UNCERTAINTY AND THE PRECAUTIONARY DEMAND FOR MONEY

THE TRANSACTIONS and precautionary demand for money have both played played an important role in economic literature. The relationship between them is complex and only recently have works appeared analyzing the specific role of each. In one of these articles, Sprenklel raised some novel questions for which answers are required. This paper discusses the Sprenkle work and indicates some of its shortcomings. More important, it constructs a realistic model and develops the implications of it. A number of issues must be faced prior to the construction of an appropriate model of the demand for money. First, the correct dimension with which one measures profits, cash flow, and so forth must be determined. It is argued below that these must be considered in general for a fixed time period. Next one must consider the real economic meaning of precautionary versus transactions balances. An addition to the precautionary balance may be defined as that additional cash balance arising from an increased degree of uncertainty with other things remaining unchanged. The economic meaning of leaving other things unchanged when the degree of certainty is changed is not self-evident; although many formal constructions are possible the choice of the correct one is difficult. Following the discussion of these issues, a model of cash balances is developed which is superior to the previous work. In particular, we show that Sprenkle's model is unsatisfactory because it considers a probability distribution on a misleading variable, considers profits and losses for varying, rather than fixed, time periods, uses an inappropriate definition of a transactions balance, and never determines the crucial variable-the average balance. Let us first consider the dimensionality problem by looking at a businessman who purchases a stock of identical items and then sells them. We assume that the rate of sale is invariant but unknown, and therefore the time until they are all sold is uncertain. In addition we assume that no other profit making activity may commence until this one is concluded. The businessman's problem is to act in such a way as to maximize his expected profits. The dimensionality question, which applies to cash balances as well as to goods, asks whether he should maximize profits per unit time, profits for the sale of his entire stock of goods, or profits measured in some other dimension. Clearly these choices are different and will lead to different solutions. With a fixed time period, the quantity sold will differ in repeated realizations of the process -and with fixed quantity the time period to sell them will vary. The key to the correct choice, we believe, lies in the opportunity cost associated with the passage of time and the requirement that no other activity be undertaken. Clearly the businessman wishes to maximize discounted profits over the firm's life. The passage of time increases the discount factor applied to all future actions and is therefore costly. If the businessman maximizes profits over the sale of his entire stock of goods, he fails to include varying time related opportunity costs and reaches erroneous conclusions. This same principle clearly should apply to the determination of profit or loss from holding a cash balance. This is true because no additional profit from the cash balance