Appraisal of the Supply Function Equilibrium Model

Abstract

There is an inconsistency in the SFE model since a firm is assumed to know rival firms’ aggregate supply function in order determine its own bid function. The paper reformulates the model so that a firm needs not know its rivals’ bid or even assume that they use the SFE model to construct its bid curve. In case of a duopoly the bid curve is the solution to one stand-alone second order differential equation for each firm.The paper also establishes the complete sufficient first and second order conditions for maximal profit, based on the “ex ante” expected profit as goal function using the Euler-Lagrange method.A general solution method is presented where the SFE system of differential equations is translated into a set of algebraic functions that can be solved by standard numerical methods.The paper applies the SFE model to sequential auctions with inventories and finds that the model does not function with sequential auctions.A method to ensure that firms submit monotonic bid functions is presented.