Abel_Bernanke_IM_C03
Chapter 3
Productivity, Output, and Employment
Learning Objectives
I. Goals of Part 2: The Macroeconomics of Full Employment
A) Analyze factors that affect the longer-term performance of the economy
B) Develop a theoretical model of the macroeconomy
1. Three markets
a. Labor market (this chapter)
b. Goods market (Ch. 4)
c. Asset market (Ch. 7)
II. Goals of Chapter 3
A) Introduce the production function as the main determinant of output
1. Discuss the marginal productivity of labor and capital
2. Analyze supply shocks
B) Discuss the determinants of labor demand and supply
C) Equilibrium in the classical model of the labor market
1. Full-employment output
2. Factors that change equilibrium
D) Unemployment
1. Definitions of employment status
2. Frictional, structural, cyclical unemployment
3. Okun’s Law
III. Notes to Fifth Edition Users
A) Data and numerical examples were updated
B) The Application, “Weekly Hours of Work and the Wealth of Nations” was deleted, though it is
available in this instructor’s manual if you would like to continue using it
C) A new Application, “Comparing U.S. and European Labor Markets” has been added
Chapter 3 Productivity, Output, and Employment 31 Teaching Notes
I. How Much Does the Economy Produce? The Production Function (Sec. 3.1)
A) Factors of production
1. Capital (K)
2. Labor (N)
3. Others (raw materials, land, energy)
4. Productivity of factors depends on technology and management
B) The production function
1. Y=AF(K, N) (3.1)
2. Parameter A is “total factor productivity” (the effectiveness with which capital and labor
are used)
C) Application: The production function of the U.S. economy and U.S. productivity growth
1. Cobb-Douglas production function works well for U.S. economy:
Y=A K 0.3N 0.7 (3.2)
2. Data for U.S. economy—Table
3.1
Numerical Problem 1 gives students practice working with a production function.
3. Productivity growth calculated using production function
a. Productivity moves sharply from year to year
Data Application
An example of the sharp movements in productivity that are possible can be seen by comparing
data on productivity for 1995 to data for 1996. Employment grew about the same amount in both years, but in 1995 productivity grew 0.4%, while in 1996 it grew 1.5%. Economists generally
believe that it is measurement error, rather than true changes in productivity, that is responsible for these swings during a given phase of the business cycle. As the business cycle changes phases, for example from recession to expansion, there may be large, true swings in productivity. For
example, in 1989, productivity grew 1.2%, in 1990 it fell 1.2%, and in 1991 it fell 0.7%.
Roy H. Webb addresses the pitfalls in using productivity statistics in his article “National Productivity Statistics,” Federal Reserve Bank of Richmond Economic Quarterly, Winter 1998,
pp. 45–64.
b. Productivity grew slowly in the 1980s and the first half of the 1990s, but increased in the
second half of the 1990s
Policy Application
Perhaps the greatest source of uncertainty facing policymakers today is trying to figure out the
underlying trend in productivity. For a discussion of this issue, see the article “How Fast Can the New Economy Grow?” by Glenn Rudebusch, Federal Reserve Bank of San Francisco Economic Letter, February 25, 2000.
32 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition
D) The shape of the production function
1. Two main properties of production functions
a. Slopes upward: more of any input produces more output
b. Slope becomes flatter as input rises: diminishing marginal product as input increases
2. Graph production function (Y vs. one input; hold other input and A fixed)
a. Marginal product of capital, MPK=?Y/?K (Figure 3.1; Key Diagram 1; like text
Figure 3.2)
Figure 3.1
1) Equal to slope of production function graph (Y vs. K)
2) MPK always positive
3) Diminishing marginal productivity of capital—MPK declines as K rises
b. Marginal product of labor, MPN=?Y/?N (Figure 3.2; like text Figure 3.3)
Figure 3.2
1) Equal to slope of production function graph (Y vs. N)
2) MPN always positive
3) Diminishing marginal productivity of labor
Numerical Problem 2 gives students practice calculating the MPK and MPN.
