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111

Think about what happens when firms respond to an increase in demand by increasing produc-tion: Higher production leads to higher employment. Higher employment leads to lower unem-ployment. Lower unemployment leads to higher wages. Higher wages increase production costs, leading firms to increase prices. Higher prices lead workers to ask for higher wages. Higher wages lead to further increases in prices, and so on. So far, we have simply ignored this sequence of events: By assuming a constant price level

in the IS–LM model, we in effect assumed that firms were able and willing to supply any amount of output at a given price level. So long as our focus was on the short run, this assumption was acceptable. But, as our attention turns to the medium run, we must now abandon this assump- tion, explore how prices and wages adjust over time, and how this, in turn, affects output. This will be our task in this and the next three chapters.

At the center of the sequence of events described in the first paragraph is the labor market, the market in which wages are determined. This chapter focuses on the labor market. It has six sections:

Section 6-1 provides an overview of the labor market.

Section 6-2 focuses on unemployment, how it moves over time, and how its movements affect individual workers.

Sections 6-3 and 6-4 look at wage and price determination.

Section 6-5 then looks at equilibrium in the labor market. It characterizes the natural rate of unemployment, the rate of unemployment to which the economy tends to return in the medium run.

Section 6-6 gives a map of where we will be going next.

The Labor Market

112 The Medium Run The Core

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Work in the home, such as cooking or raising children, is not classified as work in the official statistics. This is a reflection of the difficulty of measuring these activities— not a value judgment about what constitutes work and what doesn’t.

6-1 A Tour of the Labor Market The total U.S. population in 2010 was 308.7 million (Figure 6-1). Excluding those who were either under working age (under 16), in the armed forces, or behind bars, the number of people potentially available for civilian employment, the noninstitutional civilian population, was 237.8 million.

The civilian labor force—the sum of those either working or looking for work— was only 153.8 million. The other 84 million people were out of the labor force, neither working in the market place nor looking for work. The participation rate, defined as the ratio of the labor force to the noninstitutional civilian population, was therefore 153.8/237.8, or 64.7%. The participation rate has steadily increased over time, reflecting mostly the increasing participation rate of women: In 1950, one woman out of three was in the labor force; now the number is close to two out of three.

Of those in the labor force, 139 million were employed, and 14.8 million were unemployed—looking for work. The unemployment rate, defined as the ratio of the unemployed to the labor force, was therefore 14.8/153.8 = 9.6. As we shall see later, 9.6% is a very high unemployment rate by historical standards.

The Large Flows of Workers To get a sense of what a given unemployment rate implies for individual workers, con- sider the following analogy:

Take an airport full of passengers. It may be crowded because many planes are coming and going, and many passengers are quickly moving in and out of the airport. Or it may be because bad weather is delaying flights and passengers are stranded, waiting for the weather to improve. The number of passengers in the airport will be high in both cases, but their plights are quite different. Passengers in the second scenario are likely to be much less happy.

Total population: 308.7 million

Noninstitutional civilian

population: 237.8 million

Civilian labor force

153.8 million

Employed

139.0 million

Unemployed

14.8 million

Out of the

labor force

84.0 million

Figure 6-1

Population, Labor Force, Employment, and Unemployment in the United States (in millions), 2010

Source: Current Population Survey http://www.bls.gov/cps/

http://www.bls.gov/cps/

Chapter 6 The Labor Market 113

In the same way, a given unemployment rate may reflect two very different reali- ties. It may reflect an active labor market, with many separations and many hires, and so with many workers entering and exiting unemployment ; or it may reflect a sclerotic labor market, with few separations, few hires, and a stagnant unemploy- ment pool.

Finding out which reality hides behind the aggregate unemployment rate requires data on the movements of workers. The data are available in the United States from a monthly survey called the Current Population Survey (CPS). Average monthly flows, computed from the CPS for the United States from 1994 to 2011, are reported in Figure 6-2. (For more on the ins and outs of the CPS, see the Focus box “The Current Population Survey.”)

Figure 6-2 has three striking features:

■ The flows of workers in and out of employment are very large. On average, there are 8.5 million separations each month in the United States

(out of an employment pool of 132.4 million), 3.1 million change jobs (shown by the circular arrow at the top), 3.6 million move from employment to out of the labor force (shown by the arrow from employment to out of the labor force), and 1.8 mil- lion move from employment to unemployment (shown by the arrow from employ- ment to unemployment).

Why are there so many separations each month? About three-fourths of all separations are usually quits—workers leaving their jobs for what they per- ceive as a better alternative. The remaining one-fourth are layoffs. Layoffs come mostly from changes in employment levels across firms: The slowly changing aggregate employment numbers hide a reality of continual job destruction and job creation across firms. At any given time, some firms are suffering decreases in demand and decreasing their employment ; other firms are enjoying increases in demand and increasing employment.

■ The flows in and out of unemployment are large relative to the number of unem- ployed: The average monthly flow out of unemployment each month is 4.0 mil- lion: 2.1 million people get a job, and 1.9 million stop searching for a job and drop out of the labor force. Put another way, the proportion of unemployed leaving unemployment equals 4.0/8.4 or about 47% each month. Put yet another way, the

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Sclerosis, a medical term, means hardening of the arter- ies. By analogy, it is used in economics to describe mar- kets that function poorly and have few transactions.

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The numbers for employment, unemployment, and those out of the labor force in Figure 6-1 referred to 2010. The numbers for the same variables in Fig- ure 6-2 refer to averages from 1994 to 2011. This is why they are different.

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Put another, and perhaps more dramatic way: On aver- age, every day in the United States, about 60,000 workers become unemployed.

1.8

Employment

132.4 million

Out of the

labor force

73.3 million

Unemployment

8.4 million

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3.1

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Figure 6-2

Average Monthly Flows between Employment, Unemployment, and Nonparticipation in the United States, 1994 to 2011 (millions)

(1) The flows of workers in and out of employment are large; (2) The flows in and out of unemployment are large relative to the number of unemployed; (3) There are also large flows in and out of the labor force, much of it directly to and from employment.

Source: Calculated from the series con- structed by Fleischman and Fallick, http:// www.federalreserve.gov/econresdata/ researchdata.htm

http://www.federalreserve.gov/econresdata/researchdata.htm

114 The Medium Run The Core

average duration of unemployment—the average length of time people spend unemployed—is between two and three months.

This fact has an important implication. You should not think of unemployment in the United States as a stagnant pool of workers waiting indefinitely for jobs. For most (but obviously not all) of the unemployed, being unemployed is more a quick transition than a long wait between jobs. One needs, however, to make two remarks at this point. First, the United States is unusual in this respect: In many European countries, the average duration is much longer than in the United States. Second, as we shall see below, even in the United States, when unemployment is high, such as is the case today, the average duration of unemployment becomes much longer. Being unemployed becomes much more painful.

