1

CHAPTER 10: Economic Fluctuations: Aggregate Supply and Demand and the Phillips Curve

In this chapter, you will learn to:

LO 10.1 Define and calculate potential output and the output gap using the production function approach.

LO 10.2 Show how production based shocks will have effects on output the price level, and employment

in the short run. LO 10.3 Show conditions under which changes in the money supply will affect aggregate demand,

output, and employment in the short-run – even though money remains neutral in the long run. LO 10.4 Use the multiplier analysis to show how autonomous shocks to aggregate demand – including

consumption and investment – have impacts the output gap. LO 10.5 Show the relationship between aggregate supply, inflation and the output gap using the Phillips

Curve.

Chapter Overview

In the first chapter, we found that, over the past century, GDP in the United States has been

rising. However, this upward path is not always smooth. Over shorter periods, we see fluctuations in

output – upturns and downturns. Earlier in the book, we introduced the notion of potential output – an

economy’s production level that corresponds to its long-run capacity constraints. We also introduced

the idea that, temporarily, output can differ from that long-run level. We defined the output gap as the

difference between observed output and potential output. Macroeconomists refer to the movements in

the output gap, up and down around potential output, as the business cycle. (Key term: business cycle:

the up and down movements of output around its potential or long-run trend level)

Macroeconomists are keenly interested in the causes of the business cycle. They want to know

what kinds of economic shocks – shifts in supply, demand, or both -- cause business cycles. They also

want to know the “side effects” or consequences of business cycles. One such “side effect” is inflation. If

firms face higher than normal demand for their goods and services, the output gap will increase – and,

along with it, inflation. Another “side effect” of business cycles regards how the upturns and downturns

of economic activity affect the well-being of an economy’s residents. Some members of society suffer

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disproportionately during economic downturns – when they output gap is negative. Their income may

fall substantially, and some may even lose their jobs. They would willingly relinquish some of their extra

income during “good times” in return for a smoother path. In addition, many economists also want to

know whether authorities can reduce the severity of these up and down movements through economic

stabilization policies.

This chapter introduces key topics related to the business cycle. To begin, we examine how

economists measure an economy’s potential output and its output gap. To know a country’s level of

potential output, we must determine what the normal (or “natural”) levels of usage are for the two

main factors of production: capital and labor. Next, we ask what kinds of economic events or shocks play

a role in determining output and inflation in the short run. We do so using three distinct perspectives.

Our first approach, the real business cycle (RBC) approach, highlights the role that shocks to the

production function (including total factor productivity) play in causing business cycles. In previous

chapters, we discussed how such supply-based shocks affect output and factor employment. Here, we

learn that such shocks will affect the price level.

In our second approach, we will re-examine the role of changes in the money supply in

determining output and the price level in the short run. In a previous chapter, we learned about the

classical model, in which changes in the money supply brought about changes in the price level on a

one-to-one basis (in percent), but with no change in any real variable. However, many economists would

argue that the classical model fails in the short run. Instead, prices do not adjust fully in short run in the

way that the classical model suggests. For this reason, changes in money can have impacts on output in

the short-run – but not the long run.

Our third approach focuses on the response of the output gap to autonomous shocks of

aggregate demand: autonomous changes in consumption, investment, government spending, and non-

structural taxes. Economists often call this a Keynesian approach, since analyses like these grew out of

the work of John Manyard Keynes’ classic 1936 book the General Theory of Output, Employment,

Interest, and Money. For this analysis, we will assume that prices remain fixed. Doing so allows us to

focus on other aspects of the analysis: how an initial shock may ripple through the economy. In some

case, the shock’s impact may be enlarged or multiplied: a one-dollar increase in spending may bring

about a change in output that is greater than one dollar. This analysis will give us an important tool: a

multiplier that will tell us by how much output will change if there is an autonomous shock to

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demand.[key term: multiplier; a factor which summarizes the magnitude of a response relative to some

initial shock.] (In later chapters, we will extend this multiplier analysis to the case of flexible prices).

These approaches are very different. Each of them approaches has its ardent supporters --

researchers who are ready to debate why their approach best describes the behavior of an economy.

However, many economists would agree that these approaches are not mutually exclusive. Each has

important and useful insights.

To close the chapter, we will introduce the Phillips Curve (PC) -- a closely relation to the SRAS.

Phillips Curve (PC). Macroeconomists have come to rely on the PC as tool to help the analyze inflation in

the short run. In a PC, three key components help explain inflation. First, firms will raise their own

output prices if they expect that other firms are also raising theirs. Hence, there is a self-fulfilling

element to the PC: today’s inflation is in part due to the market’s expectations of inflation. Second,

demand pressures, as reflected in the output gap, will raise inflation. Higher demand pressures will raise

firms costs – some of which they will pass on to their customers in the form of higher prices. The third

element reflects the supply side -- production based shocks. For example, if there is an extraordinarily

good harvest food prices will go down, helping to restrain inflation.

10.1 Measuring Potential Output and the Output Gap

LO 10.1 Define and calculate potential output and the output gap, using the production function

approach.

We have used the Cobb-Douglas production function to describe a country’s total output:

In previous chapters, we learned that the installed stock of capital K(inst) is accumulation of past

investment flows taking away deprecation. The level of capital in use at any time was simply the level of

installed capital times the rate of capacity utilization: K=K(inst)*cu. Likewise, we defined the

(10.1)

Total Output Total Capital LaborFactor

Pr

α

oductivity

1-αY = A * K L

LO 10.1

4

employment of labor L as the total labor force LF times the employment rate er.1 We learned that total

output depended not only on how much of each factor we had (installed capital, labor force) but also

the level of usage of each of these factors – the total amount of the factor times its rate of utilization.

Finally, we learned that, if we knew Y, K, and L, we would be able to algebraically ‘back out’ total factor

productivity A.

Importantly, our rates of utilization and employment are not typically 100%. We do not fully use

all of our capital or our labor force any given time. For example, suppose that our installed capital stock

was a fleet of 100 trucks. We would not expect all 100 of these trucks to be in use at the same time. On

average, 20 of these trucks might remain unused. They might be in the shop for cleaning, inspection, or

maintenance. Or perhaps some of these 20 trucks may simply be held in reserve for emergency jobs.

Then, we would say that the natural rate of capacity utilization for our truck fleet would be

*cu = (100 -20) /100 = 80% , where “cu” is capacity utilization.

Likewise, suppose we had 100 workers in our labor force. We would not expect that all of these

workers are fully employed at any given time. Suppose that on average, 7 of these workers are in

between jobs – moving from one employer to the next. Such workers have chosen to remain

unemployed while they search for the next job. In a previous chapter, we discussed structural

unemployment that arises in part from the job search process. In this case, the natural rate of

unemployment would be *ur = 7 /100 = 7% , where “ur” stands for unemployment rate. Since the total

labor force equals unemployed workers plus employed workers, the corresponding natural rate of

employment would be .*er = (100 - 7) /100 = 93% That is, the natural rate of employment would be

100% minus the natural rate of unemployment.

We may now use the Cobb-Douglas function to tell us what potential output PY is:

1 We learned that a more accurate way to measure employment would be to use the ‘number of person hours.’ The ‘number of workers’ is a simpler measure, but it assumes that the number of hours worked is the same amongst all workers and does not change over time – something we know to be untrue

* * 1)

Potential Natural level of Natural levelTotalO

P

utput employmentof capital usageFactorProducitivity

α αY = A (K(inst)*cu *(LF*er ) (10.2)

5

FURTHER TO THE POINT: The Output Gap and Factor Utilization in the United

States To assess potential output and the output gap for the United States, we

rely on a frequently cited measure of the U.S. output gap that the

Congressional Budget Office (CBO) of the United States computes. 2 Figures 10.1.a and 10.1.b, in the left

part of the Figure 10.1 panel, plot the CBO’s measure of the output gap against both the rate of capacity

utilization (cu) and the employment rate (er), respectively. Both of the measures of factor usage move

quite closely with the output gap (measured in percent of potential output).

These figures also show the advantage of looking at the output gap in percent rather than in

dollars (or other currency unit): we can compare upturns and downturns over time. For example, we can

see that there was a severe downturn (negative output gap) during 1980-83. But this downturn was less

severe than the more recent on that began in 2007. In both episodes the rate of utilization of the capital

stock went down, but the drop in capacity utilization was even more severe in the later episode.

And we can see that, according to this one number, the drop in employment in these two

episodes was about as severe. However, as we mentioned in the introduction to the book, looking at

just this one number on employment will not entirely capture worker’s duress during an economic

downturn. For example, the number of long-term unemployed -- people who had been unemployed for

15 weeks or more -- was much more severe in the downturn of 2007-09 than in previous episodes.

The table to the right in Figures 10.1a and b illustrates how potential output and the output gap are

computed, using the example of the United States in 2009. Total factor productivity, computed as in

chapter 4, is A=0.14, while we assume capital’s share to be = 0.3. The total capital stock is in 2009 is

$44532 billion, while the total labor force is just over 154 million people. In Part A of the table, potential

output YP is calculated. The natural rate of capacity utilization is 81%. Accordingly, the natural level of

capital usage is .81 * $44532 billion = $36059 billion.

2 In some instances, the calculations used here are simplified versions of the CBO’s numbers, so they may not match exactly. For example, CBO itself does not rely on capacity utilization per se but instead uses an “index of capital services.” However, the ideas are similar.

Further to the Point….

6

Figure 10.1 United States

Capacity Utilization, Employment, Potential Output, and the Output Gap

-10.0

-8.0

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09

In p

erc

en

t

US: Output gap and capacity utilizationSource: CBO and BEA

Capacity utilization (cu) left axis

Output gap -- right axis

In p

erc

en

tof p

ote

nti

al o

utp

ut

-10.0

-8.0

-6.0

-4.0

-2.0

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87.0%

88.0%

89.0%

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93.0%

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95.0%

96.0%

97.0%

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In p

erc

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US: Output gap and employment rateSource: CBO and BEA

Employment rate (er) left axis

Output gap -- right axis

In p

erc

en

tof p

ote

nti

al o

utp

ut

These diagrams show that the output gap is positively correlated with capacity utilization (upper diagram) and the employment rate (lower diagram).

This table shows data for the United States in 2009. Potential output is computed by using the natural rates of capital utilization and employment (data from 2007, when the output gap was zero). The calculations confirm that the output gap was negative in 2009 because the capital stock and the labor force were both used at rates which were substantially below their natural rates.

a.

b.

Total Factor Productivity A 0.14

Labor's share 0.3

Capital Stock K 44532

Labor force L 154142

A. Potential Output YP 13792.0

Natural Rate of Capacity Utilization cu* 0.81

Natural Rate of Employment er* 0.95

Natural Level of Capital Usage K*cu* 36059

Natural Level of Employment L*er* 147017

B. Observed Output Y 12703.1

Observed Rate of Capacity Utilization cu 0.69

Observed Rate of Employment er 0.91

Observed Level of Capital Usage K*cu 30790

Observed Level of Employment L*er 139878

C. Output Gap

In Dollars GAP= -1088.9

In Percent gap= -7.9%

United States, 2009

Calculation of Potential Output and Output Gap

7

The natural rate of employment is 95% (natural unemployment rate ur*=5%). Accordingly, the natural

level of employment is .95*154 million=147 million. Thus potential output is YP=$13792 billion dollars.