Chapter 3 Productivity, Output, and Employment 33
E) Supply shocks
1. Supply shock = productivity shock = a change in an economy’s production function
2. Supply shocks affect the amount of output that can be produced for a given amount of inputs
3. Shocks may be positive (increasing output) or negative (decreasing output)
4. Examples: weather, inventions and innovations, government regulations, oil prices
5. Supply shocks shift graph of production function (Figure 3.3; like text Figure 3.4)
Figure 3.3
a. Negative (adverse) shock: Usually slope of production function decreases at each level of
input (for example, if shock causes parameter A to decline)
b. Positive shock: Usually slope of production function increases at each level of output (for
example, if parameter A increases)
Analytical Problem 1 asks students to draw production functions and show how they change when there are supply shocks.
Theoretical Application
At this point the instructor may wish to introduce the idea of real business cycle analysis
(discussed in greater detail in Chapter 10). The basic point to get across is that many business
cycle fluctuations may be caused by outside events (supply shocks) over which policy has no
control.
II. The Demand for Labor (Sec. 3.2)
A) How much labor do firms want to use?
1. Assumptions
a. Hold capital stock fixed—short-run analysis
b. Workers are all alike
c. Labor market is competitive
d. Firms maximize profits
34 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition
2. Analysis at the margin: costs and benefits of hiring one extra worker (Figure
3.4; like text
Figure 3.5)
Figure 3.4
a. If real wage (w) > marginal product of labor (MPN), the firm is paying the marginal
worker more than the worker produces, so the firm should reduce the number of workers
to increase profits
b. If w should increase the number of workers to increase profits c. Firms’ profits are highest when w=MPN B) The marginal product of labor and labor demand: an example 1. Example: The Clip Joint—setting the nominal wage equal to the marginal revenue product of labor MRPN=P×MPN (3.3) 2. W=MRPN is the same condition as w=MPN, since W=P×w and MRPN=P×MPN 3. A change in the wage a. Begin at equilibrium where W=MRPN b. A rise in the wage rate means W>MRPN, unless N is reduced so the MRPN rises c. A decline in the wage rate means W Data Application We generally assume that when we speak of labor or employment we could be referring to either the number of people employed or total hours worked. Generally, both employed workers and hours worked change in a similar way. But sometimes, as in the recovery from the 1990–91 recession, the number of employed workers grows at a very different rate than hours worked. In this case, by the end of 1993, the workweek, which is a measure of hours worked per employed worker, hit a post–World War II high of 41.7 hours. Economists speculate that the rise in costs of providing benefits, especially medical care benefits, caused employers to prefer paying workers overtime, even at time-and-a-half wages, rather than hiring new employees. See Amanda Bennett, “In Factories, a New Day Dawns—a Longer One,” Wall Street Journal, Jan. 17, 1994. Chapter 3 Productivity, Output, and Employment 35 Numerical Problem 3 sets up an example in which students calculate MPN and see what happens when the wage rate or price of the product change. C) The marginal product of labor and the labor demand curve 1. Labor demand curve shows relationship between the real wage rate and the quantity of labor demanded 2. It is the same as the MPN curve, since w=MPN at equilibrium 3. So the labor demand curve is downward sloping; firms want to hire less labor, the higher the real wage D) Factors that shift the labor demand curve 1. Note: A change in the wage causes a movement along the labor demand curve, not a shift of the curve 2. Supply shocks: Beneficial supply shock raises MPN, so shifts labor demand curve to the right; opposite for adverse supply shock 3. Size of capital stock: Higher capital stock raises MPN, so shifts labor demand curve to the right; opposite for lower capital stock E) Aggregate labor demand (Figure 3.5) Figure 3.5 1. Aggregate labor demand is the sum of all firms’ labor demand 2. Same factors (supply shocks, size of capital stock) that shift firms’ labor demand cause shifts in aggregate labor demand III. The Supply of Labor (Sec. 3.3) A) Supply of labor is determined by individuals 1. Aggregate supply of labor is sum of individuals’ labor supply 2. Labor supply of individuals depends on labor-leisure choice 36 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition B) The income-leisure trade-off 1. Utility depends on consumption and leisure 2. Need to compare costs and benefits of working another day a. Costs: Loss of leisure time b. Benefits: More consumption, since income is higher 3. If benefits of working another day exceed costs, work another day 4. Keep working additional days until benefits equal costs C) Real wages and labor supply 1. An increase in the real wage has offsetting income and substitution effects a. Substitution effect of a higher real wage: Higher real wage encourages work, since the reward for working is higher b. Income effect of a higher real wage: Higher real wage increases