977) / _ / n A D Roccy (1977) I A " 0 Rocty and Mar land (1980) / A / .t Scewarc (1981) / «i /' A P / 30 • World Energy Conference (1978) / / • Nordheusand Yohe (1983) / / 7* / rx! X Excrapolation of ' / ^. current levels cimes .' / 20 - 1X. 2%. 3%, 4X +• / / \ / fs + High projeccion ^^ ,' ^ '' - Low projection ^ Jr ^^** ^*^~~~*~~ ^.^ .— 10 f 1900 1920 1940 1960 1970-74 1980-82 2000 20 25-30 - 1 1 T \ i \_ ,1,1, . ,1 ! I 3% 1500 1200 900 600 300 YEAR FIGURE 2.22 Past and projected energy consumption. Historical data are for primary energy consumption, including noncommercial (Nakicenovic, l979; Schilling and Hildebrandt, l977; Putnam, l953). A similar figure with a different selection of estimates appears in Clark (l982). output. Table 2.2l shows assumptions and estimates that major groups have offered. As described earlier, particular assumptions, for example, high population growth in Perry and Landsberg (l977) or high GDP growth in Nordhaus (l977), explain much of the resulting projection of world energy consumption. While the sample of global, long-range energy projections is small and uneven and sporadically published, there is evidence of a reduction in projected rates of system growth over the past decade (Clark et al., in Clark, l982; Lovins et al., l982), perhaps spurred by the oil shock of l973. A survey of energy demand projections for the United States shows the lower rates of growth expected in a major study from the late l970s as opposed to studies in the mid-l970s (see Table 2.22). For example, the Rotty projections and even the perenially low projections of Lovins decline. There are several reasons offered for lowering projected rates of growth to levels considerably below the past few decades: a lowering of projected rates of population increase, an assumption that economic development in developing countries will not imitate the pattern of the developed countries, and a reversal in the historical trend toward

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l76 TABLE 2.22 U.S. Energy Demand Projections by Various Studies! Average Annual Popula- Average Rate of Total Energy tion at Annual Growth, in Final End of Growth, Consump- Year of Energy Period of Period GNP tion Projection Study Projection (millions) (%) (%) (quads) Ford Foundation^ l975-2000 Historical 265 3.02 3.4 l86.7 Technical fix 265 2.9l l.9 l24.0 Zero energy 265 2.92 l.l l00.0 growth Edison Electric l975-2000 Institute£ High 286 4.2 3.8 l79 Moderate 265 3.7 3.2 l55 Low 25l 2.3 l.6 l05 Exxon3- l977-l990 -^6 3.6 2.3 l08 Bureau of Minesi l974-2000 264 3.7 3.l l63.4 EPRI3. l975-2000 Basel ine^ 28l 3.4 3.37 l59 High electric ityi 28l 3.4 4.2l l96.l Conservation 28l 3.4 2.97 l45.6 Five tiroes prices 28l 3.4 l.98 l14.3 CONAES l975-20l0 12 279 2.0 -0.29 64 II2 279 2.0 0.45 83 III2 279 2.0 l.04 l02 IV2 279 2.0 l.95 l40 I3 279 3.0 0.52 85 II3 279 3.0 l.38 l15 III3 279 3.0 l.95 l40 IV3 279 3.0 2.82 l88 ^Source: National Academy of Sciences (l979). Energy in Transition, 1985-20l0, Final Report of the Committee on Nuclear and Alternative Energy Systems (CONAES). National Academy of Sciences, Washington, D.C. ^Source: Ford Foundation (l974). Energy Policy Project, A Time to Choose: America's Energy Future. Ballinger, Cambridge, Mass. ESource:Edison Electric Institute (l976). Economic Growth in the Future, Committee on Economic Growth, Pricing and Energy Use. Edison Electric Inst., New York. ^Source: Exxon Company, U.S.A. (l978). "Energy Outlook: 1978-l990." Available from Public Affairs Department, P.O. Box 2l80, Houston, Tex. 7700l. ±Not specified. ^Source: U.S. Bureau of Mines (l975). United States Energy Through the Year 2000, rev. ed. U.S. Govt. Printing Office, Washington, D.C. 3Source:Electric Power Research Institute, (l978). Demand '77: EPRI Annual Energy Forecasts and Consumption Model. EPRI (EA-62l-SR), Palo Alto, Calif. iwith restriction on the availability of natural gas. iwith no restrictions on the availability of natural gas.