Part B of the table shows the calculation of observed output when both capital and labor are used at

their observed rates -- rates that are lower than their natural rates. In this case, the capacity utilization

rate is 69%; therefore, the amount of capital that is used in production $30790 billion. The employment

rate is assumed to be 91% (unemployment rate is 9%). Hence, total employment is 140 million people.

Accordingly, output is $12703 billion.

Part C presents two calculations of the output gap. We may measure it in dollars: GAP = Y minus YP. In

this example, there is a negative output gap: GAP $12703-$13792= -$1088.9 billion dollars. However, it

can be more convenient to measure the output gap in percent of potential output: gap =(Y-YP)/YP. In this

case, the output gap (in percent of potential output) is ( $12703-$13792)/ -$13792=-7.9%. END

FURTHER TO THE POINT

10.2 Production Based Shocks and Economic Fluctuations: An AS/AD Approach

LO 10.2 Show how production based shocks will have effects on output the price level, and employment in the short run

In this book we have repeatedly emphasized fluctuations in economic activity can often be traced

directly to the production function. On the supply side, we note that the initial level of potential output

may be written as a function of initial levels of total factor productivity, capital, and labor (retaining the

Cobb-Douglas function that we’ve used all along):

If we inspect the Cobb-Douglas functional form, we see that output will change if any of the elements of

the production function – A,K,or L, -- change. We have previously learned reasons why these elements

may change. Total factor productivity, A, may change if there is some change to technology or policy.

Employment of labor, L, may change if people enter or leave the labor market, if workers accept a job or

are separated from their job, or if people migrate into or out of the country. The rate of capital

P α 1-α0 0 0 0Y = A *K *L

LO 10.2

(10.3)

8

utilization may rise or fall and the size of the capital stock itself will change when new capital is created

or existing capital is destroyed.

Regarding total factor productivity, our previous discussions have primarily focused on the implications

of a permanent (once-and-for-all) change in A. We noted that such a permanent shift would cause some

other variables would change temporarily, before reverting to the original steady state values. 3

In this section, we will add two new elements to our previous discussions of changes in productivity.

First, in contrast to permanent (once-and-for-all) shocks, we will now also analyze cases where A

changes for one or several periods before reverting to its previous norm -- temporary shocks to

productivity. Examples might include a temporary change in oil prices or a natural event that changes

productivity. For example, during 2012’s Superstorm Sandy, houses and buildings were destroyed,

transportation was disabled, and electricity and telephones were disabled, jobs were lost, and lives were

disrupted.

Second, we need be more explicit about an idea that we have previously discussed: since a change in A

brings about changes in the marginal products of both capital and labor and therefore the demands for

3 These included net capital accumulation (which is zero in the steady state) and the marginal product of capital. At the same time, other variables changed on a permanent basis. Important examples of such a result included output, consumption, and the capital stock (ratio per worker) and the marginal product of labor (which initially rose, and then fell somewhat, but did not return to its initial steady state but rather converged to a new, higher, steady state.)

P α 1-αY = A *K *L

Higher total factor productivity raises marginal product of labor – higher demand –brining in more workers at a higher wage rate.

Higher total factor productivity raises marginal product of capital – higher demand – increasing capital utilization (short-run) and encouraging investment (long-run).

Shocks to total factor productivity (A) will affect employment of labor (L) and capital (K):

Figure 10.2

9

each of these factors. Figure 10.2 illustrates the linkage between total factor productivity (A) and

employment of capital and labor. For example, suppose that A rises, boosting the marginal products of

labor and capital. When we studied labor markets, we learned that (as a direct impact) the labor

demand curve would shift rightward and the employment rate would rise, as more people accept jobs at

higher wage rates. In this chapter, we will extend this logic to capital utilization: when A rises,

entrepreneurs use their pre-existing capital stock more intensively.

Thus, the main message of Figure 10.2 is that a change in A can cause the other factors of production to

change as well. We can quantify this idea by defining a production based shock (pbs) that

comprehensively captures all of these effects at once:

Equation 10.4 tells us that to compute the pbs, we simply compute the growth factor as we did in a

previous chapter and then subtract one to get the growth rate. We can also see that the rightmost part

of expression (10.4) includes the contributions of both capita and labor that we developed in previous

chapters.

We have emphasized that production based shocks can be temporary. In this case, we can clearly see

that such temporary shocks will cause the aggregate supply (YS) to deviate from potential output (YP)

according to:

Thus, suppose that YP is $14.0 Trillion and pbs – the combined effect of changes in A, K and L, is 5%. This

means that YS is $14*1.05=$14.9 Trillion. Figure 10.3.a (top panel) shows aggregate supply as vertical

red lines.

Total factpr Capital stock Labor supply productivi

α 1-α

0

ty

0

0

A K Lpbs = "growth factor" -1 = * * -1

A K L

(10.4)

Production Aggregate supply Initial potential

S P0

based shockoutput

Y = Y *[1 + pbs ] (10.5)

(10.4)

10

basebase

ii

iiii

0.85

0.90

0.95

1.00

1.05

1.10

1.15

12.2 12.7 13.2 13.7 14.2 14.7 15.2 15.7

base

i

ii

80.0

85.0

90.0

95.0

100.0

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125.0 130.0 135.0 140.0 145.0 150.0 155.0 160.0 165.0

basebase

ii

iiii

2.0%

3.0%

4.0%

5.0%

6.0%

7.0%

8.0%

9.0%

10.0%

74.0% 76.0% 78.0% 80.0% 82.0% 84.0%

a. Aggregate Demand and Supply for Goods and ServicesEquilibrium Price and Output

Output -- Tril l ions of Dollars

b. Labor Demand and SupplyReal Wage and Employment

Employment -- Mill ions of Workers

c. Capacity Utilization

Usage of installed capital (in percent)

Aggregate Supply of Goods and Services (Ys): red vertical lines; determined by production function -- total factor productivity and factor usage (capital, labor).

Scenario (i): The rightward shift from solid to dotted line reflects a favorable production based shock (pbs). Initially, tot al factor productivity increases (TFP). As a response, both employment of labor and capital utilization will also rise (see charts below). While supply expands, the demand curve remains in its initial place. For markets to clear the aggregate price level must fall. The economy moves from base (b) to scenario i.

Scenario (ii): The leftward shift from solid to dotted line reflects an adverse pbs. Initially, TFP falls. Both employment of labor and capital utilization will also fall. (see charts below). While supply contracts, the demand curve remains in its ini tial

Aggregate Demand for Goods and Services (AD): blue line slopes downward, reflecting the real balance effect -- an inverse relationship between aggregate demand and the price level for a given level of the money supply.

Supply of Labor (Ls): Blue lines slope upward, reflecting substitution effect / increasing opportunity cost of leisure.

Demand for Labor (Ld): Green lines slope downward, reflecting the diminishing marginal product of labor.

Scenario (i): The increase in total factor productivity implies a rightward shift in labor demand, from solid to dotted. Thisshift brings about an increase in both employment and the real wage, from base to alt(i)

Scenario (ii): The decrease in total factor productivity implies leftward shift in labor demand, from solid to dashed. This shift brings about a decrease in both employment and the real wage, from base to alt(ii)

Capacity utilization (cu): Purple line slope upward, reflecting a positive relationship between the marginal product of capital and capacity utilization.

Scenario (i): The increase in total factor productivity implies an increase in the marginal product of capital. If the increase in TFP is temporary (a "one-off") firms will use their existing capital stock more intensively, so capacity utilization must rise, from base to alt(i).

Scenario (ii): The decrease in TFP means that the marginal product of capital will fall. If this decrease is a "one-off" firms

Pri

ce L

eve

l (in

de

x, b

ase

=1.0

)R

eal

wag

e(i

nd

ex,

bas

e=1

00)

Ma

rg. p

rod

. of

cap

ita

l min

us

dep

.

Figure 10.3 Production Based Shocks

Aggregate Supply, Demand, and Prices

11

Note that, in this figure, output is shown in the horizontal axis while the price level shown on the vertical

axis. The aggregate supply curve is vertical: in this model the aggregate supply does not depend on the

price level. 4

The solid red line shows the baseline scenario where there is no shock (pbs=0) and hence aggregate

supply equals potential output. To the right, the dotted red line for alternative scenario (i) reflects a

favorable supply shock (pbs>0). To the left, the dashed red line shows alternative scenario (ii), an

adverse supply shock (pbs<0). The aggregate demand (AD) curve is essentially the same on that we

introduced in Chapter 9. However, we re-write it in a way that shows how aggregate demand might

deviate from some initial level of output: The right hand side shows the money growth minus price

growth – the percent change in real balances.

In the right hand side of this equation, M and M0 are, respectively, the prospective and initial (or

reference) levels of money, while P and P0 are the prospective and initial (or reference) price levels. For

simplicity, we assume P0=1. In our investigation of the effect of supply-side shocks, we will hold the

money supply constant. (We will discuss the effects of money supply growth later in this chapter.)

Therefore, we may simplify the aggregate demand function even further:

This aggregate demand curve is shown as the downward sloping blue line in the Figure 10.3.a (top

panel). We previously learned why the aggregate demand curve slopes downward: when the price level

increases, our money real balances are worth less so we purchase less.

4 That is, this model has assumed that the classical neutrality result that was developed in the previous chapter must hold.

Aggregate Initial Growth of

Real balanc

prices demand Ou

e effect-constant money suppl

0 0

t ut

y

p

AD = Y *(1- (P / P -1)] (10.7)

Aggregate Initial Money growth Growth of

Real balance eff

prices demand O

0 0 0

utec

ut

p t

AD = Y *(1+(M/M -1)- (P /P -1)](10.6)

12

The figure illustrates an important implication of the model: output and prices are negatively related

with one another. When output rises as a result of a favorable production based shock (pbs>0), the price

level falls. When an adverse value of pbs causes output to fall, prices rise. Thus, in Figure 10.3.a, under

scenario (i), as output rises, the equilibrium price level falls. This must be the case, since the same

money supply (recall that we’ve assumed the money supply to be unchanged) is now used to conduct

more transactions and purchase more goods.

Therefore (and since velocity is assumed to be constant) the price level must fall. A constant money

supply is now being used to conduct more transactions and purchase more goods than previously, so

the price level must fall. In the other direction, under scenario (ii), as output falls, the equilibrium price

level rises.. A constant money supply is now being used to conduct fewer transactions and purchase

fewer goods than previously, so the price level must rise. Here, too much money is chasing too few

goods

We can also use an equation to confirm that output and the price level are negatively related to one

another. We equate aggregate supply from equation (10.5) and aggregate demand from equation (10.7)

and solve out for the current price P:

Thus, equation 10.8 confirms the idea that pbs shocks and the price level are inversely related, as we see

in the Figure 10.3.a (top panel). We also see the implications of a production based shock in for the

employment of labor in the middle panel of Figure 10.3.b (middle panel) In the diagram, horizontal axis

is employment, in millions of workers, while the vertical axis shows a real wage index (base value = 100).

