A Didactic Note on the Transactions Demand for Money and Behavior Towards Risk: Note

Abstract

There is an unsatisfactory dichotomy in much of the literature on the demand for money between the portfolio theoretic approach, which emphasizes risky asset returns but ignores transaction costs [9] and the inventory theoretic approach, which emphasizes transaction costs but ignores risky asset returns [2] 1 This dichotomy tends to be felt particularly keenly by those teaching or taking a first course in monetary theory. After the square root rule has been derived to deal with the transactions demand for money and mean-variance analysis has been applied to the portolio demand for money, it is never quite clear what the total demand for money is. Should one add the two? Does the portfolio holder consider his transactions balances to be part of the total portfolio that is to be allocated over an array of assets with different kinds and degrees of risk ? This note demonstrates that this dichotomy is not only unsatisfactory, but also unnecessary. Without any additional technical or conceptual requirements, the inventory approach and the portfolio approach can be integrated. The simple case worked out in this paper recasts Baumol's inventory theoretic approach to the demand for money in a form that permits the application of mean-variance analysis.2 The opportunity locus in risk-return (i.e., standard deviation of return-mean return) space is derived. The stochastic analogue of Baumol's square root rule is the point where mean return is maximized. An economic agent with upward-sloping convex indiSerence curves in risk-return space will always hold more money balances than the maximum mean return