We have been using the *IS*–*LM* model to explain national income in the short run when the price level is fixed. To see how the *IS*–*LM* model fits into the model of aggregate supply and aggregate demand introduced in **Chapter 10**, we now examine what happens in the *IS*–*LM* model if the price level is allowed to change. By examining the effects of changing the price level, we can finally deliver what was promised when we began our study of the *IS*–*LM* model: a theory to explain the position and slope of the aggregate demand curve.

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Recall from **Chapter 10** that the aggregate demand curve describes a relationship between the price level and the level of national income. In **Chapter 10** this relationship was derived from the quantity theory of money. That analysis showed that for a given money supply, a higher price level implies a lower level of income. Increases in the money supply shift the aggregate demand curve to the right, and decreases in the money supply shift the aggregate demand curve to the left.

To understand the determinants of aggregate demand more fully, we now use the *IS*–*LM* model, rather than the quantity theory, to derive the aggregate demand curve. First, we use the *IS*–*LM* model to show why national income falls as the price level rises—

To explain why the aggregate demand curve slopes downward, we examine what happens in the *IS*–*LM* model when the price level changes. This is done in Figure 12-5. For any given money supply *M*, a higher price level *P* reduces the supply of real money balances *M*/*P*. A lower supply of real money balances shifts the *LM* curve upward, which raises the equilibrium interest rate and lowers the equilibrium level of income, as shown in panel (a). Here the price level rises from *P*_{1} to *P*_{2}, and income falls from *Y*_{1} to *Y*_{2}. The aggregate demand curve in panel (b) plots this negative relationship between national income and the price level. In other words, the aggregate demand curve shows the set of equilibrium points that arise in the *IS*–*LM* model as we vary the price level and see what happens to income.

Figure 12.5: FIGURE 12-5: **Deriving the Aggregate Demand Curve with the ***IS*–*LM* Model Panel (a) shows the *IS*–*LM* model: an increase in the price level from *P*_{1} to *P*_{2} lowers real money balances and thus shifts the *LM* curve upward. The shift in the *LM* curve lowers income from *Y*_{1} to *Y*_{2}. Panel (b) shows the aggregate demand curve summarizing this relationship between the price level and income: the higher the price level, the lower the level of income.

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What causes the aggregate demand curve to shift? Because the aggregate demand curve summarizes the results from the *IS*–*LM* model, events that shift the *IS* curve or the *LM* curve (for a given price level) cause the aggregate demand curve to shift. For instance, an increase in the money supply raises income in the *IS*–*LM* model for any given price level; it thus shifts the aggregate demand curve to the right, as shown in panel (a) of Figure 12-6. Similarly, an increase in government purchases or a decrease in taxes raises income in the *IS*–*LM* model for a given price level; it also shifts the aggregate demand curve to the right, as shown in panel (b) of Figure 12-6. Conversely, a decrease in the money supply, a decrease in government purchases, or an increase in taxes lowers income in the *IS*–*LM* model and shifts the aggregate demand curve to the left. Anything that changes income in the *IS*–*LM* model other than a change in the price level causes a shift in the aggregate demand curve. The factors shifting aggregate demand include not only monetary and fiscal policy but also shocks to the goods market (the *IS* curve) and shocks to the money market (the *LM* curve).

Figure 12.6: FIGURE 12-6: **How Monetary and Fiscal Policies Shift the Aggregate Demand Curve** Panel (a) shows a monetary expansion. For any given price level, an increase in the money supply raises real money balances, shifts the *LM* curve downward, and raises income. Hence, an increase in the money supply shifts the aggregate demand curve to the right. Panel (b) shows a fiscal expansion, such as an increase in government purchases or a decrease in taxes. The fiscal expansion shifts the *IS* curve to the right and, for any given price level, raises income. Hence, a fiscal expansion shifts the aggregate demand curve to the right.

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We can summarize these results as follows: *A change in income in the* IS–*model resulting from a change in the price level represents a movement along the aggregate demand curve. A change in income in the* IS–*model for a given price level represents a shift in the aggregate demand curve.*

The *IS*–*LM* model is designed to explain the economy in the short run when the price level is fixed. Yet, now that we have seen how a change in the price level influences the equilibrium in the *IS*–*LM* model, we can also use the model to describe the economy in the long run when the price level adjusts to ensure that the economy produces at its natural rate. By using the *IS*–*LM* model to describe the long run, we can show clearly how the Keynesian model of income determination differs from the classical model of **Chapter 3**.

Panel (a) of Figure 12-7 shows the three curves that are necessary for understanding the short-*IS* curve, the *LM* curve, and the vertical line representing the natural level of output
. The *LM* curve is, as always, drawn for a fixed price level *P*_{1}. The short-*IS* curve crosses the *LM* curve. Notice that in this short-

Figure 12.7: FIGURE 12-7: **The Short-**Run and Long-Run Equilibria We can compare the short-run and long-run equilibria using either the *IS*–*LM* diagram in panel (a) or the aggregate supply–aggregate demand diagram in panel (b). In the short run, the price level is stuck at *P*_{1}. The short-run equilibrium of the economy is therefore point K. In the long run, the price level adjusts so that the economy is at the natural level of output. The long-run equilibrium is therefore point C.

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Panel (b) of Figure 12-7 shows the same situation in the diagram of aggregate supply and aggregate demand. At the price level *P*_{1}, the quantity of output demanded is below the natural level. In other words, at the existing price level, there is insufficient demand for goods and services to keep the economy producing at its potential.

In these two diagrams we can examine the short-*P*_{1}. Eventually, the low demand for goods and services causes prices to fall, and the economy moves back toward its natural rate. When the price level reaches *P*_{2}, the economy is at point C, the long-*IS*–*LM* diagram by a shift in the *LM* curve: the fall in the price level raises real money balances and therefore shifts the *LM* curve to the right.

We can now see the key difference between the Keynesian and classical approaches to the determination of national income. The Keynesian assumption (represented by point K) is that the price level is stuck. Depending on monetary policy, fiscal policy, and the other determinants of aggregate demand, output may deviate from its natural level. The classical assumption (represented by point C) is that the price level is fully flexible. The price level adjusts to ensure that national income is always at its natural level.

To make the same point somewhat differently, we can think of the economy as being described by three equations. The first two are the *IS* and *LM* equations:

The *IS* equation describes the equilibrium in the goods market, and the *LM* equation describes the equilibrium in the money market. These *two* equations contain *three* endogenous variables: *Y*, *P*, and *r*. To complete the system, we need a third equation. The Keynesian approach completes the model with the assumption of fixed prices, so the Keynesian third equation is

*P* = *P*_{1}.

This assumption implies that the remaining two variables *r* and *Y* must adjust to satisfy the remaining two equations *IS* and *LM*. The classical approach completes the model with the assumption that output reaches its natural level, so the classical third equation is

This assumption implies that the remaining two variables *r* and *P* must adjust to satisfy the remaining two equations *IS* and *LM*. Thus, the classical approach fixes output and allows the price level to adjust to satisfy the goods and money market equilibrium conditions, whereas the Keynesian approach fixes the price level and lets output move to satisfy the equilibrium conditions.

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Which assumption is most appropriate? The answer depends on the time horizon. The classical assumption best describes the long run. Hence, our long-**Chapter 3** and prices in **Chapter 5** assume that output equals its natural level. The Keynesian assumption best describes the short run. Therefore, our analysis of economic fluctuations relies on the assumption of a fixed price level.