This line slopes upward. As we learned in a previous chapter, when the wage rises, more workers will be

encouraged to accept a job (since the market wage now equals or exceeds the reservation wage for

more potential workers). The demand for labor (Ld) under the baseline scenario is captured by the green

line that slopes downward, reflecting the diminishing marginal product of labor.

Under scenario (i) the increase in total factor productivity (TFP) brings about a rightward shift in labor

demand, from the solid green to dotted green line. In order to draw even more workers into

employment, the real wage must increase from its baseline value. Thus, as the economy moves from

base to alt(i), we observe an increase in both employment and the real wage (w). Symmetrically, under

(10.8) 0P = P *(1-pbs)

13

scenario (i) the decrease in TFP productivity brings about a leftward shift in labor demand, from the solid

green to dashed green line. As more workers separate from their jobs, the real wage must increase from

its baseline value. This makes sense: when the economy is in a ‘down phase’ (pbs<0), workers typically

accept lower wages. Thus, as the economy moves from base to alt(ii), we observe an decrease in both

employment and the real wage rate.

Figure 10.3.c (bottom panel) shows us how temporary (one-time-only) shocks to the production

function will affect the capital utilization ratio. Recall that there is a permanent increase in TFP, the firm

will invest more and build the capital stock to a new, higher optimal level. In the other direction, if there

is a permanent decrease in TFP, the firm will invest less and let the capital stock fall to its new, lower,

optimal level. However, if the change to TFP is a ‘one off’ the long run optimum level of capital does not

change.

Instead, firms will use some of their spare capacity if there is a temporary increase in productivity, but

will let some of their capital stock remain idle if there is a temporary decrease in productivity, as shown

in Figure 10.3.c (bottom panel). The horizontal axis shows the rate of capacity utilization (natural value

– 80%), while the vertical axis shows the marginal product of capital. The purple line is a capacity

utilization relationship – the curve slopes upward, reflecting a positive relationship between the

marginal product of capital and capacity utilization. Under the baseline scenario, where the marginal

product of capital is at its long run level, capacity utilization is also at its long run (or natural) level.

Under scenario (i), the increase in total factor productivity implies an increase in the marginal product of

capital. When such a shock takes place on a "one-off" basis, firms will use their existing capital stock

more intensively. There will be more and longer shifts. Firms will now use machinery and vehicles that

might ordinarily sit idle as spare equipment. The economy moves from base to alt(i). Under scenario (i),

and TFP falls a "one-off" basis, firms will use their existing capital less more intensively. There will be

fewer and shorter shifts. Firms will now let sit idle some machinery and vehicles that might ordinarily be

in active use. The economy moves from base to alt(ii).

10.3 Output Effects of Money Supply Changes: Misperceptions and Rigidities

LO 10.3 Show conditions under which changes in the money supply will affect aggregate demand, output, and employment in the short-run – even though money remains neutral in the long run.

The classical model, which we learned about in the previous chapter, told us that money is neutral: a

change in the level of the money supply will affect only the price level while leaving real output

LO 10.3

14

unchanged. To illustrate an environment in which classical neutrality would hold, we introduced a

simple model in which participants produced and consumed pre-determined amounts of just two goods

– cookies and juice.

One important feature of this model was full information: if the money supply changed, everyone

instantly knew that that change took place and by exactly how much. In addition, the model assumes

full price flexibility: market participants are free to change the prices of their cookies and juice

immediately—and they do so. Thus, in the cookies-and-juice model, if the money supply were to

increase by, say, 10%, everyone will not only know about this change but will immediately increase the

prices of their product, be it cookies or juice, by exactly 10%, with no change in output.

We can rephrase in a more precise way what the assumption of full information means. Economists

often say that market participants form expectations about price growth based on their knowledge of

money growth. (key term: expectations). If the money supply grows by 10%, participants in the cookies

in juice expect the price level to rise by 10% -- and they act accordingly. We can thus think of classical

model as one that draws a connection between the expected price level Pe and the money supply M

relative to its baseline level M0:

This equation thus tells us that, in the classical model, the expected price level is linked one-to-one with

money growth – something known by all. As in the cookies and juice model, market participants will

price their goods exactly according to their expectations. For example, if a cookie producer expects

prices to rise by 10%, they will also increase the price of their cookies in the market – by exactly 10%.

The real world is more complex. There are several reasons why equation (10.8) may not hold in the

short run. First, people in the real world may not be as informed as those who inhabit the cookies-and-

juice world. When a money supply change takes place, not everyone may know. Rather, in complex

economies, market participants have to distinguish between aggregate shocks and sector-specific

1

EXPECTED increase Increase in in prices money supply

Classical model --all market participants fully informed.

e

0 0

P M-1

P M (10.9)

15

shocks. (Key term: sector specific shocks: an economic event that originates in a specific sector,

including a shift in the demand or supply for specific goods or services) An example of an aggregate

shock – a shock that affects the entire market – would be a change in the money supply. An example of

a sector-specific shock would be some change in the conditions to one’s own specific market – for

example, an increase in the demand for one’s own product.

Is Dave A Fool? Aggregate versus Sector-Specific Shocks

Let us now bring back Dave, the furniture maker whom we introduced in an earlier chapter. At some

point in time, Dave may observe that the demand for his chairs has risen. He may conclude that that

there has been a shock that is specific to the furniture sector: people are buying more chairs -- perhaps

because of warmer weather. Alternatively, and even better for Dave, people may be buying more of his

chairs, reflecting that the reputation of his firm’s products in particular have improved.

However, it is also possible an increase in the money supply has occurred but Dave is not aware of it.

Instead, Dave has mistakenly identified such an aggregate shock as one a sector specific shock. If Dave

has made this mistake, he will also erroneously conclude that the price level will remain constant --

when in fact it will rise.

How should we describe Dave’s behavior? Previous generations of economists, who tended to be very

gracious, might have said that Dave could make such a mistake because he suffers from money illusion

(key term: money illusion; the idea that market participants cannot distinguish nominal from real

variables). Younger economists, who are less gracious and forgiving, might say that Dave is simply

irrational – perhaps foolish or stupid.

However, such a judgment on Dave may be too rash. Dave may succumb to such a misperception

because a modern economy is dynamic and complex. Without notice, both aggregate and sector specific

shocks can take place at any time. Dave might hire an economic consultant to help him with the

daunting task of interpreting the many market signals that bombard him every day. In fact, many

entrepreneurs and labor unions do precisely that. They hire smart economists to help them make sense

16

of the market. However, even the smartest economist will make mistakes. They also may succumb to

the same misperceptions as Dave has.

Building the Short-Run Aggregate Supply Curve

We may apply our reasoning about Dave to the entire economy. Let us suppose that, in addition to

Dave, many other entrepreneurs suffer misperceive aggregate and sector-specific shocks in the same

way. Now suppose that the money supply rises. People will spend that newly created money in all

sectors of the economy. However, other entrepreneurs conclude, like Dave initially did, that the extra

spending falls on their good or service – that the shock is sector specific and not aggregate in nature.

They see their prices rising, but they not expect the general price level to rise – or they may expect it to

rise by less. Like Dave, these other entrepreneurs, who were also confused between sector-specific and

aggregate demand, also increase their output – in the short run. They do so because prices are growing

at a rate that is greater than they had expected.

Thus, we have a key idea in macroeconomics: only an unexpected change in the price level will bring

about a change in aggregate quantity of output supplied; a fully expected change in prices will not. We

may summarize this idea in an equation for short-run aggregate supply:

Note that the first term on the right hand side is a familiar one: potential output. The term SRAS,Pη is the

short-elasticity of aggregate supply. It tells us by how much supply increases if prices increase more than

we expect them to increase. Hence, suppose that all prices increase by one percent. If everyone

expected this price rise to take place, there will be no change in the quantity of goods and services

provided -- aggregate supply remains is constant at its potential level.

However, let us assume that the short run elasticity of supply is greater than zero: SRAS,Pη > 0. In this

case, if the price level is greater than expected, the quantity of goods and services supplied by firms will

rise above potential. In the other direction, if the price level is less than expected, the quantity of goods

Short-run Potential Price growth Expected Price GrowthElasticity of short Aggregate Output

run aggregate supply supply w

ssr P e

ith respect to price

SRAS,

s

P 0 0Y = Y *(1+ η *[(P / P -1) (P / P -1) ]] (10.10)

Figure 10.4 Aggregate Supply –Short- and Long- Run

17

and services supplied by firms will fall below potential. As we will see below, the expected price level

can only differ from its actual value in the short run – not the long run. For this reason, the quantity of

goods and services supplied can only deviate from potential output in the short run – not the long run.

These are key points in macroeconomics that the work of Professor Robert Lucas emphasized. For this

reason, we call a supply function such as equation (10.9), which focuses on the difference between

expected and actual prices, a Lucas Supply Function.

Figure 10.4 illustrates these ideas in a graphical manner. On the vertical axis we find the price level while

on the horizontal axis we find the level of output. The black vertical line shows the output at is long-run

or potential level. The upward sloping red curve shows the short-run aggregate supply curve for a given

level of expected prices. The upward slope of this curve ( SRAS,Pη > 0) confirms that, when prices rise

above (fall below) their expected level, the quantity of goods and services rises above (falls below) the

long-run potential level.

Forming Expectations about the Price Level: We won’t get fooled again

Let us now revisit our expression for price expectations. If there are misperceptions, price expectations

and money will not be tightly linked on a one-to-one basis. Instead, to capture misperceptions, we may

instead write:

* 1

Update

FacEXPECTED increase Increase

to i

e

0 0n

in prices money supply

r

P M-1 λ

P M

Figure 10.4

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000

Pri

ce L

eve

l (In

de

x, B

ase

= 1

)

Aggregate Supply and Demand (Y)Billion US Dollars

Aggregate Demand and Supply For Goods and ServicesPrice determination: Short- versus long- run

Long Run Aggregate Supply of Goods and Services (YP): the black

vertical line shows us potential output -- the amount that will be produced if capital and labor are both used at their natural (or

Short Run Aggregate Supply of Goods and Services (YSRAS): the red upward sloping shows us the short run relationship between the price level and output for a given, constant, level of expected prices.

In the short run, output will exceed the potential level if factors are employed at levels above their natural level; output will be less than potential level if factors are employed at levels below their natural level.

(10.11)

18

This equation is similar to equation 10.8 above but it includes a new term: we call λ (Greek

letter “lambda”) an ‘update factor’ because it reflects the degree to which market participants have

updated their information about money growth and have taken actions according to that information. If

Dave and other entrepreneurs suffer from full money illusion, λ =0. If Dave does not suffer from any

money illusion and is fully informed about money changes (much like the participants in the cookies-

and-juice model) λ =1. If Dave is only suffering partial money illusion, 0< λ <1. In this intermediate case,

it may be that market participants misperceive aggregate shocks to be market-specific ones.

While money illusion can exist over the short run, it cannot be a part of a long-term macroeconomic

model. Ultimately, market participants must ultimately know exactly by exactly how much the money

supply has grown – even if they were initially fooled. Thus, as Figure 10.5 shows, λ may start from a

very low level immediately after the change in the money supply. This indicates that people have been

fooled. However, over the long run, when people understand that the money supply has changed, the

value of λ will converge to unity.

