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Aggregate Supply and the Short-Run Tradeoff Between Inflation and Unemployment

Reading: Chapter 14, Mankiw (8th ed.)

MACROECONOMICS

N. Gregory Mankiw

PowerPoint ® Slides by Ron Cronovich

Fall 2014 update

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CHAPTER 14 Aggregate Supply

Chapter 14 has two parts. The first concerns aggregate supply. In the preceding chapters, we made the simple and extreme assumption that all prices were “stuck” in the short run. This assumption implied a horizontal short-run aggregate supply curve. More realistic models of aggregate supply imply an upward-sloping SRAS curve. The key difference is that, in the short run, a shift in AD causes P to change, which changes M/P, which shifts LM a bit, which explains why the short-run change in output is smaller when SRAS is upward-sloping than when it is horizontal. This chapter presents two of the most prominent models for AS.

The second half of the chapter is devoted to the Phillips curve and related issues. The section uses a few lines of algebra to derive an expression for the Phillips curve from the SRAS equation. This is followed by a discussion of adaptive and rational expectations, and the sacrifice ratio. The chapter concludes by contrasting the notion of hysteresis to the natural rate hypothesis.

If you are reading previous editions, note that Mankiw has cut the sticky wage model of SRAS in the 7th edition; he now emphasizes the sticky price theory (and presents the imperfect information model as an alternative).

IN THIS CHAPTER, YOU WILL LEARN:

two models of aggregate supply in which output depends positively on the price level in the short run

about the short-run tradeoff between inflation and unemployment known as the Phillips curve

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CHAPTER 14 Aggregate Supply

Introduction

In previous chapters, we made the extreme assumption that the price level P was “stuck” in the short run.

This implies a horizontal SRAS curve.

But more realistic models assume prices are “somewhat” flexible & imply upward sloping SRAS curve. Now, we consider two prominent models of aggregate supply in the short run:

Sticky-price model

Imperfect-information model

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CHAPTER 14 Aggregate Supply

Introduction

Both models imply:

natural rate of output

a positive parameter

expected price level

actual price level

agg. output

Other things equal, Y and P are positively related, so the SRAS curve is upward sloping.

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CHAPTER 14 Aggregate Supply

The sticky-price model

Reasons for sticky prices:

long-term contracts between firms and customers

menu costs

firms not wishing to annoy customers with frequent price changes

Assumption:

Firms set their own prices (e.g., as in monopolistic competition).

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CHAPTER 14 Aggregate Supply

If you don’t like the appearance of the term “monopolistic competition” in this slide, just change the parenthetical comment to “(i.e., firms have some market power)” or something to that effect.

The sticky-price model

An individual firm’s desired price is:

where a > 0.

Suppose two types of firms:

firms with flexible prices, set prices as above

firms with sticky prices, must set their price before they know how P and Y will turn out:

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CHAPTER 14 Aggregate Supply

Interpretation of the first equation:

If output is at its natural rate, then each firm’s optimal price is the same as the overall price level. When the economy is weak (output below its natural rate), firms set their prices lower, and in a boom when demand is high, firms set their prices higher.

Remember that “E” is the expectation operator introduced in Chapter 5.

Hence, EP is the expected price level and (EY – EYbar) is the expected deviation of output from its natural, full-employment level.

The sticky-price model

Assume sticky-price firms expect that output will equal its natural rate. Then,

To derive the aggregate supply curve, find an expression for the overall price level.

s = fraction of firms with sticky prices. Then, we can write the overall price level as…

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CHAPTER 14 Aggregate Supply

The sticky-price model

Subtract (1−s)P from both sides:

price set by flexible-price firms

price set by sticky-price firms

Divide both sides by s to find AS equation:

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CHAPTER 14 Aggregate Supply

The sticky-price model

High EP g High P If firms expect high prices, then firms that must set prices in advance (i.e. sticky-price firms) will set them high. Other firms respond by setting high prices.

