ABSTRACT
The holding of money involves the cost of foregoing the interest that other assets would earn; and this cost increases (usually in proportion) with the size of money holdings. In addition, the acquiring of money preliminary to spending it also involves a cost-the brokerage fee, commission, and bother of selling earning assets and so converting them into money. This cost depends largely on the frequency with which such conversions are made and so diminishes with the size of one's money holdings. If a person's annual volume of payments is T, and the sum he customarily converts from earning assets into money is C, then the number of such conversions is TIC and their annual cost is '[; (b + kC)-assuming the cost of each conversion to be a linear fuction (b + kC) of the sum converted. The average size of this person's money holding is ~, and the annual interest foregone on it is i~, where i is the market rate of interest. His total annual cost therefore of holding money is
K = ~ (b + kC) + i; . By equating to zero the derivative of this function with respect to C, Baumol obtains the value of C that minimizes the total cost of holding money:
C = ¥2~T This result is familiar from inventory analysis where it has also been borne out empirically; and it suggests that the demand for holding money increases in proportion, not with the volume of transactions, but with its square root.