■ The flows in and out of the labor force are also surprisingly large: Each month, 5.5 million workers drop out of the labor force (3.6 plus 1.9), and a slightly larger number, 5.1, join the labor force (3.3 plus 1.8). You might have expected these two flows to be composed, on one side, of those finishing school and entering the labor force for the first time, and, on the other side, of workers going into retire- ment. But each of these two groups actually represents a small fraction of the total flows. Each month only about 400,000 new people enter the labor force, and about 300,000 retire. But the actual flows in and out of the labor force are 10.6 million, so about 15 times larger.

What this fact implies is that many of those classified as “out of the labor force” are in fact willing to work and move back and forth between participation and non- participation. Indeed, among those classified as out of the labor force, a very large proportion report that although they are not looking, they “want a job.” What they really mean by this statement is unclear, but the evidence is that many do take jobs when offered them.

This fact has another important implication. The sharp focus on the unem- ployment rate by economists, policy makers, and news media is partly misdirected.

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The average duration of un- employment equals the in- verse of the proportion of unemployed leaving unem- ployment each month. To see why, consider an exam- ple. Suppose the number of unemployed is constant and equal to 100, and each un- employed person remains unemployed for two months. So, at any given time, there are 50 people who have been unemployed for one month and 50 who have been unem- ployed for two months. Each month, the 50 unemployed who have been unemployed for two months leave unem- ployment. In this example, the proportion of unemployed leaving unemployment each month is 50/100, or 50%. The duration of unemployment is two months—the inverse of 1/50%.

The Current Population Survey F

O C

U S

The Current Population Survey (CPS) is the main source of statistics on the labor force, employment, participation, and earnings in the United States.

When the CPS began in 1940, it was bas ed on in- ter views of 8,000 households. The sample has grown considerably, and now about 60,000 hous eholds are interviewed every month. (The CPS was redesigned in 1994, which is why, for consistency, Figures 6-2, 6-4, and 6-5 start only in 1994.) The households are chosen so that the sample is representative of the U.S. population. Each household stays in the sample for four months, leaves the sample for the following eight months, then comes back for another four months before leaving the sample permanently.

The survey is now based on computer-assisted inter- views. Interviews are either done in person, in which case interviewers use laptop computers, or by phone. Some questions are asked in every survey. Other questions are specific to a particular survey and are used to find out about particular aspects of the labor market.

The Labor Department uses the data to compute and publish numbers on employment, unemployment, and participation by age, sex, education, and industry. Econo- mists use these data, which are available in large compu- ter files, in two ways:

The first is to get snapshots of how things are at various points in time, to answer such questions as: What is the distribution of wages for Hispanic–American workers with only primary education, and how does it compare with the same distribution 10 or 20 years ago?

The second way, of which Figure 6-2 is an example, is answered by the fact that the survey follows people through time. By looking at the same people in two con- secutive months, economists can find out, for example, how many of those who were unemployed last month are employed this month. This number gives them an esti- mate of the probability of somebody who was unemployed last month found a job this month.

For more on the CPS, you can go to the CPS homepage. (www.bls.gov/cps/home.htm)

www.bls.gov/cps/home.htm

Chapter 6 The Labor Market 115

Some of the people classified as “out of the labor force” are very much like the un- employed. They are in effect discouraged workers. And while they are not actively looking for a job, they will take it if they find one.

This is why economists sometimes focus on the employment rate, the ratio of employment to the population available for work, rather than on the unemploy- ment rate. The higher unemployment, or the higher the number of people out of the labor force, the lower the employment rate.

We shall follow tradition in this book and focus on the unemployment rate as an indicator of the state of the labor market, but you should keep in mind that the unemployment rate is not the best estimate of the number of people available for work.

6-2 Movements in Unemployment Let’s now look at movements in unemployment. Figure 6-3 shows the average value of the U.S. unemployment rate over the year, for each year, all the way back to 1948. The shaded areas represent years during which there was a recession.

Figure 6-3 has two important features:

■ Until the mid-1980s, it looked as if the U.S. unemployment rate was on an upward trend, from an average of 4.5% in the 1950s to 4.7% in the 1960s, 6.2% in the 1970s, and 7.3% in the 1980s. From the 1980s on however, the unemployment rate stead- ily declined for more than two decades. By 2006, the unemployment rate was 4.6%. These decreases led a number of economists to conclude that the trend from 1950 to the 1980s had been reversed, and that the normal rate of unemployment in the United States had fallen. How much of the large increase in the unemployment rate since 2007 is temporary, and whether we can return to the low rates of the mid-2000s, remains to be seen.

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Working in the opposite direc- tion: Some of the unemployed may be unwilling to accept any job offered to them and should probably not be counted as unemployed since they are not really looking for a job.

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In 2010, employment was 139 million and the population available for work was 237.8 million. The employment rate was 58.5%. The employment rate is sometimes called the employment to population ratio.

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000 2005

U n

e m

p lo

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2010 2

1950

Figure 6-3

Movements in the U.S. Unemployment Rate, 1948–2010

Since 1948, the average yearly U.S. unemployment rate has fluctuated between 3% and 10%.

Source: Series UNRATE: Federal Reserve Economic Data (FRED) http://research.stlouisfed.org/fred2/

http://research.stlouisfed.org/fred2/

116 The Medium Run The Core

■ Leaving aside these trend changes, year-to-year movements in the unemployment rate are closely associated with recessions and expansions. Look, for example, at the last four peaks in unemployment in Figure 6-3. The most recent peak, at 9.6% is in 2010, is the result of the crisis. The previous two peaks, associated with the recessions of 2001 and 1990–1991 recessions, had much lower unemployment rate peaks, around 7%. Only the recession of 1982, where the unemployment rate reached 9.7%, is comparable to the current crisis. (Annual averages can mask larger values within the year. In the 1982 recession, while the average unemploy- ment rate over the year was 9.7%, the unemployment rate actually reached 10.8% in November 1982. Similarly, the monthly unemployment rate in the crisis peaked at 10.0% in October 2009.)

How do these fluctuations in the aggregate unemployment rate affect individual workers? This is an important question because the answer determines both:

■ The effect of movements in the aggregate unemployment rate on the welfare of individual workers, and

■ The effect of the aggregate unemployment rate on wages.

Let’s start by asking how firms can decrease their employment in response to a decrease in demand. They can hire fewer new workers, or they can lay off the workers they currently employ. Typically, firms prefer to slow or stop the hiring of new work- ers first, relying on quits and retirements to achieve a decrease in employment. But doing only this may not be enough if the decrease in demand is large, so firms may then have to lay off workers.

Now think about the implications for both employed and unemployed workers.

■ If the adjustment takes place through fewer hires, the chance that an unemployed worker will find a job diminishes. Fewer hires means fewer job openings; higher unemployment means more job applicants. Fewer openings and more applicants combine to make it harder for the unemployed to find jobs.

