Spatial Equilibrium, Imperfect Competition, and Calibrating Models

Abstract

Spatial models of trade among regions require a burdensome series of information: Commodity demand and supply functions for each region and bilateral unit transaction costs. Even when this formidable amount of information is available, the trade flow matrix resulting from the model solution is typically very different from the exchanged trade flow that was realized in a previous economic cycle. This discrepancy may be attributed to two sources: incorrect measurement of transaction costs and imprecise knowledge of demand and supply function parameters. To remedy the undesirable result, we assume that the matrix of bilateral trade exchanges is observed—by the researcher—together with the realized demand and supply prices. With this additional information, we discuss the calibration of three categories of spatial models—(a) cartel behavior on the supply and export markets: This model corresponds to monopsony and monopoly behavior; (b) Nash-Cournot behavior on the supply and export markets: This model corresponds to oligopsony and oligopoly behavior; (c) perfect competition on both markets. The calibrating approach presented in this contribution is in the spirit of positive mathematical programming and its prescription: To achieve satisfactory results, it is important to use all the available information. The empirical part of the contribution is divided into two sections. First, we use only the observed matrix of bilateral trade flows to reveal the necessary adjustments to the unit transaction costs and achieve a calibrating model. Second, the observed demand and supply prices are used to reveal the adjustments to the intercepts of the demand and supply functions that correspond to a more general calibrating model.