Homothetic or Cobb-Douglas Behavior Through Aggregation

Abstract

A common theme in the theory of demand aggregation is that market demand can acquire properties which are not always individually present among the agents who make up that market, a phenomenon we call heteroiosis in this paper. This paper focusses on the well known result that with a suitable distribution of demand behavior (arising perhaps from the underlying distribution of preferences), market demand can become an approximately linear function of income or even take on approximately Cobb-Douglas properties. We highlight the mathematical arguments underpinning these models and show that in the right context, it is possible to carry the arguments further and achieve exact, rather than just approximate, results: exact Cobb-Douglas market demand or exact linearity of market demand with respect to income.