■ If the adjustment takes place instead through higher layoffs, then employed work- ers are at a higher risk of losing their job.

In general, as firms do both, higher unemployment is associated with both a lower chance of finding a job if one is unemployed and a higher chance of losing it if one is employed. Figures 6-4 and 6-5 show these two effects at work over the period 1994 to 2010.

Figure 6-4 plots two variables against time: the unemployment rate (measured on the left vertical axis); and the proportion of unemployed workers finding a job each

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Note also that the unemploy- ment rate sometimes peaks in the year after the recession, not in the actual recession year. This occurred, for exam- ple, in the 2001 recession. The reason is that, while output is higher and growth is positive, so the economy is technically no longer in recession, the additional output does not re- quire enough new hires to re- duce the unemployment rate.

4.0

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finding a job each month

(inverse scale)

P e rc

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in v e rs

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c a le

)

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Figure 6-4

The Unemployment Rate and the Proportion of Unemployed Finding Jobs, 1994–2010

When unemployment is high, the proportion of unemployed finding jobs within one month is low. Note that the scale on the right is an inverse scale.

Source: See Figure 6-2.

Chapter 6 The Labor Market 117

month (measured on the right vertical axis). This proportion is constructed by dividing the flow from unemployment to employment during each month by the number of un- employed. To show the relation between the two variables more clearly, the proportion of unemployed finding jobs is plotted on an inverted scale: Be sure you see that on the right vertical scale, the proportion is lowest at the top and highest at the bottom.

The relation between movements in the proportion of unemployed workers find- ing jobs and the unemployment rate is striking: Periods of higher unemployment are associated with much lower proportions of unemployed workers finding jobs. In 2010, for example, with unemployment close to 10%, only about 18% of the unemployed found a job within a month, as opposed to 28% in 2007, when unemployment was much lower.

Similarly, Figure 6-5 plots two variables against time: the unemployment rate (measured on the left vertical axis); and the monthly separation rate from employment (measured on the right vertical axis). The monthly separation rate is constructed by dividing the flow from employment (to unemployment and to “out of the labor force”) during each month by the number of employed in the month. The relation between the separation rate and the unemployment rate plotted is quite strong: Higher unemploy- ment implies a higher separation rate—that is, a higher chance of employed workers losing their jobs. The probability nearly doubles between times of low unemployment and times of high unemployment.

Let’s summarize: When unemployment is high, workers are worse off in two ways:

■ Employed workers face a higher probability of losing their job. ■ Unemployed workers face a lower probability of finding a job; equivalently, they

can expect to remain unemployed for a longer time.

6-3 Wage Determination Having looked at unemployment, let’s turn to wage determination, and to the relation between wages and unemployment.

Wages are set in many ways. Sometimes they are set by collective bargaining; that is, bargaining between firms and unions. In the United States, however, collec- tive bargaining plays a limited role, especially outside the manufacturing sector. To- day, barely more than 10% of U.S. workers have their wages set by collective bargaining agreements. For the rest, wages are either set by employers or by bargaining between

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To be slightly more precise, we only learn from Figure 6-5 that, when unemployment is higher, separations into un- employment and out of the labor force are higher. Separa- tions equal quits plus layoffs. We know from other sources that quits are lower when unemployment is high: It is more attractive to quit when there are plenty of jobs. So, if separations go up and quits go down, this implies that lay- offs (which equal separations minus quits) go up even more than separations.

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Collective bargaining: bar- gaining between a union (or a group of unions) and a firm (or a group of firms).

1994-1 1997-1 2000-1 2003-1 2006-1 2009-1 4.0

5.0

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Monthly separation rate

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1.00

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1.60

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1.90 Figure 6-5

The Unemployment Rate and the Monthly Separation Rate from Employment, 1994–2010

When unemployment is high, a higher proportion of workers lose their jobs.

Source: See Figure 6-2.

118 The Medium Run The Core

the employer and individual employees. The higher the skills needed to do the job, the more likely there is to be bargaining. Wages offered for entry-level jobs at McDonald’s are on a take-it-or-leave-it basis. New college graduates, on the other hand, can typi- cally negotiate a few aspects of their contracts. CEOs and baseball stars can negotiate a lot more.

There are also large differences across countries. Collective bargaining plays an important role in Japan and in most European countries. Negotiations may take place at the firm level, at the industry level, or at the national level. Sometimes con- tract agreements apply only to firms that have signed the agreement. Sometimes they are automatically extended to all firms and all workers in the sector or the economy.

Given these differences across workers and across countries, can we hope to for- mulate anything like a general theory of wage determination? Yes. Although institu- tional differences influence wage determination, there are common forces at work in all countries. Two sets of facts stand out:

■ Workers are typically paid a wage that exceeds their reservation wage, the wage that would make them indifferent between working or being unemployed. In other words, most workers are paid a high enough wage that they prefer being employed to being unemployed.

■ Wages typically depend on labor-market conditions. The lower the unemployment rate, the higher the wages. (We shall state this more precisely in the next section.)

To think about these facts, economists have focused on two broad lines of explana- tion. The first is that even in the absence of collective bargaining, workers have some bargaining power, which they can and do use to obtain wages above their reservation wages. The second is that firms themselves may, for a number of reasons, want to pay wages higher than the reservation wage. Let’s look at each explanation in turn.

Bargaining How much bargaining power a worker has depends on two factors. The first is how costly it would be for the firm to replace him, were he to leave the firm. The second is how hard it would be for him to find another job, were he to leave the firm. The more costly it is for the firm to replace him, and the easier it is for him to find another job, the more bargaining power he will have. This has two implications:

■ How much bargaining power a worker has depends first on the nature of his job. Replacing a worker at McDonald’s is not very costly: The required skills can be taught quickly, and typically a large number of willing applicants have already filled out job application forms. In this situation, the worker is unlikely to have much bargaining power. If he asks for a higher wage, the firm can lay him off and find a replacement at minimum cost. In contrast, a highly skilled worker who knows in detail how the firm operates may be very difficult and costly to replace. This gives him more bargaining power. If he asks for a higher wage, the firm may decide that it is best to give it to him.

■ How much bargaining power a worker has also depends on labor market con- ditions. When the unemployment rate is low, it is more difficult for firms to find acceptable replacement workers. At the same time, it is easier for workers to find other jobs. Under these conditions, workers are in a stronger bargaining position and may be able to obtain a higher wage. Conversely, when the unem- ployment rate is high, finding good replacement workers is easier for firms, while finding another job is harder for workers. Being in a weak bargaining position, workers may have no choice but to accept a lower wage.

Peter Diamond, Dale Morten- sen, and Christopher Pissar- ides received the 2010 Nobel Prize in economics precisely for working out the charac- teristics of a labor market with large flows and wage bargaining.

