Booms and recessions IV dynamic aggregate supply and demand

What to expect

After working through this chapter, you will understand:

1 How to draw the aggregate supply curve in inflation-income space.

2 How to draw the aggregate demand curve in inflation-income space.

3 The concepts of adaptive and rational expectations, and how individuals choose to form expectations.

4 How to use the DAD-SAS model to trace how an economy moves in inflation-income space.

5 That the policy options offered by the DAD-SAS (and the AD-AS) model depend on whether we have fixed or flexible exchange rates.

6 That the economy's responses to monetary and fiscal policy depend on how individuals form expectations.

In Chapter 7 we assembled a complete macroeconomic model of the business cycle in which four markets interact and prices are endogenous. This is the model we were driving at from the beginning of this text. The form in which the aggregate demand-aggregate supply model is presented and handled graphically and algebraically has one major drawback, however: it does not permit a direct analysis of inflation. Of course, inflation is nothing but a steady increase in prices. So when we analyze prices we implicitly analyze inflation as well. From a practical viewpoint, however, it would be desirable to make inflation more explicit. After all, real-world economies rarely feature full price stability, as the long-run equilibrium in the AD-AS diagram would imply. In fact, only a minority of economists would even recommend striving for complete price stability. Monetary policy discussions these days centre on whether central banks should aim at an inflation target, not at a price level target, and if they should, whether the inflation target should be 2, 3 or 4%. When monetary policy becomes restrictive, the inflation rate falls, but rarely the level of prices. Disinflation, a reduction of the inflation rate, is something completely different from deflation, a reduction of the price level.

For the reasons stated, this chapter recasts the AD-AS model in a form that permits its graphical analysis in an inflation-income diagram. We will call this the DAD-SAS model, though it should be emphasized, however, that the

8.1 The aggregate-supply curve in an inflation-income diagram 199

DAD-SAS model is not really a new model, but simply the AD-AS model in new, more practical clothing.

A second main theme of this chapter is the formation of expectations. While expected prices already played a role in Chapter 7's AD-AS model, we were content with a rather elementary treatment. In this chapter we look at expectations formation in much more detail, discussing the whole spectrum of possibilities from adaptive via rational expectations to perfect foresight.

Equipped with a refined understanding of expectations we take a second look at fiscal and monetary policy. The key insight will be that what policymakers can achieve depends crucially on the way the public forms expectations.

The aggregate-supply curve in an inflation-income diagram

In Chapter 7 we drew the AS curve in a diagram with the (logarithm of the) price level on the vertical axis, as a straight line. The underlying formula is

The SAS curve indicates the aggregate output that firms are willing to produce at different inflation rates.

To obtain a formulation that can be drawn in an inflation-income diagram is no magic. Simply subtract (the logarithm of) last period's price level p-i from both sides of (8.1) to obtain p - p-1 = pe - p-1 + A(Y - Y*). The difference p - p-1 is the change in the logarithm of the price level. This approximates the percentage rate of change of the price level (see appendix to Chapter 1), which is the rate of inflation p. The other difference pe - p-1 is expected inflation pe. So we may rewrite equation (8.1) as p = pe + A(Y - Y*

This is simply a new way of writing the aggregate supply curve. Written like this, it states that the level of output firms are willing to supply depends on normal output Y* and on unexpected or surprise inflation. We call this curve the SAS curve, where the first S stands for surprise.

Of course, equations (8.1) and (8.2) state the same thing. Equation (8.2) is more convenient to work with in an inflationary environment and yields a basis for viewing aggregate supply in an inflation-income diagram (see Figure 8.1).

Figure 8.1 The SAS curve has a positive slope. If inflation is as expected, potential output Y* is produced. If inflation is higher than expected, real wages are too low and firms hire more labour and produce more than normal. The SAS curve shifts up as pe rises and moves to the right as Y* increases.

Figure 8.1 The SAS curve has a positive slope. If inflation is as expected, potential output Y* is produced. If inflation is higher than expected, real wages are too low and firms hire more labour and produce more than normal. The SAS curve shifts up as pe rises and moves to the right as Y* increases.

This positively sloped SAS curve shows what firms are willing to produce at different inflation rates. They will do so only if demand is there. Therefore, as in the context of last chapter's AD-AS model, the supply side represented by the SAS curve must be augmented by information about the demand side.

Equilibrium income and inflation: the DAD curve

It would be nice to have the aggregate demand curve in a form that permits us to draw demand-side equilibria in the same diagram as the SAS curve. To obtain such a representation in inflation-income space, recall that in Chapter 7 we found the AD curve to read

Note.The first appendix to this chapter derives very much the same DAD curve with more plausible endogenous depreciation expectations. Considering Aee exogenous in the main text's graphical discussion provides a handle for analyzing the role of market psychology, that is, what happens if investors lose confidence in a currency for no obvious reason.