income for the same amount of work time, and with higher income, the person can afford more leisure, so will supply less labor 2. A pure substitution effect: a one-day rise in the real wage a. A temporary real wage increase has just a pure substitution effect, since the effect on wealth is negligible 3. A pure income effect: winning the lottery a. Winning the lottery doesn’t have a substitution effect, because it doesn’t affect the reward for working b. But winning the lottery makes a person wealthier, so a person will both consume more goods and take more leisure; this is a pure income effect 4. The substitution effect and the income effect together: a long-term increase in the real wage a. The reward to working is greater: a substitution effect toward more work b. But with a higher wage, a person doesn’t need to work as much: an income effect toward less work c. The longer the high wage is expected to last, the stronger the income effect; thus labor supply will increase by less or decrease by more than for a temporary reduction in the real wage 5. Empirical evidence on real wages and labor supply a. Overall result: Labor supply increases with a temporary rise in the real wage b. Labor supply falls with a permanent increase in the real wage Theoretical Application The results of changes in labor supply due to changes in the wage rate play a major role in the real business cycle (RBC) model of the economy that we will examine in Chapter 10. Analytical Problem 7 examines how workers might change their labor supply if there are changes in Social Security taxes. Chapter 3 Productivity, Output, and Employment 37 D) The labor supply curve (Figure 3.6; like text Figure 3.7) Figure 3.6 1. Increase in the current real wage should raise quantity of labor supplied 2. Labor supply curve relates quantity of labor supplied to real wage Theoretical Application The field of labor economics studies the determinants of labor supply. One of the major issues in the 1970s and early 1980s had to do with the increased participation rates of women in the labor force. Research on both the causes and consequences of this change occupied many economists and yielded many interesting research results, such as explaining why there’s a negative relationship between family income and labor force participation across families, but over time there’s a positive relationship. 3. Labor supply curve slopes upward because higher wage encourages people to work more E) Factors that shift the labor supply curve 1. Wealth: Higher wealth reduces labor supply (shifts labor supply curve to the left; text Fig. 3.8) 2. Expected future real wage: Higher expected future real wage is like an increase in wealth, so reduces labor supply (shifts labor supply curve to the left) Analytical problem 4 asks students to think about factors that shift an individual’s labor supply curve. 38 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition F) Aggregate labor supply 1. Aggregate labor supply rises when current real wage rises a. Some people work more hours b. Other people enter labor force c. Result: Aggregate labor supply curve slopes upward 2. Factors increasing labor supply a. Decrease in wealth b. Decrease in expected future real wage c. Increase in working-age population (higher birth rate, immigration) d. Increase in labor force participation (increased female labor participation, elimination of mandatory retirement) Data Application A broad characterization of labor force participation rates (LFPR) is that men’s LFPR has declined fairly steadily over the past 20 years, while the LFPR of women has been rising. But in the 1990s, women’s LFPR growth slowed, probably due to both economics (a discouraged worker effect) and social considerations (an increased fertility rate). These factors continued in the 2000s, as women’s LFPR declined about 2.5% between 2000 and 2005. G) Application: comparing U.S. and European labor markets 1. Unemployment rates were similar in the U.S. and Europe in 1970s and 1980s, but are higher in Europe since then (Fig. 3.9) 2. Research: three main reasons for higher unemployment rates in Europe (generous unemployment insurance systems, high tax rates, government policies that interfere with labor markets) 3. European countries: more generous unemployment insurance a. Replacement rate = fraction of lost wages that a worker receives; higher in Europe than U.S. b. European workers get unemployment benefits for longer, so have incentive to remain unemployed c. The more turbulent economy of 1980s and 1990s led European job losers to take advantage of unemployment insurance system d. Ireland and Netherlands reformed their unemployment insurance systems, and unemployment rates fell significantly 4. High income-tax rates in Europe also reduce incentive to work 5. Government interference in labor markets in Europe affects demand for labor and sometimes supply of labor Chapter 3 Productivity, Output, and Employment 39 IV. Labor Market Equilibrium (Sec. 3.4) A. Equilibrium: Labor supply equals labor demand (Figure 3.7; Key Diagram 2; like text Figure 3.11) Figure 3.7 1. Classical model of the labor market—real wage adjusts quickly (later, in Chapter 11, look at other models of labor market in which real wage does not adjust