Optimal Spending and Money Holdings in the Presence of Liquidity Constraints and Random Income Fluctuations

We examine the optimal spending behavior and money holdings of a risk averse individual who faces liquidity constraints and random fluctuations in his money income. Because of a cash-in-advance constraint, the individual has a well-defined transactions requirement for money balances. In addition, because money income is uncertain and money is — by assumption — the only available store of value, the risk averse individual also holds money balances as an inventory which can be drawn down in periods of unexpectedly low earnings. We establish the strict monotonicity properties of optimal expenditure and money demand decisions and show that the average propensity to consume is directly related to expected income. We show that, in the presence of random income fluctuations, the risk averse individual has a unique target level of money balances which depends directly on the dispersion of the probability distribution which governs these fluctuations. We also establish the existence, continuity, and monotonicity properties of the unique stationary probability distributions which characterize the behavior of optimal money holdings and beginning-of-period money balances in a stochastic steady-state. In particular, the stationary distribution which characterizes optimal money holdings is shown to be almost-everywhere continuous and strictly increasing with a single mass point at zero.