Coal transportation: An undervalued aspect of energy modeling?

Within the broad goals of modeling, the purpose, scope, spatial dimensionality and resolution, temporal dimensionality and resolution, and methodology are used to characterize energy models. Examples are provided for a number of intersecting model categories, including energy models developed by American geographers. The Pennsylvania Coal Model (PCM) illustrates some of the potentials and difficulties of energy modeling with a high degree of spatial and sectoral resolution. Development, applications, and limitations of the PCM are noted. Particular challenges to energy modeling are outlined.

Environmental-economic models for energy resource development

One of the major tools of spatial interaction analyses is, needless to say, the spatial equilibrium model developed from (1) the linear programming transportation problem by Hitchcock (1941), Kantorovich (1942) and Koopmans (1949), and (2) an analogue of Kirchhoff’s law of electric circuits by Enke (1951). Samuelson (1952) showed that the Enke problem could be converted into a mathematical programming model. In 1964 Takayama and Judge reformulated it into an operationally efficient concave quadratic programming model. Since then, there has been a proliferation of theoretical advances that improve and extend the basic linear programming transportation and spatial equilibrium models. These include their transformation into a new algorithm by Liew and Shim (1978) and Nagurney (1986); Thore’s formulation with income (1982); sensitivity analyses of model performance by Yang and Labys (1981, 1982), Irwin and Yang (1982), Chao and Friesz (1984), Daffermos and Nagurney (1984), and Tobin (1984, 1987); computational evaluations by Meister, Chen and Heady (1978), and Nagurney (1987b); iterative solution methods by Pang and Chan (1982), and Irwin and Yang (1982); a linear complementarity formulation by Uri (1976) and Takayama and Uri; sensitivity analysis of the complementarity problem by Tobin (1984) and Yang and Labys (1985); a sufficient condition for the complementarity problem by Smith (1984); a flow dependent spatial equilibrium problem by Smith and Friesz (1985); nonlinear complementarity models by Irwin and Yang (1983) and Friesz, et al. (1983); variational inequality solutions by Pang and Chang (1982), Daffermos (1983), Harker (1984), Tobin (1986) and Nagurney (1987a); a path dependent spatial equilibrium model by Harker (1986); transhipment and location selection problem by Tobin and Friesz (1983, 1984); and evaluations of the spatial equilibrium models and Maxwell-Boltzmann entropy models by Yang (1990). For the detailed description of the advances in the spatial equilibrium models, readers are referred to Labys, Takayama and Uri (1989) and Labys and Yang (1991).

Le Châtelier Principle and the Flow Sensitivity of Spatial Commodity Models

A spatial equilibrium model is used to quantify the effects of a severance tax on the Pennsylvania coal market. Two regions are identified: the Pennsylvania Market Area and an import/export region. The impacts on prices and quantities of coal supplied and demanded are found to be small. Little of the tax is exported from Pennsylvania, with a high proportion of the tax being passed back to Pennsylvania coal producers. Although the tax revenue exceeds the welfare losses in Pennsylvania, this result is very sensitive to the magnitude of the Pennsylvania own-price demand elasticity.

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T.C. Campbell

Papers

Spatial equilibrium in the US coal industry