To understand how to derive the LM curve you must remember what it represents. The LM curve represents all combinations of the interest rate and income at which the money market is in equilibrium.

Let’s look at the money market (see left panel). The M^d curve represents the demand for money. Notice that it is downward sloping. It slopes downward because the interest rate represents the opportunity cost of holding assets as money and, as the opportunity cost rises, the quantity of money demanded falls. The active graph on the right shows all possible combinations of the interest rate and income. What you have to do is to figure out which combinations are consistent with equilibrium in the goods market.

First, notice the handle on the horizontal axis panel at left marking the current level of income (Y₁)

1. What level of the interest is the equilibrium level when income is Y₁ ?
2. Can you determine one of the combinations of the interest rate and the level of income consistent with equilibrium in the money market ?
3. What do you expect will happen to the M^d curve as the level of income rises ?
4. What happens to the level of the equilibrium interest rate ?
5. What does this imply about the slope of the LM curve ?
6. Move the handle that changes the level of income, rightward and leftward, clicking on the Mark button at various different levels of income. Does the LM curve look as you expected in question 5 ?