l77 lower energy costs. These and other factors having to do with either the macroeconomic environment or the energy sector can be combined in various proportions to form a slower growth in the energy system. One additional component in declining energy supply and demand projections is probably the reduction in the projected role of nuclear energy. Figure 2.23 shows the steady lowering of projections made between l970 and l978 for l985 nuclear generating capacity in countries of the Organization for Economic Cooperation and Development (OECD) (CIA, l980). Of course, withdrawal of nuclear energy from the supply picture may mean substitution of other sources rather than a reduction in demand. It is interesting to note that none of the major energy-centered projections has estimated 4% per year energy demand growth beyond the year 2000. This contrasts with the 4.3% figure for growth in CO2 emissions that prevailed for a time in the carbon cycle and climate modeling literature. Most of the studies looking beyond 2000 project energy growth between about 2% and slightly above 3% per year. The absolute range of projections spreads strikingly as the time horizon is extended. For example, the range of the more detailed projections in the year 2000 is between about l4 TW yr/yr (IIASA low) and 2l TW yr/yr (OECD A), while the range in 2025 is between about 20 TW yr/yr (IIASA low) and about 40 TW yr/yr (Perry and Landsberg, Rotty), an increase from 7 to 20 TW yr/yr, almost tripling with one generation. In fact, in the case of the IIASA low and high scenarios (which are not even presented as lower and upper bounds), the divergence increases from about 3 TW yr/yr in 2000 to l3 TW yr/yr in 2030. While an individual or group may have a particular preference, the review of estimates shows no strong signs of convergence toward a single, widely accepted projection or set of assumptions. The analysis of Lovins et al. (l98l) suggests that the "hard" path of high-energy consumption is as far from the "soft" path of low-energy consumption as when the energy debate began l0 years ago. While there has been a trend downward during the last decade, it appears to be more a parallel movement of camps than a convergence (Ausubel, l982). 2.2.7.2.2 Fuel Mix While the balance between carbon and noncarbon fuels is obviously key to projection of CO2 emissions, it is one of the weak points of many studies. Only IIASA (l98l), Nordhaus (l979), and Edmonds and Reilly (l983c) make careful attempts to calculate the balance. Other studies are notably arbitrary in assigning fuel shares. Of course, the fuel mix is likely to have a high degree of intrinsic uncertainty. Over a period of 50 years or more, substantial substitution is possible. While we know there will still be a need for transportation or home heating, how it is accomplished will depend critically on the relative prices and availabilities of different fuels. Estimates for shares of nonfossil fuel 40 to 50 years hence range from l0% (Rotty, l978), to l3% (World Energy Conference), to 25% (Marchetti), to 30% (Edmonds and Reilly), to almost 35% in the IIASA low scenario. The Perry and Landsberg study, where a case of almost

l78 563 24 542 60 18 513 60 16 486 60 19 464 60 18 49 4O0 Thousand Megawatts 202 12 184 175 41 331 13 318 203 30 13 212 167 35 259 10 141 27 214 125 12 Other 107 18 Japan 84 Western Europe 277 2BO 260 204 165 180 147 145 115 100 United States 9-70 8-73 1-74 475 1275 2-76 8-76 1-77 12-77 12-78 Date o< OECD Projection FIGURE 2.23 OECD: Past projections of year-end l985 nuclear generating capacity. (Source: CIA, l980.)

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l80 TABLE 2.23 Some CO2 Emission Projections Derived from Long-Range Energy Projections Projections 2000 2020 2025 2030 2040 2050 IIASA (l98l) High scenario l0 l6 Low scenario 7.5 l0 Niehaus and Williams (l979) 50 TW high solar/nuclear l0 32 30 TW high solar/nuclear 8 2l 50 TW high fossil l3 30 35 30 TW low fossil ll 22 24 Rotty (l977) l2 26 Rotty and Marland (l980) 9 l4 Perry and Landsberg (l977) Coal 27 Renewables l3 Nordhaus (l977) l0.7 l8.3 40.l Marchetti (l980) 8 l4 l0 Edmonds and Reilly (l983a) 6.9 l2.3 26.3 Nordhaus and Yohe (this volume) 50th percentile 5 l0 l5 total reliance on coal is contrasted with a strategy where regional shortfalls in supply are met by an undefined noncarbon source, is also indicative. Here the fossil shares are 96% and 53%, respectively. In conjunction with discussion of fuel shares, one other prominent feature of long-range energy studies should be mentioned: it is assumed or calculated that virtually all easily accessible oil and gas will be consumed. While there is contention over rates of depletion, these sources are generally posited as too attractive to remain underground. (Marchetti, who foresees a phase out of oil before exhaustion of resources, and Lovins, who argues for reduced demand and renewable substitutes, demur.) Thus, in most studies the estimates of oil and gas resources form a minimum expected increase of atmospheric CO2; the degree of extraction of coal and shales determines how much further the atmospheric buildup of CO2 will rise.