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Chapter 6 The Labor Market 119

Efficiency Wages Regardless of workers’ bargaining power, firms may want to pay more than the reserva- tion wage. They may want their workers to be productive, and a higher wage can help them achieve that goal. If, for example, it takes a while for workers to learn how to do a job correctly, firms will want their workers to stay for some time. But if workers are paid only their reservation wage, they will be indifferent between their staying or leaving. In this case, many of them will quit, and the turnover rate will be high. Paying a wage above the reservation wage makes it more attractive for workers to stay. It decreases turnover and increases productivity.

Behind this example lies a more general proposition: Most firms want their work- ers to feel good about their jobs. Feeling good promotes good work, which leads to higher productivity. Paying a high wage is one instrument the firm can use to achieve these goals. (See the Focus box “Henry Ford and Efficiency Wages.”) Economists call the theories that link the productivity or the efficiency of workers to the wage they are paid efficiency wage theories.

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Before September 11, 2001, the approach to airport secu- rity was to hire workers at low wages and accept the result- ing high turnover. Now that airport security has become a much higher priority, the approach is to make the jobs more attractive and higher paid, so as to get more mo- tivated and more competent workers and reduce turnover.

Henry Ford and Efficiency Wages

In 1914, Henr y Ford—the builder of the most popular car in the world at the time, the Model-T—made a stun- ning announcement. His company would pay all quali- fied employees a minimum of $5 a day for an eight-hour day. This was a very large salary increase for most em- ployees, who had been earning an average $2.30 for a nine-hour day. From the point of view of the Ford com- pany, this increase in pay was far from negligible—it represented about half of the company’s profits at the time.

What Ford’s motivations were is not entirely clear. Ford himself gave too many reasons for us to know which ones he actually believed. The reason was not that the company had a hard time finding workers at the previous wage. But the company clearly had a hard time retaining workers. There was a very high turnover rate, as well as high dissat- isfaction among workers.

Whatever the reasons behind Ford’s decision, the results of the wage increase were astounding, as Table 1 shows:

The annual turnover rate (the ratio of separations to em- ployment) plunged from a high of 370% in 1913 to a low of 16% in 1915. (An annual turnover rate of 370% means that on average 31% of the company’s workers left each month, so that over the course of a year the ratio of separations to employment was 31% : 12 � 370%.) The layoff rate col- lapsed from 62% to nearly 0%. The average rate of absentee- ism (not shown in the table), which ran at close to 10% in 1913, was down to 2.5% one year later. There is little question that higher wages were the main source of these changes.

Did productivity at the Ford plant increase enough to offset the cost of increased wages? The answer to this question is less clear. Productivity was much higher in 1914 than in 1913. Estimates of the productivity increases range from 30% to 50%. Despite higher wages, profits were also higher in 1914 than in 1913. But how much of this in- crease in profits was due to changes in workers’ behavior and how much was due to the increasing success of Model- T cars is harder to establish.

While the effects support efficiency wage theories, it may be that the increase in wages to $5 a day was exces- sive, at least from the point of view of profit maximization. But Henry Ford probably had other objectives as well, from keeping the unions out—which he did—to generating pub- licity for himself and the company—which he surely did.

Source: Dan Raff and Lawrence Summers, “Did Henry Ford Pay Efficiency Wages?” Journal of Labor Economics 1987 5 (No. 4 Part 2): pp. S57–S87.

F O

C U

Table 1 Annual Turnover and Layoff Rates (%) at Ford, 1913–1915

1913 1914 1915

Turnover rate 370 54 16

Layoff rate 62 7 0.1

120 The Medium Run The Core

Like theories based on bargaining, efficiency wage theories suggest that wages de- pend on both the nature of the job and on labor-market conditions:

■ Firms—such as high-tech firms—that see employee morale and commitment as essential to the quality of their work will pay more than firms in sectors where workers’ activities are more routine.

■ Labor-market conditions will affect the wage. A low unemployment rate makes it more attractive for employed workers to quit : When unemployment is low, it is easy to find another job. That means, when unemployment decreases, a firm that wants to avoid an increase in quits will have to increase wages to in- duce workers to stay with the firm. When this happens, lower unemployment will again lead to higher wages. Conversely, higher unemployment will lead to lower wages.

Wages, Prices, and Unemployment We capture our discussion of wage determination by using the following equation:

W = Pe F1u, z2 (6.1) 1- , +2

The aggregate nominal wage W depends on three factors:

■ The expected price level P e

■ The unemployment rate u ■ A catchall variable z that stands for all other variables that may affect the outcome

of wage setting.

Let’s look at each factor.

The Expected Price Level First, ignore the difference between the expected and the actual price level and ask: Why does the price level affect nominal wages? The answer: Because both workers and firms care about real wages, not nominal wages.

■ Workers do not care about how many dollars they receive but about how many goods they can buy with those dollars. In other words, they do not care about the nominal wages they receive, but about the nominal wages (W ) they receive rela- tive to the price of the goods they buy (P). They care about W>P.

■ In the same way, firms do not care about the nominal wages they pay but about the nominal wages (W ) they pay relative to the price of the goods they sell (P). So they also care about W>P.

Think of it another way: If workers expect the price level—the price of the goods they buy—to double, they will ask for a doubling of their nominal wage. If firms expect the price level—the price of the goods they sell—to double, they will be willing to dou- ble the nominal wage. So, if both workers and firms expect the price level to double, they will agree to double the nominal wage, keeping the real wage constant. This is captured in equation (6.1): A doubling in the expected price level leads to a doubling of the nominal wage chosen when wages are set.

Return now to the distinction we set aside at the start of the paragraph: Why do wages depend on the expected price level, P e, rather than the actual price level, P?

Because wages are set in nominal (dollar) terms, and when they are set, the rel- evant price level is not yet known.

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An increase in the expected price level leads to an in- crease in the nominal wage, in the same proportion.

Chapter 6 The Labor Market 121

For example, in some union contracts in the United States, nominal wages are set in advance for three years. Unions and firms have to decide what nominal wages will be over the following three years based on what they expect the price level to be over those three years. Even when wages are set by firms, or by bargaining between the firm and each worker, nominal wages are typically set for a year. If the price level goes up unexpectedly during the year, nominal wages are typically not readjusted. (How workers and firms form expectations of the price level will occupy us for much of the next three chapters; we will leave this issue aside for the moment.)

The Unemployment Rate Also affecting the aggregate wage in equation (6.1) is the unemployment rate u. The minus sign under u indicates that an increase in the unemployment rate decreases wages.

The fact that wages depend on the unemployment rate was one of the main con- clusions of our earlier discussion. If we think of wages as being determined by bargain- ing, then higher unemployment weakens workers’ bargaining power, forcing them to accept lower wages. If we think of wages as being determined by efficiency wage con- siderations, then higher unemployment allows firms to pay lower wages and still keep workers willing to work.

