Theoretical Elements of the Quantity Theory of Money

For Friedman, money is a substitute for bonds, stocks, and commodities, and the demand for money is a function of the expected return on wealth and other assets owned by individuals relative to money. Accordingly, Friedman defined his money demand formula as follows: MD/P=f(Ypη-RmRe-Rm,πe-Rm). where MD/P denotes the demand for real money balances; Yp denotes permanent income, the theoretical discounted value of all expected future income, which can also be the long-run average income; ae/aix=ad/aix-as/aix denotes the expected rate of return on money; re denotes the expected rate of return on bonds; η denotes the expected rate of return on stocks; and πe denotes the expected rate of inflation. In Friedman's view, the demand for money depends primarily on total wealth, but total wealth is practically unmeasurable and can only be replaced by permanent income rather than by unstable current income. For Yp, which is permanent income, the demand for money generally increases as income increases, i.e., as wealth increases. According to Friedman, people's permanent income is stable, it is the average expected value of people's income in the long run, and in the expansionary phase of the business cycle, people's temporary income is greater than their permanent income. The magnitude of income changes is on average relatively stable and tends to permanent income, i.e. permanent income is stable. Friedman's permanent income is composed of non-human and human wealth. Permanent income plays a dominant role in Friedman's money function, and in Keynes's consumption function, consumption is a function of current income and illustrates underconsumption and short-term economic fluctuations with the law of diminishing marginal propensity to consume, the relationship between incremental consumer spending and incremental current income. In contrast, according to the permanent income hypothesis, even if current income increases, consumption changes steadily according to permanent income and has little to do with current income. At the same time, a necessary logic of the permanent income hypothesis is that since income is positively correlated with the demand for money, then the stability of permanent income necessarily requires the stability of the demand for money, which is the theoretical basis of Friedman's "single rule" of economic policy.

For ae/aix=ad/aix-as/aix, Keynes considered the expected return on money to be a constant, while Friedman considered it not to be. When interest rates rise in the economy, banks can make more profit from loans and thus take deposits at higher interest rates, so the return on holding money in the form of bank deposits rises as interest rates on bonds and loans rise. Banks compete for deposits until there are no excess profits, a process that keeps the rb-rm fairly stable. This view of Friedman implies that changes in interest rates have a minimal effect on the demand for money, and then changes in interest rates have a small effect on output and employment in the long run, which leads Friedman to argue against the use of changing interest rates as a theoretical source of government regulation of the economy.

πe-ae/aix=ad/aix-as/aix depends on the expected rate of inflation πe when the price of the held good rises, and its value is stable. One of the ways in which Friedman differs from Keynes is that Friedman treats money and commodities as substitutes, and the assumption that commodities and money are substitutes for each other suggests that changes in the quantity of money may have an effect on aggregate output. So Friedman's permanent income is the main determinant of the demand for money, and the demand for money is insensitive to the interest rate, and the stability of permanent income leads to the stability of the demand for money.