Figure 10.5 shows examples of alternative paths for λ . The solid blue line shows the most rapid growth

of λ , corresponding to a more rapid -- but not immediate – convergence of the prices and wages to their

long run levels. The dashed red and dotted purple lines show slower convergences of λ to unity.

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

0 2 4 6 8 10 12 14 16Periods of time

Update factor lAlternative speeds of adjustment to

change in money supply

Lam

bd

a(l

)

Medium

Slow

Fast

Figure 10.5

19

FURTHER TO THE POINT: Learning about money shocks in different economic environments.

How quickly will λ converge to unity? In an influential 1973 paper, Robert Lucas suggested

that such adjustments would take place more rapidly in countries with higher and more

volatile inflation rates. In such countries, shifts to the aggregate demand curve occur more frequently

and are of greater magnitude than sector specific shocks. Hence, in these countries, any given shock

would be more likely to be an aggregate shock than a sector specific one, and market participants will

form their expectations of inflation accordingly. By contrast, in countries with low and stable inflation

rates – like the country Dave lives in – market participants may take a more gradual approach toward

concluding that a given shock is an aggregate shock. By this reasoning, we can see that if Dave’s factory

had been located in Argentina, we would have expected the adjustment of market prices to take place

more rapidly than in a country like the United States or the United Kingdom, where price growth is more

stable and predictable. END FURTHER TO THE POINT.

We are now in a position to show how the economy reacts to a one-time increase in the money supply.

To see what happens, we substitute the expression for expectations formation (equation 10.10) into

supply equation 10.9 to obtain:

When we combine the aggregate demand equation with the aggregate supply equation, we can solve

for equilibrium output and prices. Figure 10.6 shows how prices rise gradually while output temporarily

rises above its potential level when there is a one-time increase in the money supply. Initially, λ =0; this

might reflect that the central bank’s choice of money supply has come as a complete surprise to market

participants. Then, as the market gradually updates, we assume that λ will take on the values of 0.33,

0.66, and finally, 1.0.

The short-run aggregate supply curves with sticky prices (Yssr) are shown by a series of red lines. The

lines are horizontal, indicating that in the short run, sellers keep prices fixed. The aggregate demand

curve is, again, the downward sloping blue line. When the money supply increases, the aggregate

demand curve shifts to the right. Initially, the economy remains on the solid red line, which represents

the original price level; sellers have not raised their prices, even though the money supply has increased

Short-run Potential Price growth Expected Price GrowthElasticity of short Aggregate Outputrun aggregate supply

ssr PSRAS,

supply with resp

P 0 0

ect to prices

Y = Y *(1+ η *[(P / P -1) λ(M/ M -1) ]](10.12)

Further to the Point….

20

(l=0). Instead, the output gap increases, in response to extra demand (in this example, output increases

by 8%).

Then, sellers gradually update their prices. The short-run aggregate supply curve shifts upwards, as

reflected in the dotted lines (l=0.33, l=0.66). As this happens, prices rise. Output recedes, but remains

above its long run potential. When sellers fully incorporate the change in the money supply into their

prices (l=1) short run aggregate supply reaches the double red line. In the end, prices rise one-to-one

with money growth, while output has returned to its long run potential.

Further to the Point/Online Feature: Sticky wages and monetary non-neutrality. Learn

about an alternative version of the AS/AD model where wages, rather than output prices,

adjust only over time, owing to wages that were determined by a previous contract. End Callout Further

to the point online.

Figure 10.6

Figure 10.6

Where did we get those numbers/online feature: Learn

the model that produced the numbers in this chart. End

callout Where did we get those numbers?

Baseline alt(i) alt(ii)

Output 13260 13525 13931

Inflation 3 2.4 2.9

Interest Rate 4.5 4.7 4.6

Where did we get those

numbers?

ONLINE FEATURE

Further to the Point*….

*Online Feature.

Baseline alt(i) alt(ii)

Ms 6663 7329.3 5996.7

%DMs 10.0% -10.0%

l … 0.00 0.33 0.66 1.00

Peq1.0 1.02 1.05 1.07 1.10

peq 2.0% 4.6% 7.3% 10.0%

Yeq 13206 14262 13914 13565 13206

gap 0.0% 8.0% 5.4% 2.7% 0.0%

Money supply chosen

% change from baseline.

Equilbrium price level

% change from baseline

Baseline After money supply change

Update factor

Equilbrium output

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

1.40

8000 9000 10000 11000 12000 13000 14000 15000 16000 17000 18000

Pri

ce L

eve

l (In

de

x, B

ase

= 1

)

Aggregate Supply and Demand (Y)Billion US Dollars

Aggregate Demand and Supply For Goods and ServicesPrice determination: Short- versus long- run

l=0l=0.33

l=0.66l=1

Aggregate Demand for Goods and Services (Yd): blue line slopes

downward, reflecting the real balance effect -- an inverse relationship between aggregate demand and the price level for a

given level of the money supply. When the money supply

Short Run Aggregate Supply of Goods and Services (Yssr): red

upward sloping lines; in the short run. Intially,sellers remain on

the supply curve reflected by the solid line (l=0), while output

rises. As sellers gradually update their prices, the lines shift

upwards (l=0.33,0.66); as this happens, output recedes but remains above potential. Eventually, prices fully reflects money

growth (l=1). At this point, output returns to potential.

Equilbrium output gap

21

Sticky prices: when we learn something, do we act immediately – or do we wait?

So far, we have suggested that classical neutrality might break down when there agents misperceive the

magnitude of a money shock. If money rises by 10%, but λ is say, 0.1, the market will believe that the

money supply has risen by only 1% -- as their initial guess. However, we may interpret the adjustment

factor λ in another way: it is possible that market participants do know that the money supply has risen,

and by exactly how much – but they do not raise prices immediately. Instead, prices may be rigid, rather

than fully flexible: market participants may react to news about monetary policy only on a gradual

basis.5

There are several reasons why prices may not be fully flexible. In some cases, entrepreneurs may freely

choose not to adjust prices immediately. For example, a retailer may wish to earn their customers’

goodwill by keeping prices fixed rather than permitting them to change on a day-to-day basis – even as

conditions in the market change. Other prices may be held constant in a written contract. The issue of

contracts is especially important in labor markets – as we will soon see. Finally, in the short run, it may

be costly for firms to change their prices on a continual basis. A classic example is restaurant menus.

Prices for the main input of a restaurants product – food and foodstuffs – may change on a day-to-day

basis. Prices of such basics as flour, tomatoes, cheese, and pepperoni may change daily.

However, it may be prohibitively costly for restaurants to print new menus so frequently. Of course, this

depends on the physical nature of the menu itself. In some cases, new menus can be easily printed on a

computer. For a small restaurant, reprinting a menu on a daily basis may not be so costly. However,

most restaurants use menus that are more elaborate and more costly to produce. It also may be the

case that, in order to avoid angering their loyal customers, restaurants may opt to keep prices fixed on a

day-to-day basis. Such a motive to maintain client goodwill may be most important for restaurants –

even if the restaurant’s owner can easily print a new menu!

5 The idea that λ that approaches unity on a gradual basis is similar implies that each period, only a certain

fraction of firms can adjust their prices – firms must ‘wait for their turn.’ This approach is known as “Calvo-pricing,” named after Guillermo Calvo, a professor at Columbia University, who helped develop the approach. (See Calvo, Guillermo, “Staggered Prices in a Utility-Maximizing Framework,” Journal of. Monetary Economics, 1983, 12(3), pp. 383-98. )

22

FURTHER TO THE POINT: How frequently do prices change? Research by Professors Mark

Bils and Peter Klenow suggest that, on average, firms may adjust prices more frequently

than we might think. They looked at store-level data – the same data that are used to

construct the consumer price index (CPI). They found that when we take all of the goods in

the CPI, weighted by their importance (see previous chapter), businesses will adjust their prices about

every 3 and 1/3 months.

There are some services – including clothing alterations, automobile towing, parking fees, and barber

and beauty services that are adjusted relatively infrequently – approximately every two years of

thereabouts. At the other extreme, some goods and services – gasoline, tomatoes, and airline tickets –

are adjusted within the month. Overall, according to Bils and Klenow’s investigation, prices are not

sticky enough to provide a full explanation of monetary neutrality. Rather, to explain why changes in the

money supply can have real short-run effects, sticky prices do play a role – but they are not the whole

story. End FURTHER TO THE POINT.

Category Average number of months

between price changes

Average (based on CPI weights) 3.3

Clothing alterations and repairs' 29.4

Automobile towing charges 28.7

Parking fees 26.8

Haircuts/barber shop services (men) 25.5

Beauty parlor services (women) 22.9

Shoe repair 20.4

Garbage collection 20

Pet Services 19.7

Taxi fares 19.7

Beer / ale outside home 15.2

Magazines 11.2

Movie theatre admission ticket 10.9

College textbook 9.3

Power tools 8.8

Cosmetics (women) 8.5

Automobile insurance 5.9

Suits (men) 3.3

Potato chips/snacks' 2.9

Tires 2.7

Washing machines 2.3

Airline fares 0.9

Tomatoes 0.8

Gasoline (mid/premium grade) 0.7

Source: Bils, Mark and Peter Klenow, 2004, "Some Evidence on the Importance of Sticky Prices," Journal of Political Economy, vol. 112, no.5, pp. 947 - 985

Further to the Point….

Table 10.1 How Frequently Do Prices Change?

23

What’s Your View? How Rational Must Economic Models Be? We have presented

to you a model that, while small, opens up some big questions. Unless λ equals 1,

participants’ own forecast of future prices will be wrong. Since we have assumed

that λ only gradually approaches a value of unity, we’re also assuming that market participants learn

only on a gradual basis. This feature of the model violates a key tenet of modern macroeconomics:

agents must use all of the information that is available to them when they make forecasts of the key

variables in the economy, including the price level. According to the hypothesis of rational expectations,

market participants can and do make mistakes – but they will not make the same mistakes on a

repeated basis (as they do in this model). (Key term: rational expectations: the idea that market

participants use all the information that is available to them to make forecasts that are on average

correct.)

As we warned in the beginning of this book, all models are wrong – but some are useful. The question

here is whether model that is in some sense wrong on theoretical grounds – a model like the one

presented above would probably not be publishable in top economic journals – is still useful. On this

point, there is a lively debate amongst economists. Some would find a model like this one to be an

acceptable simplification of a real world that is too complex for people to figure out immediately. Such

economists would be comfortable with λ approaching unity on a gradual basis. Others would have

rejected this perspective. In their view, information is abundant, and people are smart enough to both

understand it and act on it. According to such a view, λ may depart from unity – but only for one period.

However, there is also a middle ground between these extreme perspectives. Some economist have

emphasized that market participants actors are rational, but not infinitely so. Instead, agents who

operate under conditions of bounded rationality do not know everything immediately, but they do learn

over time. For them, interesting questions might be: “Why does λ differ from one?” and “What makes

λ change over time.” Having come this far in the book, you have become more familiar with economic

models. You have probably developed some opinions as to what is a useful economic model and what is

not. So, we ask: “What is your view?” Can we accept a model like this one as it is? Should we discard it

entirely? Or, should we try to learn more about how economic agents learn? END WHAT’S YOUR VIEW.

