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Appendix A Spatial Equilibrium Models and the U.S. Grain Sector The ESSENCE Model The amount of grain that will be transported by towboats on the Upper Mississippi River-Illinois Waterway (UMR-IWW) in future years depends on many factors, including the following: the amount of grain grown in the river basin area, which depends on the cost of growing grains and alternative commodities compared to the price at which grains and alternative commodities can be sold, since the land could be used for other crops or left fallow; the amount of grain grown in other areas of the world, particularly Brazil and Argentina, and the price at which it is offered for export; the world demand for grain, particularly the demand for imported grain In each nation, which depends on population, income, home agricul- tural output, tastes, and the world price of meat for importation; . . . . 1mnortln~ nort: the price of transporting grain from each exporting port to each --r ~ --I r---7 the price of transporting grain from each growing area to each ex- porting port; 39

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40 port; ~ppend~c~ the domestic demand for grain, including raising animals for ex- the current logistic and transportation prices to transport U.S. grain from multiple origins to relevant domestic markets; . prices of grain at relevant export and domestic markets; and the use of current railroad shipping rates, rather than rates from old railroad tariffs or estimated costs from rail cost models. Only after determining the effects of these (and perhaps other) factors can future demand for grain transport on the UMR-IWW be credibly estimated. The Phase I committee recommended that the ESSENCE model not be used in the feasibility study. This model includes a traffic routing com- ponent and a simple reduced form economic model for estimating the ef- fect of shipping cost on barge movements. ESSENCE is not a spatial equi- librium model. It does not allow for alternative export ports or alternative destinations for the grain. It is silent on most of the factors noted above that are part of a full spatial equilibrium model. Furthermore, the portion of the model used to determine the impact of shipping cost is seriously mis- specif~ed. This model should not be criticized because it is simple since simple models can be useful if they describe historical experience well and if their implications are plausible. The Phase I committee noted that this model was never fit to historical data, so this simplification cannot be justified on the basis of being a good description of current data. Furthermore, the shipping demand curve used in ESSENCE is defined by a single parameter N. The implications of the model are implausible when N is outside a nar- row range. For example, N is characterized by the Corps as describing the price elasticity of barge rates. This is not correct. Price elasticity is not con- stant for a fixed value of N. The relationships embodied in ESSENCE would not fit historical data well because they do not account for the level of foreign demand, competi- tion with foreign grain, U.S. domestic demand, or other important factors. The Corps should thus abandon this model, including any reference to val- ues of N as lower or upper bounds. The Corps should not to spend time and effort fitting this model to historical data. Even if the model fit histori-

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~ppend~c~ 41 cal data well, it would not serve as a building block in implementing a full spatial equilibrium model. Spatial Equilibrium Models The rationale underpinning the spatial equilibrium concept was stated in 1951 as follows: two or more regions with demand and supply functions produce and consume a homogeneous product and are separated by a known transfer cost. Given this information, the problem is to determine the equilibrium levels of production, consumption, and prices in each re- gion and the equilibrium trade flows between regions (Enke, 1951~. A geo- metric interpretation of this problem and its solution for two regions was later developed (Samuelson, 1956), and Takayama and fudge (1971) showed how the problem could be formulated as a mathematical programming problem involving any number of regions. Numerous spatial equilibrium models of the U.S. crop sector have been developed to address issues relating to interregional trade and agricultural policy, while others have featured considerable transportation system detail for purposes of evaluating transportation policy and infrastructure issues. These models feature regional demand and supply relationships and linking transfer costs and are capable of examining the effect of transportation in- frastructure improvements or policies on commodity prices, production, trade, and welfare measures. A study (Fuller et al., 2000) that employed spatial price equilibrium models to determine the effect of Panama Canal closure and alternative toll levels on U.S. agriculture may be of interest to the Corps as it proceeds with the UMR-IWW feasibility study. This analysis of Panama Canal transporta- tion demand showed that increases in toll rates would reduce grain exports via the U.S. Gulf of Mexico ports, reduce grain flow on the Upper Missis- sippi and Illinois Rivers and lower regional grain prices, increase exports via U.S. Pacific Northwest ports and rail movements to these ports, reduce quantities transiting the Panama Canal, and increase maritime movements to East Asia via Africa's Cape of Good Hope. Further, the U.S. role in the Asian corn and soybean markets would decline, while competitors' roles (Argentina, China) would increase. Analyses indicated that the Panama Ca- nal had a value to U.S. corn and soybean producers of about $300 million per year. (These models are executed on desktop computers with 256 MB

