Money Functions and Equilibrium

Demand

A money demand function displays the influence that some aggregate economic variables will have on the aggregate demand for money. The above discussion indicates that money demand will depend positively on the level of real gross domestic product (GDP) and the price level due to the demand for transactions. Money demand will depend negatively on average interest rates due to speculative concerns. We can depict these relationships by simply using the following functional representation:

M^{D}=f\left(\stackrel{+}{P}_{\$}, \stackrel{+}{Y}_{\$}, \stackrel{\_}{i}_{\$}\right).

Here MD is the aggregate, economy-wide money demand, P$  is the current U.S. price level, Y$ is the United States' real GDP, and i$  is the average U.S. interest rate. The f stands for "function". The f is not a variable or parameter value; it simply means that some function exists that would map values for the right-side variables, contained within the brackets, into the left-side variable. The "+" symbol above the price level and GDP levels means that there is a positive relationship between changes in that variable and changes in money demand. For example, an increase (decrease) in P$ would cause an increase (decrease) in MD. A "−" symbol above the interest rate indicates that changes in  i$ in one direction will cause money demand to change in the opposite direction.

For historical reasons, the money demand function is often transformed into a real money demand function as follows. First, rewrite the function on the right side to get

M^{D}=\stackrel{+}{P}_{\$} L\left(\stackrel{+}{Y}_{\$}, \stackrel{\_}{i}_{\$}\right).

In this version, the price level (P$) is brought outside the function f( ) and multiplied to a new function labeled L( ), called the "liquidity function". Note that L( ) is different from f( ) since it contains only Y$ and i$ as variables. Since P$ is multiplied to L( ) it will maintain the positive relationship to MD and thus is perfectly consistent with the previous specification. Finally, by moving the price level variable to the left side, we can write out the general form of the real money demand function as

\frac{M^{D}}{P_{\$}}=L\left(\stackrel{+}{Y}_{\$}, \stackrel{\_}{i}_{\$}\right).

This states that real money demand (MD/P$) is positively related to changes in real GDP (Y$) and the average interest rate (i$) according to the liquidity function. We can also say that the liquidity function represents the real demand for money in the economy - that is, the liquidity function is equivalent to real money demand.

Finally, simply for intuition's sake, any real variable represents the purchasing power of the variable in terms of prices that prevailed in the base year of the price index. Thus real money demand can be thought of as the purchasing power of money demanded in terms of base year prices.