What’s Your View?

24

10.4 The Multiplier: How Autonomous Demand Shocks Ripple Through the Economy LO 10.4 Use the multiplier analysis to show how autonomous shocks to aggregate expenditures –

including consumption and investment – ripple through the economy, ultimately affecting the output gap.

Thus far, we have discussed two broad kinds of shocks that can have impacts on the output gap and the

business cycle: shocks to the production function and shocks to the money supply. However, economists

often want to view the business cycle from the standpoint of autonomous shocks to demand, including

those to consumption and investment that we introduced in previous chapters.

As Figure 10.7 suggests, such autonomous shocks can begin in one specific sector of an economy.

Initially, we will examine a closed economy – no exports or imports. In this case, we can see that shocks

may originate in households (consumption), firms (investment), the government, or the external sector.

However, very quickly, we see that the impact of such a shock is not limited to that sector but instead

can quickly spill over into other sectors of the economy. Ultimately, such an autonomous shock can have

a substantial impact on the entire economy -- aggregate spending and output.

FURTHER TO THE POINT: The Revival of the United States Housing Market. The

recent behavior of the US housing market is good example. 6 In the US, as

6 See Ydstie, John, “Housing Recovery Lifts Other Sectors, Too,.” NPR, May 2, 2013. Transcript of story: http://www.npr.org/2013/05/02/180613193/housing-recovery-lifts-other-sectors-too

Figure 10.7 The Ripple Effect

Further to the Point….

AutonomousConsumption, investment Government spending, shocks to demand

exports and (minus) i

AD C I G X M

mports

aut = aut + aut + aut + aut - aut

Discussed in previous chapters

To be discussed in later chapters

Output gap

gap

Autonomous shocks to aggregate demand ripple through the economy. They will have impacts on the output gap. *

*Spending multiplier: by how much does gap change when there is a one-unit shock to aggregate demand.

LO 10.4

25

elsewhere, low and falling housing prices are in part responsible for poor economic performance. The

drop in housing prices that began in 2006 helped bring on the great contraction and economic crisis of

2008-9. Thereafter, as housing prices remained stagnant, the recovery of spending and output was

anemic.

However, by 2012, the situation began to change. House prices began to recover. As the most direct

impact, companies hired more people to design and construct new houses. Shortly thereafter, we saw

how an initial shock to spending might ripple through an entire economy, bringing impacts to other

sectors. Construction workers who are now back on the job and need reliable transportation will

purchase more trucks. This means more income to automakers and their employees. New homeowners

purchase more furniture, appliances, and landscaping materials, benefitting the people who make and

sell such goods.

Such successive rounds of spending that ripple through an economy can raise everyone’s confidence.

According to Lawrence Yun, Chief Economist of the National Association of Realtors, "You have more

families feeling more comfortable, given the rise in housing wealth, that's just general spending into the

economy… (I)t's also helping to lift the employment in the retail sector and other segments of the

economy." Jim O'Sullivan, chief U.S. economist at High Frequency Economics, echoed this opinion, but

cautioned that cuts to government spending, which were occurring during the same period under the

‘sequestration’ that was ordered by the US Congress, might potentially pull down spending and output.

END FURTHER TO THE POINT

In this section, we will show in a quantitative way – numbers and algebra -- how spending shocks can

ripple through an economy and bring about impacts on the output gap. In some cases, autonomous

spending shocks can have an amplified effect on aggregate output; if there is an autonomous increase of

$1, the increase in output will be more than $1. Macroeconomists call this the multiplier effect. It is one

of the key insights of the Keynesian tradition in economics.

Even though such a multiplier effect assumes that prices are fixed, and most economists agree that such

an assumption of fixed prices is unrealistic, the idea of a multiplier effect remains an important part of

macroeconomic analysis. The multiplier will become an important tool for us in other parts of this book.

26

The Intuition of the Multiplier – A Closed Economy Example

We shall begin with a ‘warm up’ analysis that captures the basic intuition behind the multiplier. Suppose

that people whose house value rise decide to spend 1 percent more of potential output – autC=1%. If

potential output YP is $14 Trillion, the dollar amount of that initial spending shock will be .01*$14 Trillion

-- $140 billion.

When this happens, disposable income rises for not only individuals employed directly in the housing

construction but also for those who supply goods related to housing construction – lumber, cement,

electrical goods, etc. In a second round of spending, those who have received income from this new

housing activity will also increase their spending – but not by the full one percent. Rather, according to

our model, they will spend a fraction cyc(1 - σ ) of the increase in their income. Importantly, we will

assume that the economy is closed to foreign trade – no exports, no imports. This means that all of the

spending will take place in the domestic economy.

Thus, the second round of spending will be (1 - σ )cyctimes the original 1%. In a third round, people

spend that same fraction of the second round, or 2(1- σ )cyc times the original 1%. Note that this is a

smaller fraction than in the first round – (1- σ ) < 1cyc. In successive rounds, we see that the spending

increases become progressively smaller and smaller: 3(1- σ )cyc, 4(1- σ )cyc

… and so on.

Table 10.2 shows how ten successive rounds of spending, stemming from the original one percent

shock, accumulate. In each round, the amount of new spending becomes progressively smaller and

smaller. In the long run, it approaches zero – although these effects in this example get ‘close to zero’

after about four rounds. We can see that if we add up the successive rounds of spending, we find that

from an initial one percent shock to spending, output rises by 1.43%. In dollar terms, an initial $140

billion shock will boost output by $200 billion.

27

The table also reminds us we may obtain this result in another way. We may call a variable x as:

In this case, we note that 0<x<1. In this case, we may use a result from algebra that provides a solution

for an infinite series, namely:

By this logic, if x=.70, 1/(1-x)=1.43. This is our key multiplier result. It conveys a basic insight: an initial

spending shock may initiate successive rounds of spending which multiplies or amplifies the initial shock.

Importantly, this analysis assumes that prices are fixed; we have also assumed that the economy is

closed to the rest of the world – no exports or imports. We make these assumptions now to help us

focus on just one piece of the story. Later in this book, as we relax these assumptions, we will find that

multipliers tend to become smaller when prices are flexible, since prices will absorb some of the initial

shock. We will also find that the multiplier is smaller when the economy imports goods and services from

the rest of the world, since other countries’ economies will absorb some of the initial shock.

x = (1- σ )cyc

0 1 2 3 1x + x + x + x +..... =

1- x

Table 10.2: The Multiplier Effect –Part I

(10.13)

Propensity to consume out of gap 30.0%

Potential output (Trillion $) 14

1.00% 140.0 1.00% 140.0

0.30% 42.0 1.30% 182.0

0.09% 12.6 1.39% 194.6

0.03% 3.8 1.42% 198.4

0.01% 1.1 1.43% 199.5

0.00% 0.3 1.43% 199.9

0.00% 0.1 1.43% 200.0

0.00% 0.0 1.43% 200.0

0.00% 0.0 1.43% 200.0

0.00% 0.0 1.43% 200.0

0.00% 0.0 1.43% 200.0

… …

1.43% 200.0

Initial

shock

Spending in round

0 1 2 3 1x + x + x + x +..... =

1- x

Algebraic solution for

infinite series for x<1.

1 - σcyc

]1ADaut *[1-σcyc

]2ADaut *[1-σcyc

]3ADaut *[1-σcyc

]4ADaut *[1-σcyc

]5ADaut *[1-σcyc

]6ADaut *[1-σcyc

]7ADaut *[1-σcyc

]8ADaut *[1-σcyc

]9ADaut *[1-σcyc

]10ADaut *[1-σcyc

ADaut

Percent of YP

YP

Bill ion

Cumulative Impact

Percent of YP

Bill ion

ADautfull effect =

σcyc

Infinite horizon result

(10.14)

28

Aggregate Expenditures must equal Aggregate Output

This example thus helps us understand some intuition behind spending multipliers. It tells that

some initial shock to demand will ripple through the economy. However, in order for this model to be

correct, it must also be able to tell us that supply equals demand. Can we be assured that, if a spending

shock takes place, aggregate expenditures equal aggregate output?’ Here, we will show that the answer

is “yes!”

Let us recall that, at any moment, aggregate supply equals potential output plus the output gap.

We often restate this as PY = Y (1 + gap) , where “gap” in lower case is the dollar output gap as a fraction

of potential output. Below, we will see that households, firms and or the government may decide at any

time to increase or decrease their expenditures – for whatever reason. Such changes are the

autonomous shocks to expenditures that we previously discussed. We assume that such changes in

aggregate expenditures have no impact on the economy’s long run capacity to produce goods and

services. That is, autonomous shocks to aggregate expenditures have will have impacts only on the

output gap – not potential output.

Hence, we focus exclusively on how the output gap is determined – leaving aside potential

output. Initially, we will examine the case of a closed economy – no imports or exports. Instead, we

focus on the non-structural (or short-run) components of consumption (from chapter 7) and investment

(from chapter 8). In addition, we continue to assume that prices are fixed.

Consider first consumption. There are three elements of the non-structural component of

consumption. The cyclical component of consumption told us how much households change their

spending either when the output gap changed or when taxes changed on a temporary (“one-off”) basis.

The interest rate component told how much households change their spending when interest rates

change. In addition, the autonomous component captured other movements in consumption, including

more pessimism or optimism on the part of households. For our analysis, we will express the non-

structural component of consumption as a percent of potential output – much as we do for the output

gap itself. We will also ignore for the moment any effects of either taxes or interest rates. Thus, our

expression for non-structural consumption as a percent of potential output, which we denote by lower-

case “c” is:

+cyc

Autonomous Cyclical elementcomponen

C

t

c = (1 - σ )*gap autTax and interest rate effects omitted. (10.15)

29

This equation tells us that, when the output gap rises, households plan to save some proportion of that

transitory disposable income (as part of the life-cycle approach discussed in chapter 7). We called that

proportioncycσ -- the marginal propensity to save out transitory disposable income. This means that

households must consume a proportion cyc(1 - σ ) out of their transitory income (the output gap). Next,

the autonomous component Caut tells us that households can change those plans at any time, choosing

to spend more or less, in response to other elements not in the model. (For example, if they are afraid of

losing their jobs, they may spend less).

Now consider investment. Here we found that there were two parts to the non-structural component of

investment. The interest rate component told how by how much businesses will adjust their capital

stock when interest rates change. The autonomous component again reflects any changes to firms’

investment plans, including those reflecting more pessimism or optimism about future conditions. While

interest rates are an important determinant of investment spending, we will ignore any interest rates in

our initial analysis, focusing instead on the autonomous component of investment. Thus, our expression

for non-structural investment as a percent of potential output, which we denote by lower-case “i” is:

Finally, consider government spending – an element that we have not previously examined in detail.