The Other Factors The third variable in equation (6.1), z, is a catchall variable that stands for all the fac- tors that affect wages given the expected price level and the unemployment rate. By convention, we will define z so that an increase in z implies an increase in the wage (thus, the positive sign under z in the equation). Our earlier discussion suggests a long list of potential factors here.

Take, for example, unemployment insurance—the payment of unemploy- ment benefits to workers who lose their jobs. There are ver y good reasons why society should provide some insurance to workers who lose their job and have a hard time finding another. But there is little question that, by making the prospects of unemployment less distressing, more generous unemployment benefits do in- crease wages at a given unemployment rate. To take an extreme example, suppose unemployment insurance did not exist. Some workers would have little to live on and would be willing to accept very low wages to avoid remaining unemployed. But unemployment insurance does exist, and it allows unemployed workers to hold out for higher wages. In this case, we can think of z as representing the level of unem- ployment benefits: At a given unemployment rate, higher unemployment benefits increase the wage.

It is easy to think of other factors. An increase in the minimum wage may in- crease not only the minimum wage itself, but also wages just above the minimum wage, leading to an increase in the average wage, W , at a given unemployment rate. Or take an increase in employment protection, which makes it more expen- sive for firms to lay off workers. Such a change is likely to increase the bargain- ing power of workers covered by this protection (laying them off and hiring other workers is now more costly for firms), increasing the wage for a given unemploy- ment rate.

We will explore some of these factors as we go along.

�

An increase in unemployment leads to a decrease in the nominal wage.

�

By the definition of z, an in- crease in z leads to an increase in the nominal wage.

122 The Medium Run The Core

6-4 Price Determination Having looked at wage determination, let’s now turn to price determination.

The prices set by firms depend on the costs they face. These costs depend, in turn, on the nature of the production function—the relation between the inputs used in production and the quantity of output produced—and on the prices of these inputs.

For the moment, we will assume firms produce goods using labor as the only fac- tor of production. We will write the production function as follows:

Y = AN

where Y is output, N is employment, and A is labor productivity. This way of writing the production function implies that labor productivity—output per worker—is con- stant and equal to A.

It should be clear that this is a strong simplification. In reality, firms use other fac- tors of production in addition to labor. They use capital—machines and factories. They use raw materials—oil, for example. Moreover, there is technological progress, so that labor productivity ( A) is not constant but steadily increases over time. We shall intro- duce these complications later. We will introduce raw materials in Chapter 7 when we discuss changes in the price of oil. We will focus on the role of capital and techno- logical progress when we turn to the determination of output in the long run in Chap- ters 10 through 13. For the moment, though, this simple relation between output and employment will make our lives easier and still serve our purposes.

Given the assumption that labor productivity, A, is constant, we can make one fur- ther simplification. We can choose the units of output so that one worker produces one unit of output—in other words, so that A = 1. (This way we do not have to carry the letter A around, and this will simplify notation.) With this assumption, the production function becomes

Y = N (6.2)

The production function Y = N implies that the cost of producing one more unit of output is the cost of employing one more worker, at wage W . Using the terminology introduced in your microeconomics course: The marginal cost of production—the cost of producing one more unit of output—is equal to W .

If there were perfect competition in the goods market, the price of a unit of output would be equal to marginal cost: P would be equal to W . But many goods markets are not competitive, and firms charge a price higher than their marginal cost. A simple way of capturing this fact is to assume that firms set their price according to

P = (1 + m)W (6.3)

where m is the markup of the price over the cost. If goods markets were perfectly com- petitive, m would be equal to zero, and the price P would simply equal the cost W . To the extent they are not competitive and firms have market power, m is positive, and the price P will exceed the cost W by a factor equal to (1 + m).

6-5 The Natural Rate of Unemployment Let’s now look at the implications of wage and price determination for unemployment.

For the rest of this chapter, we shall do so under the assumption that nominal wages depend on the actual price level, P, rather than on the expected price level, P e (why we make this assumption will become clear soon). Under this additional

�

Using a term from micro- economics: This assumption implies constant returns to labor in production. If firms double the number of work- ers they employ, they double the amount of output they produce.

�

The rest of the chapter is based on the assumption that P e = P.

Chapter 6 The Labor Market 123

assumption, wage setting and price setting determine the equilibrium (also called “natural”) rate of unemployment. Let’s see how.

The Wage-Setting Relation Given the assumption that nominal wages depend on the actual price level (P) rather than on the expected price level (P e), equation (6.1), which characterizes wage deter- mination, becomes:

W = P F1u, z2

Dividing both sides by the price level,

W P

= F1u, z 2 (6.4)

1- , +2

Wage determination implies a negative relation between the real wage, W>P, and the unemployment rate, u: The higher the unemployment rate, the lower the real wage chosen by wage setters. The intuition is straightforward: The higher the unemploy- ment rate, the weaker the workers’ bargaining position, and the lower the real wage will be.

This relation between the real wage and the rate of unemployment—let’s call it the wage-setting relation—is drawn in Figure 6-6. The real wage is measured on the verti- cal axis. The unemployment rate is measured on the horizontal axis. The wage-setting relation is drawn as the downward–sloping curve WS (for wage setting): The higher the unemployment rate, the lower the real wage.

The Price–Setting Relation Let’s now look at the implications of price determination. If we divide both sides of the price–determination equation, (6.3), by the nominal wage, we get

P W

= 1 + m (6.5)

The ratio of the price level to the wage implied by the price-setting behavior of firms equals 1 plus the markup. Now invert both sides of this equation to get the im- plied real wage:

W P

= 1

1 + m (6.6)

Note what this equation says: Price-setting decisions determine the real wage paid by firms. An increase in the markup leads firms to increase their prices given the wage they have to pay; equivalently, it leads to a decrease in the real wage.

The step from equation (6.5) to equation (6.6) is algebraically straightforward. But how price setting actually determines the real wage paid by firms may not be intui- tively obvious. Think of it this way: Suppose the firm you work for increases its markup and therefore increases the price of its product. Your real wage does not change very much: You are still paid the same nominal wage, and the product produced by the firm is at most a small part of your consumption basket.

Now suppose that not only the firm you work for, but all the firms in the econ- omy increase their markup. All the prices go up. Even if you are paid the same nominal

�

“Wage setters”: Unions and firms if wages are set by col- lective bargaining; individual workers and firms if wages are set on a case-by-case ba- sis; firms if wages are set on a take-it-or-leave-it basis.

124 The Medium Run The Core

wage, your real wage goes down. So, the higher the markup set by firms, the lower your (and everyone else’s) real wage will be. This is what equation (6.6) says.

