554 PA R T V I I Monetary Theory Equation tells us that because k is a constant, the level of transactions generated by a fixed level of nominal income PY determines the quantity of money Md that people demand Therefore, Fisher s quantity theory of money suggests that the demand for money is purely a function of income, and interest rates have no effect on the demand for money.3 Fisher came to this conclusion because he believed that people hold money only to conduct transactions and have no freedom of action in terms of the amount they want to hold The demand for money is determined (1) by the level of transactions generated by the level of nominal income PY and (2) by the institutions in the economy that affect the way people conduct transactions that determine velocity and hence k APP LI CAT IO N Testable Theoretical Implications of the Quantity Theory of Money Demand A convenient linearization of Equation is achieved if we write it in logarithmic form as (ignoring the d superscript here) log M = log k + log 1PY log P log Y , = (3-A) where a log k Using Equation 3-A, we can clearly see the testable theoretical implications of the quantity theory of money demand In particular, Equation 3-A implies that the price level elasticity of the demand for nominal money balances, denoted h (M, P), is d log M = 1, d log P and that the real income elasticity of the demand for real money balances, denoted h (M/P, Y), is d log (M/P) M h a , Yb = = P d log Y Equation 3-A also suggests that the demand for money is purely a function of income and that interest rates have no effect on the demand for money In other words, the (nominal) interest rate elasticity of the demand for real money balances, denoted h (M/P, i), is d log (M/P) M = h a , ib = P d log i These are the testable theoretical implications of the quantity theory of money demand.* h1M, P2 = * Regarding the testable implications of some of the other money demand theories discussed in this chapter, see Apostolos Serletis, The Demand for Money: Theoretical and Empirical Approaches (Springer, 2007) While Fisher was developing his quantity theory approach to the demand for money, a group of classical economists in Cambridge, England, came to similar conclusions, although with slightly different reasoning They derived Equation by recognizing that two properties of money motivate people to hold it: its utility both as a medium of exchange and as a store of wealth