Having developed the theory of liquidity preference as an explanation for how the interest rate is determined, we can now use the theory to derive the LM curve. We begin by considering the following question: how does a change in the economy’s level of income $Y$ affect the market for real money balances? The answer is that the level of income affects the demand for money. When income is high, expenditure is high, so people engage in more transactions that require the use of money. Thus, greater income implies greater money demand. We can express these ideas by writing the money demand function as

$(M/P)^d = L(r, Y)$

The quantity of real money balances demanded is negatively related to the interest rate and positively related to income. Using the theory of liquidity preference, we can figure out what happens to the equilibrium interest rate when the level of income changes:

$Y$

4.00
25.5

When income increases, income shifts the money demand curve to the right. With the supply of real money balances unchanged, the interest rate must rise to equilibrate the money market. Therefore, according to the theory of liquidity preference, higher income leads to a higher interest rate.

The LM curve summarizes this relationship between the level of income and the interest rate. Each point on the LM curve represents equilibrium in the money market, and the curve illustrates how the equilibrium interest rate depends on the level of income. The higher the level of income, the higher the demand for real money balances, and the higher the equilibrium interest rate. For this reason, the LM curve slopes upward.