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42 ~ppend~c~ RAM and CPU of 1.3 GHz tPentium 4] in about 20 minutes.) Although the model is not a perfect analogue for evaluating all issues related to lock con- gestion on the Upper Mississippi and Illinois Rivers, it is a fully developed model that incorporates many elements of a full spatial equilibrium model, and it merits investigation by the Corps for its relevance to the UMR-IWW feasibility study. Existing corn and soybean market models are spatial, intertemporal equilibrium models that include the domestic and international sectors (see Fellin and Fuller, 1997; Fuller et al., 1999; Koo, 1985; and Martin, 1981~. These models include details on regional excess demands and supplies and on transportation, storage, and grain handling costs in the United States. Other trading countries, excluding Mexico, are treated as either an excess supply or an excess demand region. Mexico includes excess demand and supply regions, and linking transportation costs with grain handling and storage costs. The international corn model includes 78 excess supply regions and 99 excess demand regions. The excess corn demand regions include 64 U.S. regions, 8 Mexican regions, and 6 foreign regions. Included among the ex- cess corn demand regions are 60 U.S. regions, 14 Mexican regions, and 24 foreign demand regions. With the exception of Japan, South Korea, China, Canada, and Taiwan, the foreign excess demand regions are an aggregation of countries. The international soybean model includes 80 excess supply regions and 58 excess demand regions. Of the excess supply regions, 68 are located in the United States, 8 in Mexico, and 4 foreign supply regions that represent Argentina, Brazil, Paraguay, and Bolivia. The excess soybean de- mand regions include 24 U.S. regions, 9 Mexican regions, and 24 foreign excess demand regions. Embedded in the United States and Mexico portions of the models are extensive transportation networks that connect excess supply regions with excess demand regions and ports via truck, rail, and barge costs or rates. Excess supply regions are linked by truck and rail to 37 barge-loading facili- ties on the inland waterway system. The barge loading sites are linked to barge unloading sites on the U.S. inland waterway system and ports as ap- propriate. Of the U.S. ports, 17 receive corn and soybeans from excess supply regions via truck, rail, and barge as appropriate and then ship via maritime costs or rates to a representative port in each of the 24 foreign excess demand regions.

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~ppend~c~ 43 To represent winter freezing of the Great Lakes and Upper Mississippi waterways, the models disallow shipping via these arteries in the winter quarter. The models include four quarters. An excess supply region is rep- resented by an inverse excess supply equation, while an excess demand re- gion is represented by four (quarterly) inverse demands. Grain is produced in the fall quarter and carried through the subsequent crop year by the cost of storage. Excess supply regions are typically crop-reporting districts that include from 10 to 15 counties. As an example, in Iowa there are eight ex- cess supply regions and one excess demand region. The typical excess sup- ply region in Iowa is linked to 3 barge-loading sites (2 on the Mississippi River and 1 on the Missouri River); 28 domestic excess demand regions; 8 port areas (Chicago, Duluth, Mobile, New Orleans, Galveston, San Diego, Portland, and Seattle); and a U.S.-Mexico border-crossing site (Laredo) by truck and rail costs as appropriate. In addition, the model's barge-loading sites are linked by barge costs or rates to inland barge-unloading sites and selected U.S. port areas. Barge rates reflect seasonality, but from St. Paul, Peoria, and St. Louis to the Lower Mississippi River, ports average about $9.50, $7.30, and $5.40 per ton. U.S. ports are linked to 24 foreign excess demand regions by ship rates, and U.S.-Mexico border crossing sites are linked to 14 Mexican excess demand regions by Mexican rail rates. Further, foreign excess supply regions are linked to the 24 foreign excess demand regions by ship rates. REFERENCES Enke, S. 1951. Equilibrium among spatially separated markets: Solutions by electric analogue. Econometrica 19:40-48. Fellin, L., and S. Fuller. 1997. Effect of the proposed waterway user tax on U.S. grain flow patterns and producers. Journal of the Transporta- tion Research Forum, 36:11-25. Fuller, S., L. Fellin, and W. Grant. 1999. Grain transportation capacity of the Upper Mississippi and Illinois Rivers: A spatial analysis. [our- nal of the Transportation Research Forum 38:38-54. Fuller, S., L. Fellin, and K. Eriksen. 2000. Panama Canal: How critical to U.S. grain exports? Agribusiness: An International Journal 16~4~:435-455.

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44 ~ppend~c~ Koo, W. 1985. Tariffs and Transportation Costs and U.S. Wheat Exports: A Quadratic Programming Model in Transportation Models for Agricultural Products, W. Koo and D. L. Larson, eds. Boulder, CO: Westview Press. Martin, L. 1981. Quadratic single and multiple-commodity models of spa- tial equilibrium: A simplified exposition. Canadian Journal of Agri- cultural Economics 29:21-48. Samuelson, P. 1956. Spatial price equilibrium and linear programming. American Economic Review 38:496-509. Takayama, T., and G. fudge. 1971. Spatial and Temporal Price and Alloca- tion Models. Amsterdam: North Holland Publishing Company.