Under fixed exchange rates with occasional realignments the expected devaluation is the probability of a realignment times the expected size of the realignment. Example: ee = 0.2 X 10 = 2. If the probability of a 10% realignment rises from 0.2 to 0.5, the expected devaluation becomes 5 (%). Hence devaluation expectations have changed by Aee = 5 - 2 = 3.

p = m - bY + h(iW + ee) under flexible exchange rates and p = e + pW - bY + gYW + 8G - f(i

AD curve (8.3) flexible exchange rates

fixed exchange rates in a system of fixed exchange rates.

Looking at flexible exchange rates first, we can derive a dynamic representation of the aggregate-demand curve for inflation-income space, a DAD curve, by manipulating equation (8.3). Copying what we did in section 8.1 when we rewrote the AS curve, take first differences on both sides of equation (8.3) (which means that we deduct last period's values), remembering p = p — p-i and defining the money growth rate m = m — m—i, to obtain:

flexible exchange rates

Among the last two factors in this equation, the presence of AzW takes care of the dependence on the world economy. The presence of Aee, which we treat as an exogenous variable here, may reflect the impact of market psychology.

Why does money growth m enter with a coefficient of exactly 1? Recall from previous discussions of the Mundell-Fleming model that when all factors affecting equilibrium remain constant, income does not change. One factor that needs to remain constant under flexible exchange rates is the real money supply. So if all other factors remain unchanged as well (AzW = Aee = 0), nominal money needs to grow at the rate of inflation in order to keep real money constant and to keep income where it was one period ago (Y = Y— i).

Under fixed exchange rates with possible devaluations the DAD curve is derived by taking first differences on both sides of equation (8.4):

p = e + pW - bY + bY— 1 + gAYW + SAG - f(AiW + Aee)

fixed exchange rates

Here the rates of devaluation and world inflation enter with a coefficient of 1.

Shifts up as money growth, or the change in the world interest rate, or in expected depreciation accelerates

Flexible exchange rates

DAD curve

Dynamic aggregate demand curve

Income Y

Income Y

Figure 8.2 The DAD curve has a negative slope. As we move down DAD the real exchange rate rises, and so does aggregate demand. Panel (a) demonstrates that under flexible exchange rates the position of DAD is mainly determined by money growth, m, but also by changes in the world interest rate and changes in expected depreciation. The curve moves up as any of those factors increases. Panel (b) shows that under fixed exchange rates the position of DAD is mainly determined by world inflation pw, but also by changes in world income, government spending, the world interest rate, and expected devaluation. As any of those factors increases, DAD moves. It moves up with the first three factors and down with the last two.

The reason is that for unchanged other factors (that is AYW = AG = AzW = Aee = 0) the real exchange rate must remain constant to keep (demand-side) equilibrium income where it was last period. The real exchange rate remains unchanged if domestic inflation equals the sum of devaluation and world inflation. Our knowledge of the DAD curve is summarized in Figure 8.2.

" The DAD-SAS model

Our macroeconomic model is now complete. It boils down to two equations, or curves, which can be analyzed in a simple p-Y diagram. The equations comprising the DAD-SAS model under flexible exchange rates read p = m - bY + bY-j + h(AtW + Aee) DAD curve flexible exchange rates p = pe = A( Y - Y*) SAS curve

The DAD-SAS model under fully fixed exchange rates (e = Aee = 0) reads p = pW - bY + bY-1 + SAG + gAYW - fAiW DAD curve fixed exchange rates p = pe + A( Y - Y*) SAS curve

Do not let the unpretentious elegance of this model deceive you. The DAD curve is nothing but a new way of stating the insights obtained during our discussions of the Mundell-Fleming model. If we want to know what is

Note. In Chapter 7 we called the vertical line denoted by

Y = Y* the long-run aggregate supply curve (LAS), because under adaptive price expectations adjustment towards it takes time.We now switch terminology, calling

Y = Y* the equilibrium aggregate supply curve (EAS). This is more general and accommodates the situation when under other inflation expectations schemes, analyzed below, adjustment is immediate.

going on behind the curve, say in the money market or the balance of payments, we must go back to the Mundell-Fleming model and its constituent markets. But note again: the Mundell-Fleming model and the DAD curve are merely two different ways of stating the same thing. Therefore, the Mundell-Fleming model and the DAD curve (taken alone) cannot give different answers to the same question.

The SAS curve combines, and to some extent hides, all the insights already gained or to be gained in our discussions of the economy's supply side: the labour market (in Chapter 6), the capital stock and economic growth (in Chapters 9 and 10). The curve says that firms are ready to supply output in excess of full-capacity or potential output only if inflation turns out to be higher than anticipated. In the absence of unanticipated inflation, output rests at its normal level Y*. We treat Y* as a fixed number during graphical discussions of the model. In reality, as will be discussed in Chapter 9, potential output grows over time, due to improvements in technology, a growing labour force and accumulation of human and physical capital. Potential output also goes hand in hand with unemployment, a substantial part of which may be involuntary.

With these important reminders we now proceed to analyze how the economy's supply and demand sides interact.

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