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IS-LM-model Introduction

The main difference between the cross model and the IS- LM model is that the nominal interest rate is exogenous in the cross model but endogenous in the IS-LM model. In this chapter we will explain how the nominal interest rate is determined in the IS- LM.

P remains exogenous and constant in the IS-LM model. Therefore, inflation and expected inflation is zero. This in turn implies that the nominal interest rate is equal to the real interest rate: R = r. This will allow us to talk about "the interest rate" without specifying] whether we mean the nominal or real interest rates.

Aggregate Demand

The investment function in the IS-LM model

Investment was an exogenous variable in the cross model due to the fact that the interest rate was exogenous. Now that the interest rate is endogenous, investment will be endogenous. As for the classical model, investment depends negatively on the real interest rate but since R = r in the IS-LM model, we can make investment a function of R: I = I(R).

The consumption function in the IS-LM model

The consumption function will be the same as in the cross model, consumption will depend positively on Y. In the classical model, consumption depends negatively on the real interest rate. You may allow consumption to depend negatively on interest rates in the IS-LM as well. You must then write C = C(Y, R). In the literature, both variants are found but since the results will be largely the same, we choose to let C depend on Y only, C = C(Y). We will also, for the same reason, model imports as a function of Y only even though it may depend on R as well.

Aggregate Demand

Aggregate demand depends on Y and R in the IS-LM model

Since investments depend on R and consumption and imports depend on Y, the aggregate demand will depend on both Y and R. In the cross model, we used the notation Y_D(y) for aggregate demand. In the IS- LM model, we must instead use the notation Y_D(Y, R). We have

Y_D(Y, R) = C(Y) + I(R) + G + X - Im(Y)

It does not make much of a difference if we allow C and Im to depend on R as well, Y_D will depend positively on Y and negatively on R in any case.

It should also be clear that we can no longer determine GDP the way we did it in the cross model. We cannot successfully solve the equation Y_D(Y, R) = Y as we have only one equation but two unknowns (Y and R). We need one more equation if we want to solve for both Y and R. This equation will come from the money market.

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