quickly) 2. Determines full-employment level of employment N and market-clearing real wage w 3. Factors that shift labor supply or labor demand affect N and w 4. Problem with classical model: can’t study unemployment Numerical Problems 4, 5, and 6 are exercises in which students are given algebraic labor demand and supply curves and are asked to find the equilibrium. Analytical Problems 3 and 5 are comparative static exercises dealing with labor market equilibrium. Data Application There are, of course, many different wages in the economy; our model with just one wage is a simplification. When economists look at real data to see how wages are changing over time, they control for the fact that the mix of jobs changes over time. The employment cost index (ECI) provides a measure of the change in the wage rate that controls for changes in the mix of jobs; economists use changes in the ECI to see how wages change relative to inflation. Data Application Real wages move substantially over time. In the 1980s, real wage growth proceeded at a much slower pace than earlier, but real wage growth recovered somewhat in the 1990s. From 1959 to 1969 real average hourly compensation grew 28%; from 1969 to 1979 it grew 15%; from 1979 to 1989 it grew 6%; from 1989 to 1999 it grew 12%. (Source: Economic Report of the President 2003, table B-49.) 40 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition B) Full-employment output 1. Full-employment output = potential output =Y= level of output when labor market is in equilibrium 2. Y=AF(K,N) ( 3.4) 3. Y affected by changes in N or production function (example: supply shock, Fig. 3.11) Analytical Problem 2 asks students to show how different shocks to the economy affect full- employment output. Data Application What is full-employment output? For many of our theories about macroeconomics, we need a measure of full-employment output, but it is not obvious where to get such a measure. In practice, economists make some assumptions about the structure of the economy, including the production function or the relationship between unemployment and output (see Section 3.6 on Okun’s law), apply these assumptions to the data, and thus estimate what they think is the full-employment level of output. C) Application: output, employment, and the real wage during oil price shocks 1. Sharp oil price increases in 1973–1974, 1979–1980, 2003–2005 (Fig. 3.12) 2. Adverse supply shock—lowers labor demand, employment, the real wage, and the full- employment level of output 3. First two cases: U.S. economy entered recessions 4. Research result: 10% increase in price of oil reduces GDP by 0.4 percentage points D) Application: technical change and wage inequality 1. Two important features of U.S. real wages since 1970 a. Slowdown in growth of real wages b. Increased wage inequality 2. Slowdown in productivity growth combined with increased labor force participation has kept real wages from rising as much as they did before 1970 3. Skill-biased technical change (such as computerization) has increased real wages of highly educated workers, but reduced real wages of unskilled workers (Fig. 3.13) V. Unemployment (Sec. 3.5) A) Measuring unemployment 1. Categories: employed, unemployed, not in the labor force 2. Labor Force = Employed + Unemployed 3. Unemployment Rate = Unemployed/Labor Force 4. Table 3.4 shows current data Chapter 3 Productivity, Output, and Employment 41 Data Application The unemployment rate jumped up sharply in January 1994, not because of any true change in the labor market, but merely because the Bureau of Labor Statistics changed the survey with which it calculates the unemployment statistics. The older survey didn’t properly distinguish between the classifications of unemployed and not in the labor force. In addition, introducing laptop computers on which to perform the survey eliminated a number of errors in the way people answered questions. The result was a small increase in the measured unemployment rate, but no change in the underlying amount of unemployment. 4. Participation Rate = Labor Force/Adult Population 5. Employment Ratio = Employed/Adult Population Analytical Problem 6 tests students’ ability to use these different measures. B) Changes in employment status 1. Flows between categories (Fig. 3.14) 2. Discouraged workers: people who have become so discouraged by lack of success at finding a jo b that they stop searching Data Application For an in-depth look at job creation and destruction, see the book by Steven J. Davis, John C. Haltiwanger, and Scott Schuh, Job Creation and Destruction, Cambridge, Mass.: MIT Press, 1996. Numerical Problems 7 and 8 are quantitative exercises using the unemployment and employment concepts. C) How long are people unemployed? 