On Parametrization in Modelling Behavioral Heterogeneity.

In order to model the concept of behavioral heterogeneity, some authors have employed the following approach. By using affine transformations of the price space, a consumption sector is defined as the set of all transformed demand functions of a given "generating" demand function. This leads to a parametrization of the objects by elements of a finite dimensional Euclidian space. Increasing dispersedness of the parameter distribution is then interpreted as increasing behavioral heterogeneity of the consumption sector. In this paper, we show that such an interpretation is not valid if the generating demand function satisfies a mild regularity condition. Due to the specific parametrization, increasing heterogeneity of the parameters leads to decreasing heterogeneity of the demand functions. More precisely, we prove that they become concentrated nearby a finite set of Cobb-Douglas demand functioons.