The IS curve shows all combinations of R and Y where the goods market is in equilibrium. The IS-curve slopes downwards.
The goods market is in equilibrium when YD( Y, R) = Y. Note that when R is given, the IS-LM simplifies to the cross model:
If we know R, we can determine the equilibrium value of Y using the cross model. Also, if we know Y we can determine R from the money market. None of the methods, however, will gives us both R and Y simultaneously.
Consider the following question: What must happen to Y when we change R if we want the goods market to remain in equilibrium? To answer this question, consider two different interest rates, Rl = 5% and R2 = 10%. Since YD depends negatively on R, YD(Y, Rl) will be larger than YD(Y, R2). With a higher R, we must have a lower Y for the goods market to be in equilibrium.
We can illustrate this argument with the above diagram.
1. Start by identifying R1 and R1 in the lower graph.
2. Draw aggregate demand for both interest rates - the one corresponding to the lower interest rate will be higher than the other.
3. Identify the resulting GDP in the upper diagram for both interest rates - the highest level of GDP corresponds to the lower interest rate.
4. Extend these levels of GDP to the lower graph. This will give you two points in the lower graph.
5. Continue with other interest rates if you like. The result will be a curve in the lower graph that we call the IS-curve.
The IS curve will identify all combinations of Y and R where YD( Y, R) = Y, that is, where the goods market is in equilibrium. The economy must be on this curve if the commodity market is to be in equilibrium. However, an analysis of the goods market alone will not help us identify at which point all markets are in equilibrium. Note that the cross model is represented by a single point on the IS-curve - the point corresponding to the exogenously given interest rate. This is why we can determine Y in cross model only from the commodity market.
The LM curve
The LM curve shows all combinations of R and Y, where the money market is in equilibrium. The LM-curve slopes upwards.
The money market is in equilibrium when Md(Y, R) = Ms. In section 12.3.6 we demonstrated how the money market diagram will determine R when we know Y. In this case, the question to consider is the following: What must happen to R when we change the Y if we want the money market to remain in equilibrium?
To answer this question, we try two different values for GDP Y1 = 100 and Y1 = 200. Since the MD depends positively on Y, MD(Y1, R) will be smaller than the MD(Y2, R). R must therefore be larger when Y increases for the money market to be in equilibrium.
Fig. 12.4 Derivation of the LM-curve.
The diagram above illustrates this point.
1. Start by selecting Y1 and Y2 in the left graph (Y2 < Y2).
2. Draw the money demand for each of the different levels of GDP in the diagram to the right - the one corresponding to the lower value of GDP must be the smallest.
3. Identify the resulting interest rate in the diagram to the right for both levels of GDP - the larger of the interest rates corresponds to the larger value of GDP.
4. Extend these interest rates to diagram on the left. This will give you two points where the money market is in equilibrium.
5. Continue with the other levels of GDP. The result will be a curve in the left diagram that we call the LM-curve.
The LM curve will show you all combinations of Y and R where Md(Y, R) = Ms, that is, where the money market is in equilibrium. Again, the economy must be on the LM curve if the money market is to be in equilibrium and the money market alone cannot determine which point will lead to equilibrium in all markets.
Simultaneous determination of Y and R in the IS-LM model
By combining the IS curve and the LM curve, we can graphically illustrate what interest rate and what level of GDP that will satisfy both equations: YD( Y, R) = Y and MD( Y, R) = MS. For all points on the IS-curve, we have equilibrium in the goods market and for all points on the LM-curve, we have equilibrium in the money market. There is only one point where both markets are in equilibrium, Y* and R*.
Fig. 12.5: IS-LM model.
According to IS-LM model, the economy will move to Y* and R*. The argument is as follows.
1. Imagine that R > R*. It is the not possible to be on both the IS and the LM-curve.
2. Suppose that we are on the IS-curve, but to the left of the LM curve. The interest rate is higher than the equilibrium interest rate and R will fall as discussed in 12.3.6.
3. Suppose that we are on the LM-curve, but to the right of the IS-curve. Y is then higher than the equilibrium value and Y will fall as discussed in 11.3.2. We will then move away from the LM-curve and the interest rates will fall.
4. If we are neither on the IS- nor on the LM-curve, then Y will fall as long as we are to the right of the IS-curve and R will fall as long as we are to the left of the LM-curve.
The Labor Market
The labor market in the IS-LM model is the same as in the cross model. Therefore, the IS-LM model is only applicable if the profit-maximizing quantity of L would lead to an aggregate supply that was larger than the aggregate demand and aggregate demand will therefore determine L.
Once R and Y is determined, all the endogenous variables are determined. The diagram below shows the determination of Y, R and L in the IS-LM model.
Fig. 12.6: Determination of Y, R and L of the IS-LM model.
We start at top to the left and extend Y* down, through the "mirror" at the bottom left, on to the production function at the bottom right and then up to the diagram representing the labor market.
The IS-LM is simply an extension of the cross model in the sense that the interest rate becomes an endogenous variable and we will be able to analyze how the interest rate is affected by changes in the economy. We could have developed the IS-LM model directly, skipping the cross model as the cross model adds nothing in relation to the IS-LM model. The reason that most books (including this one) start with cross model is entirely pedagogical. The cross model is much simpler since GDP can be determined from the goods market only as the solution to one equation one equation Y(Y) = Y. Most students would probably find the IS-LM model even more complicated had they not previously encountered the cross model.