In his celebrated book, Money, Interest and Prices, Professor Patinkin took the position that an individual's demand for nominal balances was not homogeneous of the first degree in the absolute level of prices. His analysis, based on concepts of inferiority and superiority with respect to real cash balances, failed to distinguish between short-period transition and long-period equilibrium. For this failure, Patinkin was taken to task by Archibald and Lipsey, who, while accepting Patinkin's assumptions, showed that as between alternative positions of long-period equilibrium when the actual stock of real balances is equal to the desired stock, a doubling of the price level does, in fact, double the nominal quantity of cash balances demanded, thereby validating the classical position.
My primary purpose is to show that it is unnecessary to assume, as do Patinkin and his critics, a unique relation between the desired stock of balances and the flow of commodities. This stock-flow equilibrium should not be assumed, but rather can be deduced, as is done in capital theory, from initial assumptions. Indeed, the accumulation of cash balances to attain a long-run equilibrium level is properly treated as an aspect of the theory of capital accumulation. Specifically, if we assume that real cash balances have positive carrying costs and that the rate of time preference is zero, we can show that an individual in long-run equilibrium will hold the satiety level of cash balances and that the equilibrium is unique and stable.