Capturing Direct and Cross Price Effects in a Differentiated Products Duopoly Model

We show that a frequently used direct demand system with product differentiation in a duopoly market generates unexpected effects of increasing the substitutability of firms’ products on prices, outputs, profits and welfare. Using the original demand system introduced by Bowley (The Mathematical Groundwork of Economics, Oxford, Oxford University Press, 1924) as a reference, we argue that this alternative model does not capture a consumer's taste for variety. Moreover, we demonstrate that positive values for the parameter which represents cross-price effects in the alternative demand system corresponds to the regime of complementary products in the original Bowley model. As a consequence, for increasing values of this parameter—meant to capture increasing competition in the usual sense—prices do not converge towards marginal costs and profits do not vanish. Finally, we study a duopoly with international transfer pricing and demonstrate that conflicting policy conclusions are derived depending on which of the models is used to capture demand.