l8l 2.2.7.2.3 CO2 Emissions Combining estimates of energy and fuel mix leads to projections of CO2 emissions. Figure 2.24 and Table 2.23 show CO2 projections derived from long-range energy projections. Average annual rates of increase in CO2 emissions to 2030 range from about l% to 3.5%. Estimated annual emissions range from the past studies between about 7 and l3 Gt of C in the year 2000 and, with a couple of exceptions, between about l0 and 30 Gt of C in 2030. 2.2.8 Conclusion Careful analysis of the economy, of energy, and of CO2 emissions is vital. Such efforts are a key to better understanding of how the future atmosphere will evolve and what the likely costs and benefits of alternative CO2 control or adaptation strategies will be. Consider- able progress has been made over the last decade in developing more reliable and theoretically grounded models. As in other aspects of the issue of climate change, in economic and energy modeling a strong fundamental research program is a prerequisite for responding in an agile way to the concerns of today and images of the next century. References Allen, E. L., C. Davison, R. Dougher, J. A. Edmonds, and J. Reilly (l98l). Global energy consumption and production in 2000. ORAU/IEA-8l-2(M). Institute for Energy Analysis, Oak Ridge, Tenn. Ausubel, J. H. (l982). Review of Least-Cost Energy: Solving the CO2 Problem by Lovins et al. (l982). Climatic Change 4:3l3-3l7. Baumgartner, A. (l979). Climatic variability and forestry. In Proceedings of the World Climate Conference. World Meteorological Organization, Geneva. Bolin, B. (l979). Climate and global ecology. In Proceedings of the World Climate Conference. World Meteorological Organization, Geneva. Central Intelligence Agency (CIA) (l980). OECD countries: prospects for nuclear power in the l980s. NFAC/OER/M/IE. Washington, D.C., ll July l980. Chan, Y.-H, J. Olson, and W. Emanuel (l980). Land use and energy scenarios affecting the global carbon cycle. Environ. Internat. .4:l89-206. Clark, W. C., ed. (l982). Carbon Dioxide Review: l982. Oxford U. Press, New York. Clark, W. C., K. H. Cook, G. Marland, A. M. Weinberg, R. M. Rotty, P. R. Bell, L. J. Allison, and C. L. Cooper (l982). The carbon dioxide question: a perspective for l982. In W. C. Clark, ed., Carbon Dioxide Review: l982. Oxford U. Press, New York. Climatic Impact Assessment Program (CIAP) (l975). The Effects of Stratospheric Pollution by Aircraft. U.S. Department of Transportation, Washington, D.C.

l82 Council on Environmental Quality (CEQ) (l98l) . Global energy futures and the carbon dioxide problem. CEQ, Washington, D.C. Edmonds, J. A., and J. M. Reilly (l983a). Global energy and CO2 to the year 2050. Institute for Energy Analysis, Oak Ridge, Tenn. Submitted to the Energy Journal. Edmonds, J. A., and J. M. Reilly (l983b). Global energy production and use to the year 2050. Energy 8:4l9-432. Edmonds, J. A., and J. M. Reilly (l983c). A long-term global energy- economic model of carbon dioxide release from fossil fuel use. Energy Econ. 5:74-88. Edmonds, J. A., J. M. Reilly, and R. Dougher (l98l). Determinants of Global Energy Demand to the Year 2050 (draft). Oak Ridge Associated Universities, Institute for Energy Analysis, Oak Ridge, Tenn. Exxon Corporation (l980). World Energy Outlook. Exxon Corp., New York, December. Flohn, H. (l980). Possible climatic consequences of a man-made global warming. RR-80-30. International Institute for Applied Systems Analysis, Laxenburg, Austria. Grunfeld, Y., and Z. Griliches (l960). Is aggregation necessarily bad? Rev. Econ. Stat., pp. l-l3, February. Hameed, S., R. D. Cess, and J. S. Hogan (l980). Response of the global climate to changes in atmospheric chemical composition due to fossil fuel burning. J. Geophys. Res. 85:7537. Hansen, J., D. Johnson, A. Lacis, S. Lebedeff, P. Lee, D. Rind, and G. Russell (l98l). Climatic impact of increasing atmospheric CO2. Science 2l3: 957-966. Interfutures Project (l979) . Facing the Future. Organization for Economic Cooperation and Development (OECD), Paris. International Institute for Applied Systems Analysis (IIASA) (l98l). Energy in a Finite World: A Global Systems Analysis. Ballinger, Cambridge, Mass. JASON (l979). The long term impact of atmospheric carbon dioxide on climate. Technical report JSR-78-07. SRI International, Arlington, Va. Kahn, H., W. Brown, and L. Martel (l976). The Next 200 Years. William Morrow, New York. Keeling, C. D. (l973). Industrial production of carbon dioxide from fossil fuels and limestone. Tellus 25:l74. Keeling, C. D., and R. B. Bacastow (l977). Impact of industrial gases on climate. In NRC Geophysics Study Committee, Energy and Climate. National Academy of Sciences, Washington, D.C. Lacis, A., J. Hansen, P. Lee, T. Mitchell, and S. Lebedeff (l98l). Greenhouse effect of trace gases, l970-l980. Geophys. Res. Lett. 8.:l035-l038. Legasov, V. A., and I. I. Kuz'min (l98l). The problem of energy production. Priroda(2). Logan, J. A., M. J. Prather, S. C. Wofsy, and M. B. McElroy (l978). Atmospheric chemistry: response to human influence. Trans. R. Soc. 290:l87. Lovins, A. B. (l980). Economically efficient energy futures. In Interactions of Energy and Climate, W. Bach, J. Pankrath, and J. Williams, eds. Reidel, Dordrecht, pp. l-3l.

