addressed the questions of gradual climate change. Recently, a few researchers have investigated the impact of threshold events, such as a weakening and eventual shutdown of the North Atlantic thermohaline circulation (for shorthand, such events are called thermohaline circulation collapse or THCC). One set of studies has examined “inverse” analyses in which emissions trajectories were constructed that would keep greenhouse gas accumulations away from the threshold at which a THCC would occur (Toth, 2000). A further set of studies examined policies that would keep climate short of a “catastrophic” threshold (Nordhaus, 1994; Nordhaus and Boyer, 2000).

One recent set of studies (Keller, 2000; Keller et al., 2001) is particularly relevant because it shows that threshold effects can have surprising impacts on efficient economic policies. These studies begin with the dynamic integrated model of climate and the economy model of climate change (Nordhaus, 1994; Nordhaus and Boyer, 2000) and introduce an ocean-circulation model that allows for a THCC. They assume that the THCC was essentially irreversible and would impose a large economic penalty (either in the sense of actual economic losses or in the sense of a large willingness to pay to prevent the THCC). They then couple the dynamic integrated model of climate and the economy model of climate change with their ocean circulation model to investigate the efficient economic policy. An “efficient” policy is one that minimizes the net economic impact or maximizes net incomes when taking into account both the damages from climate change as well as the costs of slowing climate change.

Figure 5.10 shows the result of the Keller et al. (2001) calculations. This shows the abatement rate (measured as a percent of baseline emissions reduced) as a function of time on the horizontal axis and the damage on the vertical axis. Low abatement rates occur early and for low THCC costs, while high abatement rates occur in later periods and for high THCC costs. Two features of the result are worth noting. First, the abatement rate or carbon tax is relatively insensitive to the cost of the THCC for the first half of the twenty-first century. The reason is that it is economically advantageous to postpone costly abatement because of such factors as discounting due to the productivity of investments or because society might discover an economical low-carbon fuel. A second and surprising result occurs for damage cost in the range of 0.5 to 1.5 percent of gross world product. For this region, abatement rises rapidly until around 2100 and then actually declines. The reason is that the early high abatement delays the THCC for a few years and thereby postpones the costs; however, once reversal has oc-

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