High Y g High P When income is high, the demand for goods is high. Firms with flexible prices set high prices.

The smaller the fraction of sticky-price firms, the smaller is s and the bigger the effect of ΔY on P.

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CHAPTER 14 Aggregate Supply

The sticky-price model

We can also express AS equation by solving for Y :

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CHAPTER 14 Aggregate Supply

The imperfect-information model

Assumptions:

All wages and prices are perfectly flexible, all markets are clear.

Each supplier produces one good, consumes many goods.

Each supplier knows the nominal price of the good she produces, but does not know the overall price level.

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CHAPTER 14 Aggregate Supply

The imperfect-information model

Supply of each good depends on its relative price: the nominal price of the good divided by the overall price level.

Supplier does not know price level at the time she makes her production decision, so uses EP.

Suppose P rises but EP does not.

Supplier thinks her relative price has risen, so she produces more.

With many producers thinking this way, Y will rise whenever P rises above EP.

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CHAPTER 14 Aggregate Supply

Summary & implications

Both models of agg. supply imply the relationship summarized by the SRAS curve & equation.

LRAS

SRAS

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CHAPTER 14 Aggregate Supply

The following is not in the text, but you may find it worthwhile:

There are good reasons to believe that the SRAS curve is bow-shaped in the real world; that is, the curve is steeper at high levels of output than at low levels of output. And there are good reasons why we should care about this.

Why the SRAS curve is bow-shaped:

At low levels of output, there are lots of unutilized and under-utilized resources available, so it is not terribly costly for firms to increase output, and therefore firms do not require a big increase in prices to make them willing to increase output by a given amount. In contrast, at very high levels of output, when unemployment is below the natural rate and capital is being used at higher than normal intensity levels, it is relatively costly for firms to increase output further. Hence, a larger increase in prices is required to make firms willing to increase their output.

Why the curvature matters:

When policymakers increase aggregate demand, output rises (good) and prices rise (not good). An important question arises: how much of the bad thing (higher prices) must we tolerate to get some of the good thing (higher output)? The answer depends on how steep the SRAS curve is.

When President Reagan cut taxes in the early 1980s, the economy was just coming out of a severe recession, and was on the flatter part of the SRAS curve; hence, the tax cuts affected output a lot and inflation very little. In contrast, when taxes are cut during normal or boom times, when we’re on the steeper part of the SRAS curve, tax cuts would likely be inflationary.

Figure 14-1, p.404

Idiosyncrasy alert:

If  is constant, then the SRAS curve should be linear, strictly speaking. However, in the text, it is drawn with a bit of curvature (which I have reproduced here).

Summary & implications

Suppose a positive AD shock moves output above its natural rate and P above the level people had expected.

LRAS

SRAS1

SRAS equation:

AD1

AD2

Over time, EP rises, SRAS shifts up, and output returns to its natural rate.

SRAS2

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CHAPTER 14 Aggregate Supply

This graph has two lessons for students:

First, changes in the expected price level shift the SRAS curve (this should be clear from the equation, as should the fact that a change in the natural rate of output will shift the SRAS curve).

The second lesson concerns the adjustment of the economy back to full-employment output.

Inflation, unemployment, and the Phillips curve

The Phillips curve states that π depends on

expected inflation, Eπ

cyclical unemployment: the deviation of the actual rate of unemployment from the natural rate

supply shocks, υ (Greek letter “nu”).

where β > 0 is an exogenous constant.

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CHAPTER 14 Aggregate Supply

 measures the responsiveness of inflation to cyclical unemployment.

Deriving the Phillips curve from SRAS

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CHAPTER 14 Aggregate Supply

Here are the explanations:

Equation (1) is the SRAS equation.

Solve (1) for P to get (2).

To get (3), add the supply shock term to (2).

To get (4), subtract last year’s price level (P-1) from both sides.

To get (5), write  in place of (P- P-1) and e in place of (Pe- P-1). Note that the change in the price level is not exactly the inflation rate, unless we interpret P as the natural log of the price level.