l83 Lovins, A. B., L. H. Lovins, F. Krause, and W. Bach (l982). Least Cost Energy: Solving the CO? Problem. Brick House Publishing, Cambridge, Mass. Marchetti, C. (l980). On energy systems in historical perspective. International Institute for Applied Systems Analysis, Laxenburg, Austria. Marchetti, C., and N. Nakicenovic (l979). The dynamics of energy systems and the logistic substitution model. RR-79-l3. International Institute for Applied Systems Analysis, Laxenburg, Austria. Marland, G., and R. Rotty (l979). Atmospheric carbon dioxide: implications for world coal use. In Future Coal Supply for the World Energy Balance, M. Grenon, ed. Third IIASA Conference on Energy Resources, Nov. 28-Dec. 2, l977. Pergamon, Oxford, pp. 700-7l3. Nakicenovic, N. (l979). Software Package for the Logistic Substitution Model. Report RR-79-l2, International Institute for Applied Systems Analysis, Laxenburg, Austria. Niehaus, F. (l979). Carbon dioxide as a constraint for global energy scenarios. In Man's Impact on Climate, W. Bach, J. Pankrath, and W. Kellogg, eds. Elsevier, Amsterdam, pp. 285-297. Niehaus, F., and J. Williams (l979). Studies of different energy strategies in terms of their effects on the atmospheric CO2 concentration. J. Geophys. Res. 84:3l23-3l29. Nordhaus, W. D. (l977). Strategies for the control of carbon dioxide. Cowles Foundation Discussion Paper No. 443. Yale U., New Haven, Conn. Nordhaus, W. D. (l979). The Efficient Use of Energy Resources. Yale U. Press, New Haven, Conn. Nordhaus, W. D. (l980). Thinking about carbon dioxide: theoretical and empirical aspects of optimal control strategies. Cowles Foundation Discussion Paper No. 565. Yale U., New Haven, Conn. Nordhaus, W. D. (l982). How fast should we graze the global commons? Am. Boon. Rev. 72(2). NRC Geophysics Study Committee (l977). Energy and Climate. National Academy of Sciences, Washington, D.C. Perry, A. M. (l982). CO2 production scenarios: an assessment of alternative futures. In The Carbon Dioxide Review: l982, W. C. Clark, ed. Oxford U. Press, New York. Perry, A. M., K. J. Araj, W. Fulkerson, D. J. Rose, M. M. Miller, and R. M. Rotty (l982). Energy supply and demand implications of CO2. Energy 7:99l-l004. Perry, H., and H. H. Landsberg (l977). Projected world energy consumption. In NRC Geophysics Study Committee, Energy and Climate, National Academy of Sciences, Washington, D.C. Putnam, P. (l953). Energy in the Future. Van Nostrand, New York. Ramanathan, V. (l980). Climatic effects of anthropogenic trace gases. In Interactions of Energy and Climate, W. Bach, J. Pankrath, and J. Williams, eds. Reidel, Boston, Mass., pp. 269-280.

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