Like consumption and investment, government also have spending plans. Short-term changes in their

plans will be reflected in the autonomous component -- Gaut . Governments often change spending

plans in the short-term to achieve a particular goal. They may decide to build a bridge or a road; they

may allocate funds for a one-time celebration -- for example, when the country wins a war. In these

cases, Gaut >0. In the other direction, some in government may call for spending cuts on temporary

basis -- Gaut <0. Also, in many countries, to support the chances of the incumbent political party,

spending goes up before and election ( Gaut >0), only to be cut afterwards ( Gaut <0). Another example of

such shocks might be the increases of spending implemented under the American Recovery and

Reinvestment Act (ARRA) of 2009. We discuss this policy earlier in the book (Chapter 7) and will do so I

Autonomous comp e t

I

on n

i = autInterest rate effects omitted. (10.16)

30

more detail later in the book (Chapter 13). For our current analysis, we will write that element,

expressed again as a percentage of potential output, as lower-case “g”, namely:

As we previously mentioned, since demand shocks cannot affect potential output, the output gap must

equal the sum of the non-structural elements --- all in percent of potential output. Thus, for a closed

economy with no external trade, we see that the output gap must be equal to the non-structural

elements of consumption, investment, and government spending:

Now, some algebra is necessary. We now substitute the expressions for consumption (10.15),

investment (10.16) and government spending (10.17) into this equation for the output gap in a closed

economy:

Next, we solve out for the output gap and combine three autonomous shocks into one term:

In this equation, ADaut is simply the sum of the autonomous components – changes in spending plans by

households, firms, and the government (closed economy). You can see that the messages of Table (10.2)

and equation (10.20) are exactly the same: an initial spending shock will ripple through the economy

and cause a change in the output gap of which is proportional to the multiplier – in this case over the

marginal cyclical propensity to save: multiplier = 1/cycσ . What’s more, we also learned that the gap must

be equal to the non-structural elements of consumption, investment, and government spending (closed

economy). That is: non-structural production must equal non-structural expenditures.

Autonomous comp e t

G

on n

g = aut

gap = c +i+ gClosed economy – no exports or imports.

+cyc Autonomous Cyclical element ofcomponentsconsumptio

C I G

n

gap = (1 - σ )*gap aut aut aut

* cyc Autonomous

componentsMultip

eqA

lier

D

1gap = aut

σ

Closed economy – no exports or imports.

Closed economy – no exports or imports.

(10.20)

(10.17)

(10.18)

(10.19)

31

.

Propensity to consume out of gap 30.0%

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

-4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Aggregate Demand and Aggregate Supply

Non-structural elements --in percent of potential output

45 degreesNo

n-s

tru

ctu

rale

lmen

ts o

f a

ggre

gate

dem

an

d

In p

erce

nt

of

YP

Output gap - In percent of YP

Aggregate supply = Aggregate demand

cyc Autonomous Cyclcial componencomponents

C+I

AD

+G

gap = (1 - σ )*gap aut

cycSlope = (1 - σ )

Closed economy example: non-structural elements of aggregate demand.

cyc(1 - σ )

Figure 10.8

base alt(i) alt(ii)

Autonomous demand shock autAD 0.00% -1.00% 1.00%

Equilibrium output gap gapeq0.00% -1.43% 1.43%

Propensity to consume out of gap 30.0%

Multiplier 1.43

base

alt(i)

alt(ii)

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

-4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Agg

rega

te d

ema

nd

--

no

n-s

tru

ctu

ral c

om

po

nen

ts

(per

cen

t o

f YP

)

Output gap (percent of YP)

Multiplier Analysis:Effect of autonomous shocks to aggregate demand

45 degrees

cyc(1- σ )

This example shows how an autonomous shock to aggregate demand can

result in a change in the output gap that exceeds the size of the original shock. In the baseline, there are no shocks; the equilibrium output gap is zero. Under

alt (i) there is an adverse shock to demand. This might have happened because households and/or firms became more pessimistic. The magnitude of this shock is autAD=-1%. As a result, the equilibrium output gap falls by more

than the initial shock, to minus 1.43%. By contrast, under alt(ii), there is a favorable shock to aggregate demand 1%. This might reflect additional

optimism by households and/or firms. As a result, the equilibrium output gap rises to 1.43%.

* cyc Autonomous

componentsMultipli

A

er

D

1gap = aut

σ

cyc

1

σ

Closed economy example: non-structural elements of aggregate demand.

Figure 10.9

32

Figure 10.8 illustrates an initial equilibrium for a baseline case. The horizontal axis plots the non-

structural component of aggregate supply – the output gap. The vertical axis plots the non-structural

components of aggregate demand. Along the black dotted 45-degree line, aggregate supply output

(gap) aggregate expenditures (c+i+g) - at each point.

The solid red line that slopes upward represents the aggregate demand equation: it shows us the sum of

the non-structural elements of aggregate demand. The slope tells the extent to which aggregate

demand changes in the economy when of non-structural output (aggregate supply) changes by one unit

(i.e. one percent of YP).

In this example, the marginal propensity to consume out of cyclical income is 30%. Hence, when output

increases by one unit (the ‘run’ of the line along the horizontal axis) domestic expenditures

(consumption minus imports) will increase by 0.3 units (30% of the change in output).

Equilibrium must occur where aggregate supply and aggregate demand are equal – where the dotted

black line and the solid red line intersect. In this diagram, since we have assumed that there are no

demand shocks (autAD=0), the equilibrium output gap is zero.

Figure 10.9 graphically illustrates the impact of demand shocks on the output gap in the closed

economy. Under a baseline, there are no shocks; the equilibrium output gap is zero. Under alt(i), there is

an adverse shock to demand. Under this scenario, the red line shifts downward – from the solid one to

the dashed one. Such a downward shift in this line might reflect a wave of pessimism by consumers

and/or firms, or both. Alternatively, this shift might be due to temporary cuts in government spending.

The new equilibrium output gap occurs where the dashed red line crosses the black dotted 45% line. As

we previously showed in Table 10.2 we calculate the final impact of the initial demand shock as follows:

ADaut /cycσ =-1.0%/.7=1.43%. By contrast, under alt(ii), there is a favorable shock to aggregate demand

autAD=1%. Such a shift may reflect more optimism on the part of consumers and/or firms, or a boost to

government spending. In either case, the aggregate demand line shifts upward from the red solid line to

the red dotted line. Again, the equilibrium occurs where the dotted red line intersects the black dotted

45% line. Using the same calculation as above we find that the equilibrium output gap rises to 1.43% of

potential output.

33

Finally, it is important to note that the equality of output and expenditures must always hold – even if

there is no change to production. Instead, inventories play a critical role in equating output and

expenditures. To see how, suppose that planned spending by households increases autonomously.

Firms, surprised by the extra demand, need not produce more to increase sales; instead, they sell down

their inventories. Recall that a fall of inventories is negative investment. Hence investment (i.e. the

inventory component) will fall enough to keep maintain the equality of output and expenditures. In the

other direction, an increase in inventories will offset a planned decrease in consumption, again equating

output and expenditures.

Government Spending and Tax Multipliers

As discussed above, governments sometimes spend more with the objective of increasing output. This

was true for the American Recovery and Reinvestment Act (ARRA) of 2009 discussed earlier. Politicians

and policy-oriented economists vigorously debated the merits of this policy. A question asked by many

was “What is the government spending multiplier?” In this section, we have given a preliminary answer

to this question. We would treat a shock to government spending Gaut just the same as we would if the

shock came from the private sector. Hence, if the government increases spending by $1 ( Gaut =$1), the

impact on output would be / cycGaut σ > $1 (in our example $1.43).

In addition, governments can also have impacts on spending by changing taxes. In Chapter 7, we

introduced the idea of a transitory or “one-time-only” change to taxes, which we called the non-

structural element of taxes -- NSt . That is, if government increases taxes by $1 on a transitory basis,

NSt =$1; if the government cuts taxes by $1 on a transitory basis, NSt =-$1. Holding everything else equal,

such a tax increase reduces disposable income and consumption; a tax cut increases both.

Consumers will treat short-run taxes as if it was part of their transitory (not permanent) income. Hence,

if the government cuts taxes by $1, the initial increase in spending will be - cyc(1 - σ ) *$1. In our

example, this means that households will initially only spend 30 cents out of that tax cut. However, that

initial spending will again “ripple through” the economy: 30 cents times cyc

1(1- σ ) +cyc

2(1- σ ) +

34

cyc

3(1- σ ) + 4(1- σ )cyc… and so on. The final effect which we will call the tax multiplier is thus: minus

cyc cyc(1- σ ) / σ . Why must this multiplier be a minus? Higher taxes mean less spending. We can also see

that a $1 tax cut will have a smaller impact on the economy than a $1 increase in spending – precisely

because households treat the tax cut as if were transitory income – initially, they will save some portion

of that $1.

Finally, we show what happens when the government increases spending and taxes by the same

amount. Such a balanced budget policy can be attractive for a government: they can increase spending

without having run a deficit. In this case, we may say that the government both adds demand to the

economy (by spending more) but also takes demand away (by taxing more). The balanced budget

multiplier is simply the spending multiplier minus the tax multiplier – and the result is one:

Unsurprisingly, economists vigorously debate the value of these multipliers. There are several reasons

that some would argue that 1.43 would be simply too high. For example, as we discuss in Chapter 17,

some economists criticize the notion of a government spending multiplier as a fundamentally flawed

concept. 7 In their view, rational households will recognize that more public spending must mean higher

taxes – if not now, then in the future. In the view of these economists, in order to save for those higher

future taxes, people will reduce their spending today – thus effectively neutralizing any multiplier effect

of government spending. In addition, some have suggested that the tax multiplier should be zero: if we

cut taxes today, we will simply have to raise them tomorrow. We leave discussion of this idea for that

later chapter.

7 A recent exponent of this view is Professor Valerie Ramey from the University of California, San Diego. We discuss her research on this topic in Chapter 17.

1 cyc cyc

cyc cyc cyc

spending taxmultiplier multiplier

(1- σ ) σbalanced budget multiplier = - 1

σ σ σ(10.21) Closed economy – no

exports or imports.

35

The Multiplier in an Open Economy

If the economy open – if, as most countries do, the economy trades with the rest of the world -- the

results change in two ways. First, autonomous shocks to the external sector – exports and imports – can

now have impacts on the economy. For example, foreigners can decide to purchase more or our goods.

This would be seen as an autonomous shock to exports ( Xaut >0) that would ripple through the

economy much in the same way as domestically based shock – as Figure 10.7 indicates. Second, as we

alluded to earlier, the multiplier becomes smaller since households devote some portion of the extra

spending to imported goods. This is spending that ‘leaks out’ of our country and falls onto foreign

countries.

Let us develop the extension from closed to open economy more formally. As our first step, we will

write the non-structural elements of exports as:

Equation (10.22) tells us that the non-structural component exports will rise or fall as foreigners choose

to buy more of our goods (perhaps when income rises in their country) or less (perhaps when income

falls in their country).

