Optimal Spending and Money Holdings in the Presence of Liquidity Constraints

MANY PROBLEMS IN MACROECONOMICS, both of closed and open economies, are analyzed by means of expenditure and money demand functions. The properties of these functions play a major role in the derivation of results in these investigations. Although specifiers of such functions have in mind optimizing behavior by economic agents, explicit derivation of their properties from optimizing behavior is seldom undertaken. In many cases in which they are undertaken, it is assumed that utility depends on real money balance (e.g. 2), an assumption which many find undesirable. There have been recently attempts to deal with macroeconomic issues by explicitly modeling the role of money in the economy thus avoiding the need to model it as an argument of the utility function-and by explicitly using optimizing behavior of economic agents (e.g. 3,5,6). However, in those cases either the expenditure and money demand functions were characterized for steady states (e.g. 5,6), or they were not derived because they were not required 3. In this paper I derive an expenditure and a money demand function which arise from a problem of optimal allocation of consumption over time in which all payments are made in the form of money, there are liquidity constraints, and money is the only asset. Utility is derived only from consumption. These functions can be used to investigate macroeconomic problems as demonstrated