Spatial Equilibrium Models with Gams

This document gives a short introduction into Spatial Equilibrium modeling with GAMS. 1. Intertemporal-Spatial Price Equilibrium Solving spatial equilibrium models by mathematical programming is pioneered by [9],[12], [11], and [13]. One of the most basic forms is the transportation problem, also known as the “Koopmans-Hitchcock” model. An example is found in the GAMS model library in trnsport.gms. 2. Spatial Price Equilibrium Here we will develop a Spatial and Temporal Price and Allocation (STPA) model. We assume that a (linear) demand and supply curve is available [4]: dj = αj + βjpj si = γi + δiπi (1) with βj < 0, δi > 0. The indices i and j are used to denote supply and demand regions. p and π are demand and supply prices. Inverse formulations of the demand and supply equations are as follows: pj = ζj + ηjdj πi = θi + λisi (2) with ζj , θi, λi > 0 and ηj < 0. In addition we have standard constraints on supply and demand quantities with respect to transportation quantities xi,j ≥ 0: n ∑