On the Microtheoretic Foundations of Cagan’s Demand for Money Function

An extensive literature, both theoretical (see for instance, Bruno and Fischer (1990), Calvo and Leiderman (1992), Friedman (1971), Goldman (1974), Sargent and Wallace (1973)) and empirical, (see for instance, Aghevli and Khan (1977), Anderson, Bomberger, and Makinen (1988), Babcock and Makinen (1975), Cagan (1956), Christiano (1987), Easterly, Mauro, and Schmidt-Hebbel (1995), Engsted (1993), Metin and Maslu (1999), Michael, Nobay, and Peel (1994), Pickersgill (1968), Salemi and Sargent (1979), Taylor (1991)) has arisen around the special semi-logarithmic demand for money function introduced by Cagan (1956). Cagan’s motivation behind the demand for money function was mainly in terms of transactions costs and its relationship to the consumer’s ability to affect the real value of cash balances. Cagan argued that the real cost of holding cash balances fluctuates widely enough to account for the dramatic changes in the holding of cash balances observed during hyperinflation. He hypothesized that during periods of hyperinflation the demand for money is almost entirely explained by the variation in the expected rate of change in prices and that changes in expected inflation have the same effect on real balances in percentage terms regardless of the absolute amount of initial cash balances. In other words, during hyperinflations, the demand for money takes the special form: m = ke^{−λπ e}, where m is the real demand for money, π ^(e) is the expected rate of inflation and k, λ are positive constants.