The story about imports is more complex. Like consumption, we assume that there is a cyclical

component to imports: during economic upturns (gap>0) we purchase more goods/services from

abroad, while during economic downturns (gap<0) we purchase less. For example, suppose that the

output gap is 1% of potential of potential output. During such an economic upturn, households in the

United States may purchase more fine South African wines or Korean luxury automobiles. Firms may

purchase more foreign-made computers and machinery. We summarize this fact in the marginal cyclical

propensity to import, whose symbol iscycim , whose value is we assume to be positive. Thus, suppose

that cycim =.05. If the output gap is 1%, imports will rise above their structural value by 0.05*1%= 0.05%

Autonomous comp e t

X

on n

x = aut (10.22)

36

of potential output. 8 And, like consumption, imports also have an autonomous component whose

symbol is IMaut . For example, suppose that our domestic nuclear power plants were to fail (as

happened in Japan after the earthquake and tsunami of 2011). In this case, as a substitute for

domestically generated power, imports of gas and oil would increase, IMaut >0. Thus, we may

summarize the non-structural component of imports (in percent of potential output) as:

This equation tells us that imports will increase imports on a short-term basis when the output gap

increases or when there is some other factor (autonomous shock). Now, we rewrite the expression of

the output gap as the sum of non-structural elements of demand for an open economy:

As we did for the closed economy, we now substitute in all of the individual elements (equations

(10.15), (10.16), (10.17), (10.22) and (10.23) into the equation and solve for the equilibrium output gap:

In this equation ADaut now includes exports and (minus one times) imports

( ADaut = Caut + Iaut + Gaut + Xaut - IMaut ). The denominator of the open economy multiplier term now has

two elements: the cyclical marginal propensities to save σcycand to import

cycim . Using our previous

assumptions, the value of this this open economy multiplier term is 1/(0.70+.05) =1.33. This open

economy multiplier, like the closed economy one, is greater than one. However, the open economy

multiplier is smaller than the closed economy multiplier. To see why, visualize again the multiplier effect

through successive rounds of spending that ripple through an economy.

8 To turn this into a dollar value, suppose that potential output is PY is $14 Trillion; in this case 0.05*1% = $7 billion.

+cycimAutonomous Cyclical elementcompon

I

ent

Mim = *gap aut

Open economy

gap = c + i + g + x - imOpen economy example

* cyc cycim Autonomous

componentsMultiplier-

Open Eco

eqA

nomy

D

1gap = aut

σ

(10.23)

(10.24)

(10.25)

37

In a second round of spending, those who have received income from the initial spending shock

autAD=1%, recipients of the associated income will also increase their spending. They will still spend 30

percent of the original shock (cyc1 - σ * ADaut ), the spending on imports, which we assume to be 5% if

the original shock (cycim =5%) is not spent at home but instead leaks out to foreign countries – purchases

of imports. Hence, in that first round, only 25% (not 30%) will be spent at home: (1 - σ - )cyc cycim =25%.

As before, in successive rounds, people continue less in domestic economy than they would have in a

closed economy. In our example, the sequence of spending would now be [25% + 25%2+ 25%3+….]. Since

this sequence converges to =1/.75 =1.33, we confirm that the multiplier for the open economy will be

1.33.

base alt(i) alt(ii)

Autonomous demand shock autAD 0.00% -1.00% 1.00%

Equilibrium output gap gapeq0.00% -1.33% 1.33%

Propensity to consume out of gap 30.0%

Propensity to import out of gap 5.0%

Slope of red lines in diagram 0.25

base

alt(i)

alt(ii)

-4.0%

-3.0%

-2.0%

-1.0%

0.0%

1.0%

2.0%

3.0%

4.0%

-4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Agg

rega

te d

ema

nd

--

no

n-s

tru

ctu

ral c

om

po

nen

ts

(per

cen

t o

f YP

)

Output gap (percent of YP)

Multiplier Analysis:Effect of autonomous shocks to aggregate demand

45 degrees

cyc(1- σ )

cycim

This example illustrates the effects of antonomous shock to aggregate

demand in an open economy. In the baseline, there are no shocks; the equilibrium output gap is zero. Under alt (i) there is an adverse shock to

demand -- autAD=-1%. Since some of the missing expenditures are reflected in lower imports, the equilibrium output gap falls by 1.33%; in a closed economy, the output gap would have fallen by more. Under alt(ii), there is a

favorable shock to aggregate demand of 1%. The equilibrium output gap rises to 1.33%; in a closed economy, the output gap would have increased more.

*

cyc cycim Autonomous components

Multiplier-Open Eco

eqA

nomy

D

1gap = aut

σ

cyc cycimslope = (1 - σ ) -

Figure 10.10

38

Figure 10.10 graphically illustrates the impact of demand shocks on the output gap in the open

economy. Under a baseline, there are no shocks; the equilibrium output gap is zero. Under alt(i), there is

an adverse shock to demand – identical to the previous Figure 10.9. As before, the new equilibrium

output gap occurs where the dashed red line crosses the black dotted 45% line. Here, the final impact of

the initial demand shock is calculated as ADaut / ]cyc cycim[σ =-1.0%/.75=1.33% -- a less severe drop

than in the closed economy. By contrast, under alt(ii), there is a favorable shock to aggregate demand

autAD=1% -- identical to Figure 10.9. Again, the aggregate demand line shifts upward from the red solid

line to the red dotted line and the equilibrium occurs where the dotted red line intersects the black

dotted 45% line. Using the same calculation as above we find that the equilibrium output gap rises to

1.33% of potential output – a less severe increase than in the closed economy.

10.5 From SRAS to the Phillips Curve (PC).

LO 10.5 Show the relationship between inflation and the output gap using the Phillips Curve. In this chapter, we have discussed two reasons why the quantity of goods and services produced might

differ from the long-run potential level. First, prices might differ from the level that people had expected

or had built into their contracts. If prices are higher than expected, the quantity supplied will increase; if

prices are lower than expected, the quantity supplied will decrease. Second, in the short run, production

based shocks may bring about increases or decreases in the quantity of goods/services supplied. A

favorable production-based shock will increase supply while and adverse shock will reduce supply. To

summarize the relationship between aggregate supply, prices, and production-based shocks, let us

revisit an equation that was previously developed:

The above equation is the “Lucas supply function” introduced earlier, but with an additional element:

the production based shock (pbs). We can express this augmented “Lucas supply function” in a more

compact manner. First, we rewrite the price changes. The percent change in the price level that is

observed 0(P / P -1) π . This is the inflation rate. The percent change in the price level that is expected

Short-run Potential Production Price growth Expected Price GrowthElasticity of short Aggregate Output based shrun aggregate supply supply

with

SRAS P eSRAS,P 0 0

respect to prices

Y = Y *{1+ η *[(P / P -1) (P / P -1) ]+ pbs

ock

} (10.26)

LO 10.5

39

e e0(P / P - 1) π . This is expected inflation. We then divide both sides of the equation by potential

output YP, and then we rearrange to obtain:

Note that: /SRAS Pgap = Y Y = 1 . Hence, equation 10.27 is simply the Lucas supply function that is written

more compactly than before – as a function of the output gap. Now, let us look at closely related

economic questions. Why do prices move? Why might we see an increase or decrease in the price level

(relative to the level that was initially expected)? Not surprisingly, to know about prices, we must

examine supply and demand.

For example, suppose that aggregate demand rises but there is no shift in supply (pbs=0). In order to

meet that extra demand, firms will employ more labor and they will use their existing capital stock more

intensively. When this happens, the marginal products of both labor and capital fall. For firms, the

marginal cost of producing goods and services must rise. In turn firms will pass these higher costs on to

consumers as higher prices. Thus, we see more production – a higher output gap -- and higher prices.

The example is symmetric for lower demand: factor usage falls, cost falls, so we see a lower output gap

and lower prices. However, we also learned that production-based shifts in aggregate supply will also

have impacts on prices. A favorable supply shock (pbs>0) pushes prices down while an adverse supply

shock (pbs<0) pushes prices up.

We can easily summarize all of these ideas by inverting our compact Lucas supply function from above,

solving for inflation:

In words, equation 10.28 tells that the inflation rate equals the expected rate of inflation plus some

function of the output gap minus productivity based shocks – supply minus demand. This relationship is

most widely known as a “Phillips Curve” (PC). This name comes from Professor A.W. Phillips, an

Difference betweenOutput gap Production based shock observed(SRAS relationship in percent of potential

and expected outputinflation

eSRAS,Pgap = η * [π - π ] + pbs

* [ e

SRAS,Observed Expected Output gap minus Inflation Inflation production based shocks

P

1π π gap pbs]

η

(10.27)

(10.28)

40

economist from New Zealand who first hypothesized in 1958 that there was an inverse relationship

between inflation and unemployment. The article was highly influential amongst both academic

economists and policy makers. However, the economists have since expanded his idea to include the

output gap and production based shocks, rather than narrowly focusing on unemployment.

Further to the Point/Online Feature -- The History of the Phillips Curve. Learn about the

tradeoff between inflation and unemployment that A. W. Phillips illustrated. Why was it

such an important idea? How did the idea evolve? End Further to the Point Callout.

Figure 10.11 illustrates how we may apply the short run aggregate supply curve and the Phillips curve.

The left hand side of the figure shows the short-run aggregate supply function (also known as a Lucas

supply function) which permits us to solve for the output gap. Under the baseline, actual and expected

inflation are equal and there are no disturbances to the short-run aggregate supply curve from the

production side (pbs=0); hence under the base, the gap is zero. Under alt(i), inflation is greater than

expected, so the gap is positive. Under alt(ii), there is an adverse shock to short-run aggregate supply

(pbs<0); hence the gap is negative.

Further to the Point*….

*Online Feature.

Figure 10.11

The short-run aggregate supply function (also known as a Lucas supply function) permits us to solve for the output gap. Under the baseline, actual and expected inflation are equal and there are no disturbances to the short-run aggregate supply curve from the production side (pbs=0); hence under the base, the gap is zero. Under alt(i), inflation is greater than expected, so the gap is positive. Under alt(ii), there is an adverse shock to short-run aggregate supply (pbs<0); hence the gap is negative.

The Phillips Curve (PC) rephrases the short-run aggregate supply in a way that we may solve for the inflation rate. Under the baseline, both the gap and supply shock (pbs) are equal to zero; hence actual and expected inflation are equal. Under alt(i), the gap is above zero. Since there was no shock to short-run aggregate supply (pbs=0), the gap rose because aggregate demand rose; hence, actual inflation exceeds its expected value. Under alt(ii), the value of the gap is the same as in alt(i), but there has also been a favorable supply shock (pbs>0). This means that inflation is still above its expected value – but less than under alt(i).

base alt(i) alt(Ii) base alt(i) alt(Ii)

1 1 1 1 1 1

3.0% 3.5% 3.0% 3.0% 4.0% 3.6%

3.0% 3.0% 3.0% 0.0% 0.7% 0.7%

0.0% 0.0% -0.8% 0.0% 0.0% 0.3%

0.0% 0.5% -0.8% 3.0% 4.7% 4.0%

Difference betweenOutput gap Production based shock observed(SRAS relationship) in percent of potential

and expected outputinflation

eSRAS,Pgap = η * [π - π ] + pbs

SRAS,Pη

πeπ

pbsgap

solve

* [ e

SRAS,Observed Expected Output gap minus Inflation Inflation production based shocks

P

1π π gap pbs]

η

SRAS,Pηeπ

pbs

gap

π

solve

"Alternative Perspectives on the Same Equation"

Short-run aggregate supply

Lucas Supply FunctionPhillips Curve (PC)

41

To the right, the Phillips Curve (PC) illustrates how we may use the same concepts to solve for the

inflation rate. Under the baseline, both the gap and supply shock (pbs) are equal to zero; hence actual

and expected inflation are equal. Under alt(i), the gap is above zero. Since there was no shock to short-

run aggregate supply (pbs=0), the gap rose because aggregate demand rose; hence, actual inflation

exceeds its expected value. Under alt(ii), the value of the gap is the same as in alt(i), but there has also

been a favorable supply shock (pbs>0). This means that inflation is still above its expected value – but

less than under alt(i).

base

alt(i)

alt(ii)

-2.0%

0.0%

2.0%

4.0%

6.0%

8.0%

-4.0% -3.0% -2.0% -1.0% 0.0% 1.0% 2.0% 3.0% 4.0%

Phillips Curve (PC)

Output gap (gap) in percent

Infl

atio

nra

te in

pe

rce

nt

Increase in expected inflation or adverse supply shock (pbs<0)

Decrease in expected inflation or favorable supply shock (pbs>0)

The Phillips Curve slope upward since, all else equal, an increase in the output gap (horizontal axis) brings about an increase of inflation (vertical axis). Under the baseline, actual and expected inflation are equal and there are no productivity-based (short run aggregate supply) shocks. Under alt(i), the curve shifts down – either because the expected inflation rate decreased or there was a favorable supply shock (pbs>0). This means that, for any level of the output gap, the inflation rate will now be lower than under the baseline. Under alt(ii), the curve shifts up – either because the expected inflation rate increased or there was an adverse supply shock (pbs<00). This means that, for any level of the output gap, the inflation rate will now be higher than under the baseline.

