A Mathematical Approach To Demand Estimation In Multi-Segment Oligopoly Markets - With An Application To The Automobile Market

Abstract

The purpose of this paper is to develop a purely mathematical approach to determining consumer demand. The model developed allows the researcher to derive demand in an oligopoly market from observed firm output and market prices using only assumptions about each firm, modest restrictions on consumer behavior, and limitations on market structure. The advantage of this revealed demand approach is that it does not require the specification of the consumer’s utility function or any firm’s production function. In addition, this mathematical approach allows for the estimation of own price and cross price elasticities of demand without statistical regression.

The mathematical model developed is applied to the automobile industry assuming a market characterized by Cournot-Nash behavior and divided into five homogenous vehicle segments. A global optimization program is used to mathematically determine the range of values the coefficients of demand must take in each segment to satisfy market equilibrium. These coefficients can be used to estimate own and cross price elasticities of demand and construct demand equations.

The elasticity estimates generated by the mathematical model of the automobile industry are compared to other estimates of elasticity found by statistical estimation. It is shown that the mathematical model generates results that are consistent with the statistical methods of the automobile market used by other researchers.