The price-setting relation in equation (6.6) is drawn as the horizontal line PS (for price setting) in Figure 6-6. The real wage implied by price setting is 1>(1 + m); it does not depend on the unemployment rate.

Equilibrium Real Wages and Unemployment Equilibrium in the labor market requires that the real wage chosen in wage setting be equal to the real wage implied by price setting. (This way of stating equilibrium may sound strange if you learned to think in terms of labor supply and labor demand in your microeconomics course. The relation between wage setting and price setting, on the one hand, and labor supply and labor demand, on the other, is closer than it looks at first and is explored further in the appendix at the end of this chapter.) In Figure 6-6, equilibrium is therefore given by point A, and the equilibrium unemployment rate is given by un.

We can also characterize the equilibrium unemployment rate algebraically; elimi- nating W>P between equations (6.4) and (6.6) gives

F(un, z) = 1

1 + m (6.7)

The equilibrium unemployment rate, un, is such that the real wage chosen in wage setting—the left side of equation (6.7)—is equal to the real wage implied by price set- ting—the right side of equation (6.7).

The equilibrium unemployment rate, un is called the natural rate of unemploy- ment (which is why we have used the subscript n to denote it). The terminology has be- come standard, so we shall adopt it, but this is actually a bad choice of words. The word “natural” suggests a constant of nature, one that is unaffected by institutions and policy. As its derivation makes clear, however, the “natural” rate of unemployment is anything but natural. The positions of the wage-setting and price-setting curves, and thus the equilibrium unemployment rate, depend on both z and m. Consider two examples:

■ An increase in unemployment benefits. An increase in unemployment benefits can be represented by an increase in z: Since an increase in benefits makes the

Unemployment rate, u

Price-setting relation

Wage-setting relation

R e a l w

a g

e , W /P

A1 1 1 m

Figure 6-6

Wages, Prices, and the Natural Rate of Unemployment

The natural rate of unemploy- ment is the unemployment rate such that the real wage chosen in wage setting is equal to the real wage implied by price setting.

�

“Natural,” in Webster’s Dic- tionar y, means “in a state provided by nature, without man-made changes.”

Chapter 6 The Labor Market 125

prospect of unemployment less painful, it increases the wage set by wage setters at a given unemployment rate. So it shifts the wage-setting relation up, from WS to WS� in Figure 6-7. The economy moves along the PS line, from A to A�. The natural rate of unemployment increases from un to u�n.

In words: At a given unemployment rate, higher unemployment benefits lead to a higher real wage. A higher unemployment rate is needed to bring the real wage back to what firms are willing to pay.

■ A less stringent enforcement of existing antitrust legislation. To the extent that this allows firms to collude more easily and increase their market power, it will lead to an increase in their markup—an increase in m. The increase in m implies a decrease in the real wage paid by firms, and so it shifts the price-setting relation down, from PS to PS� in Figure 6-8. The economy moves along WS. The equilibrium moves from A to A�, and the natural rate of unemployment increases from un to u�n.

In words: By letting firms increase their prices given the wage, less stringent enforcement of antitrust legislation leads to a decrease in the real wage. Higher unemployment is required to make workers accept this lower real wage, leading to an increase in the natural rate of unemployment.

Factors like the generosity of unemployment benefits or antitrust legislation can hardly be thought of as the result of nature. Rather, they reflect various characteristics of the structure of the economy. For that reason, a better name for the equilibrium rate of unemployment would be the structural rate of unemployment, but so far the name has not caught on.

From Unemployment to Employment Associated with the natural rate of unemployment is a natural level of employment, the level of employment that prevails when unemployment is equal to its natural rate.

�

An increase in unemployment benefits shifts the wage set- ting curve up. The economy moves along the price-setting curve. Equilibrium unemploy- ment increases.

WS9

Unemployment rate, u

u 9un

A A9

R e a l w

a g

e , W /P

1 1 1 m

Figure 6-7

Unemployment Benefits and the Natural Rate of Unemployment

An increase in unemploy- ment benefits leads to an in- crease in the natural rate of unemployment.

� This has led some economists to call unemployment a “dis- cipline device”: Higher unem- ployment is the device that forces wages to correspond to what firms are willing to pay.

� An increase in the markup shifts the price setting curve (line in this case). The econ- omy moves along the wage- setting curve. Equilibrium unemployment increases.

� This name has been sug - gested by Edmund Phelps, from Columbia University. Phelps was awarded the No- bel Prize in 2006. For more on some of his contributions, see Chapters 8 and 25.

126 The Medium Run The Core

Let’s review the relation among unemployment, employment, and the labor force. Let U denote unemployment, N denote employment, and L the labor force. Then:

u K U L

= L - N

L = 1 -

N L

The first step follows from the definition of the unemployment rate (u). The sec- ond follows from the fact that, from the definition of the labor force, the level of unem- ployment (U ) equals the labor force (L) minus employment (N ). The third step follows from simplifying the fraction. Putting all three steps together: The unemployment rate u equals 1 minus the ratio of employment N to the labor force L.

Rearranging to get employment in terms of the labor force and the unemployment rate gives:

N = L (1 - u)

Employment N is equal to the labor force L, times 1 minus the unemployment rate u. So, if the natural rate of unemployment is un and the labor force is equal to L, the natural level of employment Nn is given by

Nn = L(1 - un)

For example, if the labor force is 150 million and the natural rate of unemployment is, say, 5%, then the natural level of employment is 150 * (1 - 0.05) = 142.5 million.

From Employment to Output Finally, associated with the natural level of employment is the natural level of output, the level of production when employment is equal to the natural level of employment. Given the production function we have used in this chapter (Y = N ), the natural level of output Yn is easy to derive. It is given by

Yn = Nn = L (1 - un)

Unemployment rate, u

u9un

PS9

R e a l w

a g

e , W /P

1 1 1 m

1 1 1 m9

Figure 6-8

Markups and the Natural Rate of Unemployment

An increase in markups de- creases the real wage and leads to an increase in the natural rate of unemployment.

�

L = N + U 1 U = L - N

Chapter 6 The Labor Market 127

Using equation (6.7) and the relations among the unemployment rate, employ- ment, and the output we just derived, the natural level of output satisfies the following equation:

F a1 - Yn L

, zb = 1

1 + m (6.8)

The natural level of output (Yn) is such that, at the associated rate of unemploy- ment (un = 1 - Yn>L), the real wage chosen in wage setting—the left side of equa- tion (6.8)—is equal to the real wage implied by price setting—the right side of equation (6.8). As you will see, equation (6.8) will turn out to be very useful in the next chapter. Make sure you understand it.

We have gone through many steps in this section. Let’s summarize: Assume that the expected price level is equal to the actual price level. Then:

■ The real wage chosen in wage setting is a decreasing function of the unemploy- ment rate.