Figure 10.12

42

Figure 10.12 graphically illustrates the PC. The output gap, in percent, is on the horizontal axis, while the

vertical axis shows the inflation rate, also in percent. The Phillips Curve must slope upward since, when

all else is held constant, an increase in the output gap (horizontal axis) brings about an increase of

inflation (vertical axis). The solid green line shows the baseline scenario. In this case, actual and

expected inflation are equal and there are no productivity-based (short run aggregate supply) shocks.

Under alt(i), the curve shifts down to the green dashed line. This may occur either because the expected

inflation rate has fallen or there was a favorable supply shock (pbs>0). On the green dotted line, for any

level of the output gap, the inflation rate will now be lower than under the baseline (solid green). Under

alt(ii), the curve shifts up to the green dotted line either because the expected inflation rate had risen or

there was an adverse supply shock (pbs<00). Hence, along this green dotted line, for any level of the

output gap, the inflation rate will now be higher than under the baseline.

Chapter Summary

Potential output which reflects an economy’s capacity constraints, is summarized by the

production function at normal or ‘natural’ levels of utilization of the labor force

(employment) and the capital stock. In the short-run, an economy’s output will deviate

from that potential level. Several kinds of economic events or shocks would bring about

an output gap that is positive or negative. We also wanted to know the responses of

other variables, including (but not limited to) prices, wages, and employment. In this

chapter, we highlighted three approaches to this question. (LO 10.1)

Our first approach stressed the importance of changes in productivity. We found that an

increase in total factor productivity – what we often call a favorable production based

shock (pbs), or more simply a supply shock – would increase employment of labor and

capital utilization. Aggregate supply rises and prices fall. We also found that increased

marginal productivity of factors would increase the employment of factors – both labor

and capital. (LO 10.2)

Our second approach showed how changes in the money supply, by boosting aggregate

demand, can affect output – in the short-run, and provided that there are certain

nominal rigidities that prevent prices and/or wages from fully and immediately adjusting

to changes in money. We found, for example, that in the short run, when the money

supply increases, and some prices were ‘sticky’, output would rise. Unlike the RBC

43

approach, however, we found that the price level went up, not down. In the long-run, as

all prices and wages fully adjust, money remains neutral. (LO 10.3)

Our third approach showed how autonomous shocks to the specific elements of

aggregate demand – consumption, investment government expenditures, net exports –

would ripple through the economy and cause changes the output gap. Under this

approach, we assumed that prices are completely fixed. This assumption brought forth

an important result. The final impact on output of an initial shock is larger than the

shock itself. This is the multiplier effect. However, if prices are flexible, the multiplier is

smaller. (LO 10.4)

The chapter closed with a general version of the short-run aggregate supply (SRAS)

curve which links aggregate supply to both production based shocks and surprises in the

price level. If we invert this function, we find that the inflation rate is determined by

expected inflation, the output gap, and production based shocks. We call this the

modern version of the Phillips Curve (PC). (LO 10.5)

Key Terms

44

Questions

1. Suppose that oil prices went down as a result of a glut on world markets that people expect to

be temporary. What would be the likely effects on: (a) Capacity utilization; (b) The overall price

level; (c) Employment of labor, (d) Output?

2. Suppose that an earthquake substantially reduces the electricity generating capacity of a

country. People expect that full generating capacity will be restored, but not immediately. What

would be the likely effects on: (a) Output; (b) Capacity utilization and the marginal product of

capital; (c) labor productivity; (d) wages?

3. In the chapter, we discussed the implications of price and wage rigidities for short-term

fluctuations in economic activity. Suppose there is an increase in the supply of money. If prices

and wages are sticky - that is if they do not fully respond immediately to changes in the money

supply -- what will happen to (a) output; (b) employment of labor; (c) the real wage.

4. Suppose that we observe output and employment to rise. If we also observe the real wage to

have risen, should we conclude that the shock that caused the economic fluctuations was an

increase in money or an increase in productivity?

5. Discuss the effects on the demand side multiplier of the following: (a) an increase in the

propensity to save out of cyclical income σcyc ;(b) an increase in the propensity to import out of

cyclical income cycim ;(c ) complete flexibility in prices.

6. An increase in the output gap is due entirely to a positive production based shock. The expected

rate of inflation will not change. According to the Phillips curve, should the inflation rate

increase, decrease, or stay constant?

45

Problems

1 .

Total Factor Productivity A 1.2

Capital's share 0.35

Capital Stock K 14100

Labor force L 3000

A. Potential Output YP

Natural Rate of Capacity Utilization cu* 0.85

Natural Rate of Employment er* 0.91

Natural Level of Capital Usage K*cu*

Natural Level of Employment L*er*

B. Observed Output Y

Observed Rate of Capacity Utilization cu 0.73

Observed Rate of Employment er 0.89

Observed Level of Capital Usage K*cu

Observed Level of Employment L*er

C. Output Gap

In Dollars GAP=

In Percent gap=

Complete the table. Using the data provided, calculate potential output, natural levels of

capital and employment, observed output and levels of capital and labor employment,

2 .

Initial Output Y0 4003

Initial Price Level P0 1

Price Level Aggregate Demand

P AD

0.8

0.97

1.02

Using the following data ,calculate aggregate demand.(Assume that the moneysupply is constant).

LO 10.1

LO 10.2

46

3 .

Capital share 0.3

A K L

Initial (Per 0) 2.2 15000 40000

Post shock 2.21 15071 39817

Growth factor

Contribution

Production based shock (pbs) in percent

Aggregate Supply

Initial YP 1456

Post Shock YS

Total FactorProductivity Capital Labor

Using the data provided, calculate the growth factor of total factor productivity, capital, and labor. Using these intermediate calculations, calculate the contributions and then the overall production based shock (pbs) and aggregate

4 .

Money Supply Update Factor Price Level Price Growth

M lambda (l) P P/P0-1

Period

0 10000 … 100 …

1 11000 0.2

2 11000 0.4

3 11000 0.6

4 11000 1

%DM

Using the data provided, calculate the growth rate of money and prices in each period.

LO 10.2

LO 10.3

47

5 .

Money Supply Update Factor Price Level Price Growth Output Output Gap

M lambda (l) P P/P0-1 Yssr

Yssr

/YP-1

Period

0 35000 … 100 … 60700 0.0%

1 36750 0.3

2 36750 0.6

3 36750 0.9

4 36750 1

%DM

Potential output (YP) Billions of dollars 60700

Price elasticity of short-run aggregate supply 2SRAS,Pη

Using the data provided, calculate the growth rate of money, prices, and short-run aggregate supply in each period.

6 .

Propensity to consume out of gap 25.0%

Potential output (Trillion $) 12

1.30%

… …

Infinite horizon result

Initial shock

Spending in round

1 - σcyc

Percent of YP

YP

Billion Dollars

Cumulative Impact

Percent of YP

Billion Dollars

]1ADaut *[1-σcyc

]2ADaut *[1-σcyc

]3ADaut *[1-σcyc

]4ADaut *[1-σcyc

ADaut

Use the data provided to show the multiplier effects of an initial autonomous shock to aggregate demand autAD. For rounds 0 through 4 calculate the period by period impact and the cumulative impact. Also, calcuate the infinite horizon result.

IS/RT/PC

LO 10.3

LO 10.4

48

7 .

base alt(i) alt(ii)

Autonomous demand shock autAD 0.00% 1.00% -3.00%

"One off" tax policy tNS 0.0% 0.0% 0.0%

Real Interest Rate r 2.8% 2.8% 2.8%

Numerator

Denominator

Equilibrium output gap gapeq

Propensity to consume out of gap 27.0%

Propensity to import out of gap 7.0%

Consumption response to interest rate -0.10

Investment response to interest rate -0.70

Natural rate of interest rNAT 2.8%

cyc(1- σ )

cycimC,r

I,r

(cyc NS NATC,r I,r AD(1-σ )*t )(r -r ) aut

*{ ( }Equilbrium Autonomous shockslnterest rate responseTemporay tax policies output gap to aggregate demand

Mult

eq NS NATC,r I,r A

ipli

D

er term

1gap = (1- σ )*t )(r -r ) aut

σcyc

cyc cycim

σcyc cycim

Using the data provided, calculate the equilibrium gap for

scenarios (i) and (ii). Where required, make the necessary intermediate calculations to obtain your answer.

IS/RT/PCLO 10.4

49

8 .

base alt(i) alt(ii)

Autonomous demand shock autAD 0.00% 0.00% 0.00%

"One off" tax policy tNS

0.0% -1.0% 1.0%

Real Interest Rate r 2.8% 2.8% 2.8%

Numerator

Denominator

Equilibrium output gap gapeq

Propensity to consume out of gap 23.0%

Propensity to import out of gap 12.0%

Consumption response to interest rate -0.05

Investment response to interest rate -0.60

cyc(1- σ )

cycimC,r

I,r

(cyc NS NATC,r I,r AD(1-σ )*t )(r -r ) aut

*{ ( }Equilbrium Autonomous shockslnterest rate responseTemporay tax policies output gap to aggregate demand

Mult

eq NS NATC,r I,r A

ipli

D

er term

1gap = (1- σ )*t )(r -r ) aut

σcyc

cyc cycim

σcyc cycim

Using the data provided, calculate the equilibrium gap

for scenarios (i) and (ii). Where required, make the necessary intermediate calculations to obtain your

IS/RT/PC

9 .

Initial price level P0 Index 1

Expected prce level Pe Index 1.05

Output gap gap % of YP 3.0%

Productivity based shock pbs % of YP -1.0%

Price elasticity of short-run aggregate supply 0.5

Expected inflation pe %

Observed inflation p %

SRAS,Pη SRAS,Pη

Using the Phillips curve and the data provided compute the observed inflation rate.

IS/RT/PC

LO 10.4

LO 10.5