Equation (6) captures the relationship between output and unemployment from Okun’s law (Chapter 2): the deviation of output from its natural rate is inversely related to cyclical unemployment.

Substituting (6) into (5) gives (7), the Phillips curve equation introduced on the preceding slide.

Comparing SRAS and the Phillips curve

SRAS curve: Output is related to unexpected movements in the price level.

Phillips curve: Unemployment is related to unexpected movements in the inflation rate.

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CHAPTER 14 Aggregate Supply

Adaptive expectations

Adaptive expectations: an approach that assumes people form their expectations of future inflation based on recently observed inflation.

A simple version: Expected inflation = last year’s actual inflation

Then, P.C. becomes

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CHAPTER 14 Aggregate Supply

Inflation inertia

In this form, the Phillips curve implies that inflation has inertia:

In the absence of supply shocks or cyclical unemployment, inflation will continue indefinitely at its current rate.

Past inflation influences expectations of current inflation, which in turn influences the wages & prices that people set.

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CHAPTER 14 Aggregate Supply

Two causes of rising & falling inflation

cost-push inflation: inflation resulting from supply shocks

Adverse supply shocks typically raise production costs and induce firms to raise prices, pushing inflation up.

demand-pull inflation: inflation resulting from demand shocks

Positive shocks to aggregate demand cause unemployment to fall below its natural rate, which pulls the inflation rate up.

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CHAPTER 14 Aggregate Supply

Of course, a favorable supply shock that lowers production costs will push inflation down, and a negative demand shock which raises cyclical unemployment will pull inflation down.

Graphing the Phillips curve

In the short run, policymakers face a tradeoff between π and u.

The short-run Phillips curve

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CHAPTER 14 Aggregate Supply

Here, the “short run” is the period until people adjust their expectations of inflation.

Shifting the Phillips curve

People adjust their expectations over time, so the tradeoff only holds in the short run.

E.g., an increase in Eπ shifts the short-run P.C. upward.

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CHAPTER 14 Aggregate Supply

After displaying this slide, you might consider giving your students an exercise using the P.C. curve. One possibility would be to ask them to draw a graph of the PC curve, then show what happens to it in the face of an adverse supply shock or an increase in the natural rate of unemployment, giving intuition for each.

The intuition for why an increase in the natural rate shifts the PC upward (or rightward) is as follows:

At any given value of actual unemployment, an increase in the natural rate implies a decrease in cyclical unemployment, which increases inflation by increasing pressures for wages to rise. Thus, each value of unemployment has a higher value of inflation than before.

The sacrifice ratio

To reduce inflation, policymakers can contract agg. demand, causing unemployment to rise above the natural rate.

The sacrifice ratio measures the percentage of a year’s real GDP that must be forgone to reduce inflation by 1 percentage point.

A typical estimate of the ratio is 5.

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CHAPTER 14 Aggregate Supply

The sacrifice ratio

Example: To reduce inflation from 6 to 2 percent, must sacrifice 20 percent of one year’s GDP:

GDP loss = (inflation reduction) × (sacrifice ratio) = 4 × 5

This loss could be incurred in one year or spread over several, e.g., 5% loss for each of four years.

The cost of disinflation is lost GDP. One could use Okun’s law to translate this cost into unemployment.

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CHAPTER 14 Aggregate Supply

Rational expectations

Ways of modeling the formation of expectations:

adaptive expectations: People base their expectations of future inflation on recently observed inflation.

rational expectations: People base their expectations on all available information, including information about current and prospective future policies.

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CHAPTER 14 Aggregate Supply

Here’s a good example to illustrate the difference between adaptive and rational expectations.

Suppose the Fed announces a shift in priorities, from maintaining low inflation to maintaining low unemployment w/o regard to inflation; this shift will start affecting policy next week.

If expectations are adaptive, then expected inflation will not change, because it is based on past inflation. The Fed’s announcement pertains to the future, and has no impact on past inflation.

