Kreps & Scheinkman with Product Differentiation

Kreps and Scheinkman (1983)’s celebrated result is that in a two-stage model of a market with homogeneous products in which firms noncooperatively pick capacities in the first stage and set prices in the second stage, the equilibrium outcome is that of a one-shot Cournot game. This note derives capacity best response functions for the first stage and extends the Kreps and Scheinkman result to the case of differentiated products.