■ The real wage implied by price setting is constant. ■ Equilibrium in the labor market requires that the real wage chosen in wage setting

be equal to the real wage implied by price setting. This determines the equilibrium unemployment rate.

■ This equilibrium unemployment rate is known as the natural rate of unemployment. ■ Associated with the natural rate of unemployment is a natural level of employment

and a natural level of output.

6-6 Where We Go from Here We have just seen how equilibrium in the labor market determines the equilibrium un- employment rate (we have called it the natural rate of unemployment), which in turn determines the level of output (we have called it the natural level of output).

So, you may ask, what did we do in the previous four chapters? If equilibrium in the labor market determines the unemployment rate and, by implication, the level of output, why did we spend so much time looking at the goods and financial mar- kets? What about our earlier conclusions that the level of output was determined by factors such as monetary policy, fiscal policy, consumer confidence, and so on—all factors that do not enter equation (6.8) and therefore do not affect the natural level of output?

The key to the answer lies in the difference between the short run and the medium run:

■ We have derived the natural rate of unemployment and the associated levels of employment and output under two assumptions. First, we have assumed equilib- rium in the labor market. Second, we have assumed that the price level was equal to the expected price level.

■ However, there is no reason for the second assumption to be true in the short run. The price level may well turn out to be different from what was expected when nominal wages were set. Hence, in the short run, there is no reason for unemploy- ment to be equal to the natural rate or for output to be equal to its natural level. As we will see in the next chapter, the factors that determine movements in out- put in the short run are indeed the factors we focused on in the preceding three chapters: monetary policy, fiscal policy, and so on. Your time (and mine) was not wasted. �

In the short run, the factors that determine movements in output are the factors we focused on in the preced- ing three chapters: monetary policy, fiscal policy, and so on.

■ But expectations are unlikely to be systematically wrong (say, too high or too low) forever. That is why, in the medium run, unemployment tends to return to the nat- ural rate, and output tends to return to the natural level. In the medium run, the factors that determine unemployment and output are the factors that appear in equations (6.7) and (6.8).

These, in short, are the answers to the questions asked in the first paragraph of this chapter. Developing these answers in detail will be our task in the next three chapters.

�

In the medium run, output tends to return to the natu- ral level, and the factors that determine output are the fac- tors we have focused on this chapter.

128 The Medium Run The Core

level turns out to be different from what was expected, wages are typically not readjusted.

■ The price set by firms depends on the wage and on the markup of prices over wages. The higher the markup cho- sen by firms, the higher the price given the wage, and thus the lower the real wage implied by price-setting decisions.

■ Equilibrium in the labor market requires that the real wage chosen in wage setting be equal to the real wage implied by price setting. Under the additional assumption that the expected price level is equal to the actual price level, equi- librium in the labor market determines the unemployment rate. This unemployment rate is known as the natural rate of unemployment.

■ In general, the actual price level may turn out to be different from the price level expected by wage setters. Therefore, the unemployment rate need not be equal to the natural rate.

■ The coming chapters will show that: In the short run, unemployment and output are determined

by the factors we focused on in the previous three chapters, but, in the medium run, unemployment tends to return to the natural rate, and output tends to return to its natural level.

■ The labor force consists of those who are working (em- ployed) or looking for work (unemployed). The unemploy- ment rate is equal to the ratio of the number of unemployed to the number in the labor force. The participation rate is equal to the ratio of the labor force to the working-age population.

■ The U.S. labor market is characterized by large flows between employment, unemployment, and “out of the la- bor force.” On average, each month, about 47% of the un- employed move out of unemployment, either to take a job or to drop out of the labor force.

■ Unemployment is high in recessions and low in expan- sions. During periods of high unemployment, the probabil- ity of losing a job increases and the probability of finding a job decreases.

■ Wages are set unilaterally by firms or by bargaining be- tween workers and firms. They depend negatively on the unemployment rate and positively on the expected price level. The reason why wages depend on the expected price level is that they are typically set in nominal terms for some period of time. During that time, even if the price

Summary

noninstitutional civilian population, 112 labor force; out of the labor force, 112 participation rate, 112 unemployment rate, 112 separations, hires, 113 Current Population Survey (CPS), 113 quits, layoffs, 113 duration of unemployment, 114 discouraged workers, 115 employment rate, 115 collective bargaining, 117 reservation wage, 118 bargaining power, 118

efficiency wage theories, 119 unemployment insurance, 121 employment protection, 121 production function, 122 labor productivity, 122 markup, 122 wage-setting relation, 123 price-setting relation, 124 natural rate of unemployment, 124 structural rate of unemployment, 125 natural level of employment, 125 natural level of output, 126

Key Terms

Chapter 6 The Labor Market 129

QUICK CHECK All Quick Check questions and problems are available on MyEconLab. 1. Using the information in this chapter, label each of the fol- lowing statements true, false, or uncertain. Explain briefly. a. Since 1950, the participation rate in the United States has

remained roughly constant at 60%. b. Each month, the flows into and out of employment are

very small compared to the size of the labor force. c. Fewer than 10% of all unemployed workers exit the unem-

ployment pool each year. d. The unemployment rate tends to be high in recessions and

low in expansions. e. Most workers are typically paid their reservation wage. f. Workers who do not belong to unions have no bargaining

power. g. It may be in the best interest of employers to pay wages

higher than their workers’ reservation wage. h. The natural rate of unemployment is unaffected by policy

changes.

2. Answer the following questions using the information pro- vided in this chapter. a. As a percentage of the employed workers, what is the size

of the flows into and out of employment (i.e., hires and separations) each month?

b. As a percentage of the unemployed workers, what is the size of the flows from unemployment into employment each month?

c. As a percentage of the unemployed, what is the size of the total flows out of unemployment each month? What is the average duration of unemployment?

d. As a percentage of the labor force, what is the size of the total flows into and out of the labor force each month?

e. In the text we say that there is an average of 400,000 new workers entering the labor force each month. What per- centage of total flows into the labor force do new workers entering the labor force constitute?

3. The natural rate of unemployment Suppose that the markup of goods prices over marginal

cost is 5%, and that the wage-setting equation is

W = P11 - u2, where u is the unemployment rate. a. What is the real wage, as determined by the price-setting

equation? b. What is the natural rate of unemployment? c. Suppose that the markup of prices over costs increases to

10%. What happens to the natural rate of unemployment? Explain the logic behind your answer.

DIG DEEPER All Dig Deeper questions and problems are available on MyEconLab. 4. Reservation wages

In the mid-1980s, a famous supermodel once said that she would not get out of bed for less than $10,000 (presumably per day).

a. What is your own reservation wage? b. Did your first job pay more than your reservation wage at

the time? c. Relative to your reservation wage at the time you accept

each job, which job pays more: your first one or the one you expect to have in 10 years?

d. Explain your answers to parts (a) through (c) in terms of the efficiency wage theory.

e. Part of the policy response to the crisis was to extend the length of time workers could receive unemployment benefits. How would this affect reservation wages if this change was made permanent?