1. Most unemployment spells are of short duration a. Unemployment spell = period of time an individual is continuously unemployed b. Duration = length of unemployment spell 2. Most unemployed people on a given date are experiencing unemployment spells of long duration 3. Reconciling 1 and 2—numerical example: a. Labor force = 100; on the first day of every month, two workers become unemployed for one month each; on the first day of every year, four workers become unemployed for one year each b. Result: 28 spells of unemployment during year; 24 short (one month), four long (one year); so most spells are short c. At any date, unemployment = six; four have long spells (one year), two have short spells (one month); so most unemployed people on a given date have long spells 42 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition D) Why there are always unemployed people 1. Frictional unemployment a. Search activity of firms and workers due to heterogeneity b. Matching process takes time Policy Application Because the matching process in labor markets takes time, government policy often provides income support for people without jobs in the form of unemployment insurance. But this has disincentive effects—people may prefer to prolong their job searches so they may receive unemployment benefits for a longer time, thus getting income without working. Indeed, some economists believe that the high average rates of unemployment in Europe in the 1980s were in part a consequence of generous unemployment insurance. 2. Structural unemployment a. Chronically unemployed: workers who are unemployed a large part of the time b. Structural unemployment: the long-term and chronic unemployment that exists even when the economy is not in a recession c. One cause: Lack of skills prevents some workers from finding long-term employment d. Another cause: Reallocation of workers out of shrinking industries or depressed regions; matching takes a long time 3. The natural rate of unemployment a. u= natural rate of unemployment; when output and employment are at full-employment levels b. u= frictional + structural unemployment Data Application There is much controversy about how to measure the natural rate of unemployment, as we will discuss in greater detail in Chapter 12. The problem is that the natural rate of simply not observable directly, so we must use the data we have to try to estimate what the natural rate is based on some model of the labor market. Doing so is quite difficult, and there is much debate among empirical macroeconomists as to the size of the natural rate at any date. c. Cyclical unemployment: difference between actual unemployment rate and natural rate of unemployment (u – u) 4. In touch with the macroeconomy: labor market data a. BLS employment report 1) Household survey: unemployment, employment 2) Establishment survey: jobs Chapter 3 Productivity, Output, and Employment 43 Data Application The household and establishment surveys often give conflicting results. In March 2000, the household survey showed a decline in employment of 203 thousand, while the establishment survey showed an increase of 458 thousand jobs. Part of the difference is that the establishment survey doesn’t count the self-employed, and seems to miss much hiring in small firms. But over longer periods these surveys are closer; from October 1999 to March 2000 the household survey showed an increase of 1.7 million employed, while the establishment survey showed an increase of 1.5 million jobs. VI. Relating Output and Unemployment: Okun’s Law (Sec. 3.6) A) Relationship between output (relative to full-employment output) and cyclical unemployment Data Application What’s more closely related to output? Employment growth (from the establishment survey) or the unemployment rate? Business economists usually focus on employment growth (or the average number of hours worked) rather than the unemployment rate, in part because changes in the labor force participation rate lead to fluctuations in the unemployment rate that are not correlated with output. B) (Y – Y)/Y= 2 (u – u) (3.5) C) Why is the Okun’s Law coefficient 2, and not 1? 1. Other things happen when cyclical unemployment rises: Labor force falls, hours of work per worker decline, average productivity of labor declines 2. Result is 2% reduction in output associated with 1 percentage point increase in unemployment rate Numerical Problems 9 and 10 are exercises dealing with Okun’s Law. D) Alternative formulation if average growth rate of full-employment output is 3%: 1. ?Y/Y= 3 – 2 ?u (3.6) 2. Text Fig. 3.15 shows U.S. data 44 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition Additional Teaching Material The following material was deleted from the Fifth Edition of the textbook, but is presented here for instructors who wish to present the material in class. You may copy these pages and hand them out to your students. Weekly Hours of Work and the Wealth of Nations In 1869, the typical worker in the U.S. manufacturing sector worked approximately fifty-six hours per week. However, as shown in Fig. 3.9, the average workweek in U.S. manufacturing declined steadily into the 1930s. Although various forces contributed to the shortening of the workweek prior to 1930, the main factor underlying this trend was sharply raising real wages. Increases in real wages over the late nineteenth and early twentieth centuries in the United States were driven by technological innovation and increased productivity and thus were largely permanent. In response to permanent increases in the real wage, workers reduced the amount of labor they supplied. The response of labor supply to increases in real wages doesn’t explain all of the changes in weekly hours worked. For example, the relatively low number