Concepts and Properties of Substitute Goods

Paul Milgrom
Stanford University, USA

Bruno Strulovici
Nuffield College, Oxford


Abstract
 

We distinguish two notions of substitutes for discrete inputs of a firm.
Class substitutes are defined assuming that units of a given input have the 
same price while unitary substitutes treat each unit as a distinct input with 
its own price. Unitary substitutes is necessary and sufficient for such results
as the robust existence of equilibrium, the robust inclusion of the Vickrey
outcome in the core, and the law of aggregate demand, while the class 
substitutes condition is necessary and sufficient for robust monotonicity of 
certain auction/tatonnement processes. We analyze the concept of pseudo-equilibrium 
which extends, and in some sense approximates, the concept of equilibrium when 
no equilibrium exists. We characterize unitary substitutes as class substitutes 
plus two other properties. We extend the analysis to divisible inputs, with a 
particular focus on robustness of the concepts and their relation to the 
generalized law of aggregate demand.