The Welfare Cost of Inflation: A Critique of Bailey and Lucus

THE CONCEPT OF THE OPTIMAL MONEY STOCK The concept of the optimal stock of money introduced by Milton Friedman (1969) has stimulated much discussion and controversy. More recently, Lucas (1994) has provided new estimates of the welfare gain for the American economy from setting the optimal level of real cash balances. Before turning to a critique of Lucas, let us provide a rationale for this concept of optimality. To society, real balances are produced at zero marginal costs. To an individual, however, there is a cost to holding cash that bears no interest rather than bonds, which yield a money rate of interest. An individual would willingly incur this cost only if real balances produced services on the margin equal to the foregone interest. A lower interest rate reduces this cost and increases the total services provided by real cash balances. One estimate of the consumption the consumer would forego—to get this potential maximum gain from holding cash—is the area under the money demand schedule between the quantity of cash held at the lowest possible rate of interest (perhaps zero) and the smaller quantity that would be held at a higher interest rate.1 Clearly any measure of this gain depends on the particular demand schedule used. Lucas utilizes a double log schedule rather than the semi-log schedule used by Friedman (1969) and Martin Bailey (1956). The Lucas’ double log schedule yields greater welfare gains since the level of cash balances always increases as the interest rate approaches zero. In contrast, the semi-log schedule implies a finite level of cash is held at a zero nominal interest. In a later section we will provide a fuller discussion of these schedules.