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Theory of Consumer Behavior When Prices Enter the Utility Function

Peter Jason Kalman

Abstract

In this paper, an extension of the theory of consumer behavior to cover situations when prices enter the utility function is considered. In Section 1 we formulate the problem. In Section 2 we derive a generalized Slutsky equation of which the traditional Slutsky equation is a special case. We investigate the class of utility functions that yield homogeneous of degree zero in prices and income demand functions and also see that these can't exist for a certain class of utility functions. We then establish theorems on "substitutable" and "complementary" commodities which are not, in general, valid for the traditional theory. Finally, a set of qualitative restrictions on demand functions is deduced, of which a subset is identical to the traditional restrictions.