of hours worked per week during the 1930s reflects primarily the general economic collapse that occurred during the Great Depression. The sharp increase in weekly hours of work during the 1940s resulted in part from the threat to national survival posed by World War II, which induced workers to work more hours per week. Since World War II, the workweek in U.S. manufacturing has stabilized at around forty hours, with little decline despite increases in the real wage rate in the 1950s and 1960s. Post–World War II workers, however, have reduced the quantities of labor supplied in other ways, notably by retiring earlier and taking more vacation time. The historical data given in Fig. 3.9 provide some evidence that, in response to a permanent increase in the real wage, workers choose to have more leisure and to work fewer hours per week. Figure 3.10 presents additional evidence, drawn from thirty-six nations. Each point in the diagram represents a different country. The horizontal axis measures real gross domestic product (GDP) per person, and the vertical axis measures the average number of hours worked per week by production workers in manufacturing. Workers in richer countries with higher wage rates (the United States, Canada) tend to work fewer hours per week than do workers in poorer countries with lower wage rates (South Korea, Bolivia). Because the differences in wages among countries reflect long-term differences in productivity, the fact that high-wage countries have shorter workweeks provides further support for the idea that permanent increases in the real wage cause workers to supply less labor. Additional Issues for Classroom Discussion 1. Is the Unemployment Rate a Good Measure of Economic Distress? Macroeconomists often treat the unemployment rate as the key indicator of the business cycle. But terms like “discouraged worker” and “underemployed” suggest that the unemployment rate by itself doesn’t reveal the whole picture. A useful topic for classroom discussion is to have students suggest ways in which the unemployment rate doesn’t reveal fully the economic distress of people in the economy. 2. What Else Is Important for Production? To ensure that your students haven’t forgotten what they learned in their principles course, you may want to ask them to discuss some of the factors besides capital and labor that are factors of production. Typically, they’ll bring up things like land, entrepreneurial ability, and natural resources. When we write the equation for the production function Y=A F(K, N), all these other things are lumped together in total factor productivity (A). Chapter 3 Productivity, Output, and Employment 45 3. As Your Wage Rises, Do You Supply More Labor? Or Less? The textbook discusses the offsetting income and substitution effects on labor supply of an increase in the wage rate in the Appendix to Chapter 4. Since this chapter uses the basic ideas that an increase in wealth reduces labor supply while an increase in the reward to working increases labor supply, you can combine these effects and enter a discussion of the overall effect. You could start by asking students if they’d work more if they received a higher wage. Would someone who’s wealthy make the same decision? Then you might point out that some firms offer employees the chance to “purchase” additional vacation time, based on their wage. Some people buy a lot of extra vacation time when their wage is low, but don’t buy as much when their wage rises because the value of their time has increased. 4. Why Do Oil Price Shocks Hurt the Economy So Much? The textbook points out that our last three recessions were all associated with increases in oil prices. The reasons that increases in oil prices cause such great economic distress are interesting to discuss with your students. See if your students can relate such shocks to their impact on the production function and whether they recognize the very different sectoral implications of the shocks. 5. Should the Minimum Wage Be Increased? Many politicians and labor leaders suggest that the minimum wage should be increased. But economists often point to the minimum wage as a cause of unemployment. Ask your students if they think the minimum wage should be increased. They are likely to come up with the usual arguments on both sides—fairness, equity, and labor market imperfections on the one side; unemployment of the least skilled on the other. As a discussion point, you might wish to talk about comparing the nominal minimum wage to the real minimum wage. Since Congress must vote to change the nominal minimum wage, it has tended to rise in spurts over time. Most recently, the minimum wage had been $4.25 per hour from 1991 to 1996, then went up to $4.75 in 1996 and to $5.15 in 1997. But, after accounting for inflation, we can see that the real minimum wage hasn’t kept pace since 1968. Here’s a short history of the nominal and real minimum wages (deflated by the CPI): Year 1950 1961 1968 1974 1980 1990 1997 2005 Nominal $0.75 $1.15 $1.60 $2.00 $3.10 $3.80 $5.15 $5.15 Real $3.11 $3.85 $4.60 $4.06 $3.76 $2.91 $3.20 $2.64 Answers to Textbook Problems Review Questions 1. A production function shows how much output can be produced with a given amount of capital and labor. The production function can shift due to supply shocks, which affect overall productivity. Examples include changes in energy supplies, technological breakthroughs, and management practices. Besides knowing the production function, you must also know the quantities of capital and labor the economy has. 2. The upward slope of the production function means that any additional inputs of capital or labor produce more output. The fact that the slope declines as we move from left to right illustrates the idea of diminishing marginal productivity. For a fixed amount of capital, additional workers each add less additional output as the number of workers increases. For a fixed number of workers, additional capital adds less additional output as the amount of capital increases. 