Pigou put forward this money demand function, and its theoretical basis is A. Marshall's money quantity theory. Marshall believes that the speed of currency circulation depends on the time and quantity of people holding money, which in turn depends on how much people's property and income are stored in the form of money. The property and income that people store in the form of money is "the purchasing power of reserves that people are willing to maintain", and the level of this purchasing power depends on the physical value maintained in the form of money. According to Marshall and Pigou's hypothesis, this "true value" is expressed by a certain amount of wheat, so the purchasing power of money (that is, the value of money) is expressed as the number of wheat that can be purchased by unit money. Let R be the total value of all commodities represented by a certain amount of wheat (that is, total social income and total wealth), K be the ratio of purchasing power of reserves held in monetary form to total social income and total wealth, M be the monetary amount, and P be the unit monetary value represented by a certain amount of wheat, then: P = KR/M.
So Pigou's money demand function, that is, the mathematization of Marshall's money quantity theory.
In the money demand function of M=kPy, y is a constant, and it is assumed that it is a constant, because the people are fully employed, and the money demand depends on the changes of K and P when the economic output reaches the highest level. The change of k depends on people's choice of wealth: wealth can be invested in production in kind, can also be directly used for consumption, and can also be maintained in monetary form. How to choose needs to weigh the pros and cons. If you choose to save in the form of money, then you will definitely increase the cash balance, and the increase of the cash balance will inevitably increase K. Under the condition that Y and M are unchanged, the increase of K will inevitably decrease P, because P=M/ky. This shows that the value of money is inversely proportional to ky and directly proportional to M. The economic significance expressed by Cambridge equation is called "cash balance theory", which mainly emphasizes the influence of cash balance held by people on the value of money and thus on the price. In addition, Pigou also believes that the supply of money affects the value of money and thus the price, that is, P is directly proportional to M. He once assumed that K is also a constant, because the transaction mode (payment mode) is unchanged for a certain period of time. In this way, the level of P depends on the number of M. At this point, what Cambridge Equation wants to express is that the value of money depends on the supply and demand of money.