A Random Utility Model of Demand for Variety under Spatial Differentiation

This paper studies a linear random utility model of demand for variety under spatial product differentiation. A motivation is given by previous work establishing a connection between the demand generated by linear random utility and CES demand. Two interpretations of the random utility model are considered. First, the utility of a representative consumer from a given variety is assumed to be random e.g. due to a random linear trade cost or unobservable quality. In the second interpretation the uncertainty is due to the incomplete information of the modeller regarding the utility parameters. The demand system implied by stochastic utility maximization has some resemblance with a CES demand system. An application of the demand for variety model to new economic geography is discussed. The approach to stochastic utility is based on maximizing linear random utility functions via probabilistic constraints. The main focus is on the case where the random utility/cost parameters are i.i.d. normal random variables. In economic geography linear random utility implies aggregate demand for variety and can explain intra-industry trade between symmetric regions. 1