46 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition 3. The marginal product of capital (MPK) is the output produced per unit of additional capital. The MPK can be shown graphically using the production function. For a fixed level of labor, plot the output provided by different levels of capital; this is the production function. The MPK is just the slope of the production function. 4. The marginal revenue product of labor represents the benefit to a firm of hiring an additional worker, while the nominal wage is the cost. Comparing the benefit to the cost, the firm will hire additional workers as long as the marginal revenue product of labor exceeds the nominal wage, since doing so increases profits. Profits will be at their highest when the marginal revenue product of labor just equals the nominal wage. The same condition can be expressed in real terms by dividing through by the price of the good. The marginal revenue product of labor equals the marginal product of labor times the price of the good. The nominal wage equals the real wage times the price of the good. Dividing each of these through by the price of the good means that an equivalent profit-maximizing condition is the marginal product of labor equals the real wage. 5. The MPN curve shows the marginal product of labor at each level of employment. It is related to the production function because the marginal product of labor is equal to the slope of the production function (where output is plotted against employment). The MPN curve is related to labor demand, because firms hire workers up to the point at which the real wage equals the marginal product of labor. So the labor demand curve is identical to the MPN curve, except that the vertical axis is the real wage instead of the marginal product of labor. 6. A temporary increase in the real wage increases the amount of labor supplied because the substitution effect is larger than the income effect. The substitution effect arises because a higher real wage raises the benefit of additional work for a worker. The income effect is small because the increase in the real wage is temporary, so it doesn’t change the worker’s income very much, thus the worker won’t reduce time spent working very much. A permanent increase in the real wage, however, has a much larger income effect, since a worker’s lifetime income is changed significantly. The income effect may be so large that it exceeds the substitution effect, causing the worker to reduce time spent working. 7. The aggregate labor supply curve relates labor supply and the real wage. The principal factors shifting the aggregate labor supply curve are wealth, the expected future real wage, the country’s working-age population, or changes in the social or legal environment that lead to changes in labor force participation. Increases in wealth or the expected future real wage shift the aggregate labor supply curve to the left. Increases in the working-age population or in labor-force participation shift the aggregate labor supply curve to the right. 8. Full-employment output is the level of output that firms supply when wages and prices in the economy have fully adjusted; in the classical model of the labor market, this occurs when the labor market is in equilibrium. When labor supply increases, full-employment output increases, as there is now more labor available to produce output. When a beneficial supply shock occurs, then the same quantities of labor and capital produce more output, so full-employment output rises. Furthermore, a beneficial supply shock increases the demand for labor at each real wage and leads to an increase in the equilibrium level of employment, which also increases output. 9. The classical model of the labor market assumes that any worker who wants to work at the equilibrium real wage can find a job, so it is not very useful for studying unemployment. Chapter 3 Productivity, Output, and Employment 47 10. The labor force consists of all employed and unemployed workers. The unemployment rate is the fraction of the labor force that is unemployed. The participation rate is the fraction of the adult population that is in the labor force. The employment ratio is the fraction of the adult population that is employed. 