Extended linear-homothetic preferences and the Cournot-Bertrand profit differential

This paper introduces the ‘extended linear-homothetic’ preferences to model consumer choice. Specifically, we extend Datta and Dixon’s (2000) ‘standard linear-homothetic’ preferences by adding an additional term to the unit cost function. This term captures the relative importance of price interactions within sectors on the unit cost of utility. In an economy composed of a large number of sectors (K) with a sufficiently large number of firms (n) in each, the ‘extended linear-homothetic’ preferences yield (perceived) linear demands in own strategy and competitors’ strategies - where goods are characterized as substitutes. Thus, the linearity and homotheticity properties of the preferences open the possibility to develop a tractable model of oligopoly in general equilibrium. An additional novelty introduced by the ‘extended linear-homothetic’ preferences is the presence of a sectoral-specific price index in product demand. For n small, this implies that firms internalize the sectoral price effects of their individual pricing strategies. The latter, we argue, may provide us with a link between nonatomistic price and wage setters and the monetary authority.