Baumol and Tobin 1 applied the principle of profit maximization to the management of money balances. Under fairly restrictive assumptions they obtained the conclusion that the income elasticity of the transactions demand for money should be plus one half and the interest elasticity minus one half. The hypothesis is not directly testable because estimates of the transactions demand for money are not available. However, tests using the total demand for money do not support the Baumol-Tobin (BT) elasticities. We show that if profit maximization is assumed and more general assumptions employed the only restriction is that the interest elasticity of the total demand for money is between zero and minus one. This finding offers theoretical justification for many previously published statistical results. A very primitive theory of the demand for money may be obtained by assuming that income is distributed at the beginning of each month and that the individual spends it (all) evenly in the course of the month. The only money he holds is the as yet unspent balance. This model implies that the demand for money is proportionate to income. In the 1950's, BT demonstrated that these money balances would be interest responsive because some individuals would find it profitable to switch their funds from money into interest-earning assets at the beginning of the month and back into money when the expendiitures had to be made later in the month. The profit maximizing economic unit was to compare the marginal interest earned from making an additional switch to the marginal cost of making that switch. Let r represent the interest rate on risk-free wealth. Then the gross revenue (R) from any allocation of wealth (W) between money, (M), defined as demand deposits plus currency, and other assets is R = r(W-M). (1) In the simplest version of their model they assumed that -the cost of making each switch was a constant, which we call b. Therefore, the total cost (C) of T money-bond (or bond-money) conversions would be C = bT. (2)