A compound note: Or, a note on Harry Johnson's note on the theory of transactions demand for cash

Abstract

In a recent note Harry Johnson observes that the Baumol-Tobin inventory model of the demand for money assumes the individual maximizes end-of-period wealth subject to a consumption constraint. Johnson argues that a better assumption is individual maximization of consumption subject to an end-ofperiod wealth constraint. He claims that this reversal of the role of objective and constraint functions gives rise to a different demand function for cash. In this note it is maintained that both assumptions are unduly restrictive. It is more consistent with standard consumer theory to assume the individual maximizes utility, a function of both consumption and end-of-period wealth, subject only to the constraint that his choice be attainable. This note is divided into two parts. In the first part (section 2) a generalized model of the transactions demand for money is described. By assuming extreme types of utility functions, both the Baumol-Tobin model and a corrected version of Johnson’s model fall out as special cases. In section 3 conditions are derived which utility functions over the consumption-end-of-period wealth space must satisfy in order for standard money demand relationships to obtain.