5. Bargaining power and wage determination Even in the absence of collective bargaining, workers do

have some bargaining power that allows them to receive wages higher than their reservation wage. Each worker’s bargain- ing power depends both on the nature of the job and on the economy-wide labor market conditions. Let’s consider each factor in turn. a. Compare the job of a delivery person and a computer net-

work administrator. In which of these jobs does a worker have more bargaining power? Why?

b. For any given job, how do labor market conditions affect a worker’s bargaining power? Which labor-market variable would you look at to assess labor-market conditions?

c. Suppose that for given labor-market conditions [the vari- able you identified in part (b)], worker bargaining power throughout the economy increases. What effect would this have on the real wage in the medium run? in the short run? What determines the real wage in the model described in this chapter?

6. The existence of unemployment a. Suppose the unemployment rate is very low. How easy is it

for firms to find workers to hire? How easy is it for workers to find jobs? What do your answers imply about the rela- tive bargaining power of workers and firms when the un- employment rate is very low? What do your answers imply about what happens to the wage as the unemployment rate gets very low?

b. Given your answer to part (a), why is there unemployment in the economy? (What would happen to real wages if the unemployment rate were equal to zero?)

7. The informal labor market You learned in Chapter 2 that informal work at home

(e.g., preparing meals, taking care of children) is not counted as part of GDP. Such work also does not constitute employ- ment in labor-market statistics. With these observations in mind, consider two economies, each with 100 people, divided into 25 households, each composed of four people. In each household, one person stays at home and prepares the food, two people work in the nonfood sector, and one person is unemployed. Assume that the workers outside food preparation produce the same actual and measured output in both economies.

Chapter 6 The Labor Market 129

Questions and Problems

130 The Medium Run The Core

In the first economy, EatIn, the 25 food-preparation work- ers (one per household) cook for their families and do not work outside the home. All meals are prepared and eaten at home. The 25 food-preparation workers in this economy do not seek work in the formal labor market (and when asked, they say they are not looking for work). In the second economy, EatOut, the 25 food-preparation workers are employed by restaurants. All meals are purchased in restaurants. a. Calculate measured employment and unemployment and

the measured labor force for each economy. Calculate the measured unemployment rate and participation rate for each economy. In which economy is measured GDP higher?

b. Suppose now that EatIn’s economy changes. A few restau- rants open, and the food preparation workers in 10 house- holds take jobs restaurants. The members of these 10 households now eat all of their meals in restaurants. The food-preparation workers in the remaining 15 households continue to work at home and do not seek jobs in the for- mal sector. The members of these 15 households continue to eat all of their meals at home. Without calculating the numbers, what will happen to measured employment and unemployment and to the measured labor force, unem- ployment rate, and participation rate in EatIn? What will happen to measured GDP in EatIn?

c. Suppose that you want to include work at home in GDP and the employment statistics. How would you measure the value of work at home in GDP? How would you alter the definitions of employment, unemployment, and out of the labor force?

d. Given your new definitions in part (c), would the labor- market statistics differ for EatIn and EatOut? Assuming that the food produced by these economies has the same value, would measured GDP in these economies differ? Under your new definitions, would the experiment in part (b) have any effect on the labor market or GDP statistics for EatIn?

EXPLORE FURTHER 8. Unemployment spells and long-term unemployment

According to the data presented in this chapter, about 47% of unemployed workers leave unemployment each month. a. What is the probability that an unemployed worker will

still be unemployed after one month? two months? six months?

Now consider the composition of the unemployment pool. We will use a simple experiment to determine the proportion of the unemployed who have been unem- ployed six months or more. Suppose the number of unem- ployed workers is constant and equal to x (where x is some constant). Each month, 47% of the unemployed find jobs, and an equivalent number of previously employed work- ers become unemployed.

b. Consider the group of x workers who are unemployed this month. After a month, what percentage of this group will still be unemployed? (Hint: If 47% of unemployed workers find jobs every month, what percentage of the original x unemployed workers did not find jobs in the first month?)

c. After a second month, what percentage of the original x unemployed workers has been unemployed for at least two months? [Hint: Given your answer to part (b), what percentage of those unemployed for at least one month do not find jobs in the second month?] After the sixth month, what percentage of the original x unemployed workers has been unemployed for at least six months?

d. Using Table B-44 of the Economic Report of the President (www.gpoaccess.gov/eop/), compute the proportion of un- employed who have been unemployed six months or more (27 weeks or more) for each year between 1996 and 2010. How do these numbers compare with the answer you obtained in part (c)? Can you guess what may account for the difference between the actual numbers and the answer you obtained in this problem? (Hint: Suppose that the probability of exiting unemployment goes down the longer you are unemployed.)

e. Part of the policy response to the crisis was an extension of the length of time that an unemployed worker could re- ceive unemployment benefits. How would you predict this change would affect the proportion of those unemployed more than six months?

9. Go to the Web site maintained by the U.S. Bureau of Labor Statistics (www.bls.gov). Find the latest Employment Situation Summary. Look under the link “National Employment.” a. What are the latest monthly data on the size of the U.S. ci-

vilian labor force, on the number of unemployed, and on the unemployment rate?

b. How many people are employed? c. Compute the change in the number of unemployed from

the first number in the table to the most recent month in the table. Do the same for the number of employed work- ers. Is the decline in unemployment equal to the increase in employment? Explain in words.

10. The typical dynamics of unemployment over a recession. The table below shows the behavior of annual real GDP

growth during three recessions. These data are from Table B-4 of the Economic Report of the President:

Year Real GDP Growth Unemployment Rate

1981 2.5

1982 � 1.9

1983 4.5

1990 1.9

1991 � 0.2

1992 3.4

2008 0.0

2009 � 2.6

2010 2.9

Use Table B-35 from the Economic Report of the President to fill in the annual values of the unemployment rate in the table above and consider these questions. a. When is the unemployment rate in a recession higher, the

year of declining output or the following year?

www.gpoaccess.gov/eop/

www.bls.gov

Chapter 6 The Labor Market 131

b. Explain the pattern of the unemployment rate after a re- cession if the production function is not linear in the workforce.

c. Explain the pattern of the unemployment rate after a re- cession if discouraged workers return to the labor force as the economy recovers.

d. The rate of unemployment remains substantially higher after the crisis-induced recession in 2009. In that reces- sion, unemployment benefits were extended in length from 6 months to 12 months. What does the model predict the effect of this policy will be on the natural rate of unem- ployment? Do the data support this prediction in any way?

■ A further discussion of unemployment along the lines of this chapter is given by Richard Layard, Stephen Nickell,

and Richard Jackman in The Unemployment Crisis (Oxford: Oxford University Press, 1994).