If expectations are rational, then expected inflation will increase right away, as people factor this announcement into their forecasts.

Painless disinflation?

Proponents of rational expectations believe that the sacrifice ratio may be very small:

Suppose u = un and π = Eπ = 6%,

and suppose the Fed announces that it will do whatever is necessary to reduce inflation from 6 to 2 percent as soon as possible.

If the announcement is credible, then Eπ will fall, perhaps by the full 4 points.

Then, π can fall without an increase in u.

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CHAPTER 14 Aggregate Supply

Here’s an interesting and important implication:

Central banks that are politically independent are typically more credible than those that are puppets of elected officials. Hence, in countries with central banks that are NOT politically independent, it is usually far costlier to reduce inflation. A very worthwhile reform, therefore, would be for governments to give their central banks independence.

Calculating the sacrifice ratio for the Volcker disinflation

1981: π = 9.7%

1985: π = 3.0%

year	u	u n	u−u n
1982	9.5%	6.0%	3.5%
1983	9.5	6.0	3.5
1984	7.4	6.0	1.4
1985	7.1	6.0	1.1

Total 9.5%

Total disinflation = 6.7%

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CHAPTER 14 Aggregate Supply

The natural rate of unemployment is assumed to be 6.0% during the early 1980s.

Calculating the sacrifice ratio for the Volcker disinflation

From previous slide: Inflation fell by 6.7%, total cyclical unemployment was 9.5%.

Okun’s law: 1% of unemployment = 2% of lost output.

Thus, 9.5% cyclical unemployment = 19.0% of a year’s real GDP.

Sacrifice ratio = (lost GDP)/(total disinflation)

= 19/6.7 = 2.8 percentage points of GDP were lost for each 1 percentage point reduction in inflation.

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CHAPTER 14 Aggregate Supply

The natural-rate hypothesis

Our analysis of the costs of disinflation, and of economic fluctuations in the preceding chapters, is based on the natural-rate hypothesis:

Changes in aggregate demand affect output and employment only in the short run.

In the long run, the economy returns to the levels of output, employment, and unemployment described by the classical model (Chaps. 3–9).

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CHAPTER 14 Aggregate Supply

The natural rate hypothesis allows us to study the long run separately from the short run.

An alternative hypothesis: Hysteresis

Hysteresis: the long-lasting influence of history on variables such as the natural rate of unemployment.

Negative shocks may increase un, so economy may not fully recover.

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CHAPTER 14 Aggregate Supply

Hysteresis: Why negative shocks may increase the natural rate

The skills of cyclically unemployed workers may deteriorate while unemployed, and they may not find a job when the recession ends.

Cyclically unemployed workers may lose their influence on wage setting; then, insiders (employed workers) may bargain for higher wages for themselves.

Result: The cyclically unemployed “outsiders” may become structurally unemployed when the recession ends.

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CHAPTER 14 Aggregate Supply

CHAPTER SUMMARY

1. Two models of aggregate supply in the short run:

sticky-price model

imperfect-information model

Both models imply that output rises above its natural rate when the price level rises above the expected price level.

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CHAPTER 14 Aggregate Supply

CHAPTER SUMMARY

2. Phillips curve

derived from the SRAS curve

states that inflation depends on

expected inflation

cyclical unemployment

supply shocks

presents policymakers with a short-run tradeoff between inflation and unemployment

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CHAPTER 14 Aggregate Supply

CHAPTER SUMMARY

3. How people form expectations of inflation

adaptive expectations

based on recently observed inflation

implies “inertia”

rational expectations

based on all available information

implies that disinflation may be painless

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CHAPTER 14 Aggregate Supply

CHAPTER SUMMARY

4. The natural rate hypothesis and hysteresis

the natural rate hypotheses

states that changes in aggregate demand can affect output and employment only in the short run

hysteresis

states that aggregate demand can have permanent effects on output and employment

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CHAPTER 14 Aggregate Supply

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