The early quantity theory of money can be roughly divided into the quantity theory of money represented by Fisher and the quantity theory of Cambridge School represented by Marshall and others, that is, the cash balance theory. Friedman reiterated his views on the quantity theory of money along the Cambridge equation. It is considered that the Cambridge equation M=kPT=ky can be regarded as a function of money demand, where PT is two variables in money demand and K represents all other variables, so it cannot be regarded as a constant in numerical value, and K is regarded as a function containing other variables. Like the early theory of money quantity, monetarism also recognizes that money quantity plays a leading role in economic life. The difference is that the monetarist money quantity theory holds that the change of money supply not only affects the change of price level, but also affects the change of total output or national income.

Keynesianism does not deny the important role of money, thinking that "money is also very important", but they emphasize the total demand, especially the investment demand. Monetarism draws the conclusion that "money is the most important" from the modern theory of money quantity, and holds that the direct cause of economic fluctuation is the excessive and irregular change of money supply. As for the money supply, Friedman believes that the money supply basically depends on the monetary system, that is, the amount of money is determined by the law and the monetary authorities. In Friedman's view, money is a substitute for bonds, stocks and commodities, and money demand is a function of the expected rate of return of wealth and other assets owned by individuals relative to money. Therefore, Friedman defined his money demand formula as follows:

Among them,

Md/p represents the demand for real money balance;

Yp stands for permanent income, that is, the discounted value of all theoretically expected future income, which can also be long-term average income;

Rm represents the expected rate of return of money;

Re represents the expected yield of bonds;

η represents the expected rate of return of the stock;

πe represents the expected inflation rate.

In Friedman's view, the demand for money mainly depends on the total wealth, but the total wealth is actually immeasurable, and the unstable regular income can only be replaced by permanent income.

For Yp, it is permanent income. Generally speaking, with the increase of income, that is, the increase of wealth, the demand for money increases. Friedman believes that people's permanent income is stable, which is people's average expectation of long-term income. In the expansion stage of the economic cycle, people's temporary income is greater than their permanent income. On the average, the fluctuation range of income is relatively stable and tends to permanent income, that is, permanent income is stable. Friedman's permanent income consists of non-human wealth and human wealth.

Permanent income plays a leading role in Friedman's monetary function. In Keynes's consumption function, consumption is a function of current income, and the relationship between consumption expenditure increment and current income increment-the law of diminishing marginal propensity to consume shows insufficient consumption and short-term economic fluctuation. According to the permanent income hypothesis, even if the current income increases, consumption will change steadily according to the permanent income, which has little to do with the current income. At the same time, an inevitable logic of the permanent income hypothesis is that since income is positively related to money demand, the stability of permanent income inevitably requires the stability of money demand, which is the theoretical basis of Friedman's "single rule" economic policy.

Relatively speaking, Keynes thought that the expected rate of return of money was constant, but Friedman thought it was not. When the interest rate in the economy rises, banks can get more profits from loans, thus absorbing deposits at higher interest rates. Therefore, the return rate of holding money in the form of bank deposits increases with the increase of bond and loan interest rates. The competition for bank deposits until there is no excess profit, which makes rb-rm quite stable. Friedman's point of view means that the change of interest rate has little influence on money demand, so the change of interest rate has little influence on output and employment in the long run, which also makes Friedman oppose the change of interest rate as the theoretical source of government regulation and control of the economy.

Depending on the expected inflation rate πe when the price of the commodity held rises, its value is stable. One difference between Friedman and Keynes is that Friedman regards money and goods as substitutes, and the hypothesis that goods and money are substitutes for each other shows that the change of money quantity may have an impact on total output.

Therefore, Friedman's permanent income is the main factor that determines the demand for money, and it is insensitive to interest rates. The stability of permanent income leads to the stability of the demand for money.