THE SYMMETRIC AND ASYMMETRIC CASH BALANCE MODEL OF MILLER AND ORR WITH FIXED AND VARIABLE TRANSFER COSTS DEPENDENT ON THE DIRECTION OF TRANSFER*

Abstract

THE PAPER extends the three parameter stochastic Miller and Orr cash balance model to admit a generalized linear transfer cost function in the cases of symmetric, asymmetric, and extreme asymmetric probability distributions of cash flows. Cash balance policies with optimal properties are developed for the fixed and variable cost symmetric models where transfer costs are permitted to differ depending on whether transfers are made from securities to cash or vice versa. The full transfer cost models are analytically intractable and solutions are obtained using numerical procedures in specific cases. Sufficient conditions for optimality are established for all symmetric models. The asymmetric cash balance models are developed, but analytical intractability precluded satisfaction of sufficient conditions for optimality and the development of closed form expressions for policies with optimal properties. Numerical procedures are applied to determine the regularity of the expected cost functions. Some conclusions can be drawn from sensitivity studies. Thesedemonstrate the relationships between these and the symmetric-extreme asymmetric models. The models admit a variety of policy implications for cash management and for the behavior of cash economizing economic entities. These implications depend on the character of the probability distribution of cash flows and the nature and magnitude of the transfer cost functions. A variety of interest rate elasticities of the demand for cash balances are obtained. Elasticities are higher when cash flows are asymmetric (asynchronous). This indicates that monetary policy may be more effective during cyclical swings than at any other time. Large firms may be somewhat unaffected by these circumstances in so far as they are able to synchronize cash flows with sophisticated cash management techniques, greater credit availability, and operational diversification. These implications are consistent with the variety of interest rate elasticity results found in empirical studies of money demand and in the declining liquidity ratios of manufacturing firms.