11. An unemployment spell is a period of time that a person is continuously unemployed. Duration is the length of time of an unemployment spell. Two seemingly contradictory facts are that most unemployment spells have a short duration and that most people who are unemployed at a particular time are experiencing spells with long durations. These can be reconciled by realizing that there may be a lot of people with short spells and a few people with long spells. On any given date, a survey finds a fairly long average duration for the unemployed, because of the people with long spells. For example, suppose that each week one person becomes unemployed for one week, so there are fifty-two such short unemployment spells during the year. And suppose that there are four people who are unemployed all year, so there are four long unemployment spells during the year. In any given week five people are unemployed: one unemployed person has a spell of one week, while four have spells of a year. So most spells have a short duration (fifty-two short spells compared to four long spells), but most people who are unemployed at a given time are experiencing spells with long duration (one short spell compared to four long spells). 12. Frictional unemployment arises as workers and firms search to find matches. A certain amount of frictional unemployment is necessary, because it is not always possible to find the right match right away. For example, an unemployed banker may not want to take a job flipping hamburgers if he or she cannot find another banking job right away, because the match would be very poor. By remaining unemployed and continuing to search for a more suitable job, the banker is likely to make a better match. That will be better both for the banker (since the salary is likely to be higher) and for society as a whole (since the better match means greater productivity in the economy). 13. Structural unemployment occurs when people suffer long spells of unemployment or are chronically unemployed (with many spells of unemployment). Structural unemployment arises when the number of potential workers with low skill levels exceeds the number of jobs requiring low skill levels, or when the economy undergoes structural change, when workers who lose their jobs in shrinking industries may have difficulty finding new jobs. 14. The natural rate of unemployment is the rate of unemployment that prevails when output and employment are at their full-employment levels. The natural rate of unemployment is equal to the amount of frictional unemployment plus structural unemployment. Cyclical unemployment is the difference between the actual rate of unemployment and the natural rate of unemployment. When cyclical unemployment is negative, output and employment exceed their full-employment levels. 15. Okun’s Law is a rule of thumb that tells how much output falls when the unemployment rate rises. It is written either in terms of the levels of output and unemployment, as in Eq. (3.5), (Y– Y)/Y= 2 (u – u), or in terms of changes in output and unemployment, as in Eq. (3.6), ?Y/Y= 3 – 2 ?u. Since the Okun’s law coefficient is 2, a 2 percentage point increase in the unemployment rate causes output to decline by 4%. 48 Abel/Bernanke/Croushore ? Macroeconomics, Sixth Edition Numerical Problems 1. (a) To find the growth of total factor productivity, you must first calculate the value of A in the production function. This is given by A=Y/(K.3N.7). The growth rate of A can then be calculated as [(A year 2 – A year 1 )/A year 1 ] × 100%. The result is: A % increase in A 1960 12.484 — 1970 14.701 17.8% 1980 15.319 4.2% 1990 17.057 11.3% 2000 19.565 14.7% (b) Calculate the marginal product of labor by seeing what happens to output when you add 1.0 to N; call this Y 2, and the original level of output Y 1 . [A more precise method is to take the derivative of output with respect to N; dY/dN= 0.7A(K/N).3. The result is the same (rounded).] Y 1 Y 2 MPN 1960 2502 2529 27 1970 3772 3805 33 1980 5162 5198 36 1990 7113 7155 42 2000 9817 9867 50 2. (a) The MPK is 0.2, because for each additional unit of capital, output increases by 0.2 units. The slope of the production function line is 0.2. There is no diminishing marginal productivity of capital in this case, because the MPK is the same regardless of the level of K. This can be seen in Figure 3.8 because the production function is a straight line. Figure 3.8 Chapter 3 Productivity, Output, and Employment 49 N is 100, output is Y= 0.2(100 + 100.5) = 22. When N is 110, Y is 22.0976. So the MPN for (b) When raising N from 100 to 110 is (22.0976 – 22)/10 = 0.00976. When N is 120, Y is 22.1909. So the MPN for raising N from 110 to 120 is (22.1909 – 22.0976)/10 = 0.00933. This shows diminishing marginal productivity of labor because the MPN is falling as N increases. In Figure 3.9 this is shown as a decline in the slope of the production function as N increases. Figure 3.9 3. (a) (P =5) MRPN (P =10) N Y MPN MRPN 1 8 8 40 80 2 15 7 35 70 3 21 6 30 60 4 26 5 25 50 5 30 4 20 40 6 33 3 15 30 P= $5. (b) W= $38. Hire one worker, since MRPN ($40) is greater than W ($38) at N= 1. Do not hire (1) two workers, since MRPN ($35) is less than W ($38) at N= 2. W= $27. Hire three workers, since MRPN ($30) is greater than W ($27) at N= 3. Do not hire (2) four workers, since MRPN ($25) is less than W ($27) at N= 4. W= $22. Hire four workers, since MRPN ($25) is greater than W ($22) at N= 4. Do not hire (3) five workers, since MRPN ($20) is less than W ($22) at N= 5.