## The Lm Model

The other half of the famous IS-LM paradigm is the LM, or money market equilibrium, relation, which gives the combinations of the interest rate and level of income such that the money market is cleared, that is, the demand for money is equal to its supply. Algebraically, the model, in the nonstochastic form, may be expressed as:

Money demand function: Mf = a + bYt - crt (18.2.15)

Equilibrium condition: Mf = Mf (18.2.17)

(Continued )

CHAPTER EIGHTEEN: SIMULTANEOUS-EQUATION MODELS 723

EXAMPLE 18.5 (Continued)

where Y = income, r = interest rate, and MM = assumed level of money supply, say, determined by the Fed.

Equating the money demand and supply functions and simplifying, we obtain:

where

For a given M = MM, the LM curve representing the relation (18.2.18) is as shown in Figure 18.4.

The IS and LM curves show, respectively, that a whole array of interest rates is consistent with goods market equilibrium and a whole array of interest rates is compatible with equilibrium in the money market. Of course, only one interest rate and one level of income will be consistent simultaneously with the two equilibria. To obtain these, all that needs to be done is to equate (18.2.13) and (18.2.18). In exercise 18.4 you are asked to show the level of the interest rate and income that is simultaneously compatible with the goods and money market equilibrium.

Income

FIGURE 18.4 The LM curve.

Income

FIGURE 18.4 The LM curve.