Chapter 7

The residents of a certain dormitory have collected the following data: people who live in the dorm can be classified as either involved in a relationship or uninvolved. Among involved people, 10 percent experience a breakup of their relationship every month. Among uninvolved people, 5 percent enter into a relationship every month. What is the steady-state fraction of residents who are uninvolved?

Call the number of residents of the dorm who are involved I, the number who are uninvolved U, and the total number of students T = I + U. In steady state the total number of involved students is constant. For this to happen we need the number of newly uninvolved students, (0.10)I, to be equal to the number of students who just became involved, (0.05)U. Following a few substitutions: (0.05)U = (0.10)I = (0.10)(T - U), so U/T= .10/.10+.05 =2/3 We find that two-thirds of the students are uninvolved

Suppose that Congress passes legislation making it more difficult for firms to fire workers. (An example is a law requiring severance pay for fired workers.) If this legislation reduces the rate of job separation without affecting the rate of job finding, how would the natural rate of unemployment change? Do you think it is plausible that the legislation would not affect the rate of job finding? Why or why not?

Consider the formula for the natural rate of unemployment, U/L = S/ S+F If the new law lowers the chance of separation s, but has no effect on the rate of job finding f, then the natural rate of unemployment falls. For several reasons, however, the new law might tend to reduce f. First, raising the cost of firing might make firms more careful about hiring workers, since firms have a harder time firing workers who turn out to be a poor match. Second, if job searchers think that the new legislation will lead them to spend a longer period of time on a particular job, then they might weigh more carefully whether or not to take that job. If the reduction in f is large enough, then the new policy may even increase the natural rate of unemployment.

Is most unemployment long-term or short-term? Explain your answer.

Depending on how one looks at the data, most unemployment can appear to be either short term or long term. Most spells of unemployment are short; that is, most of those who became unemployed find jobs quickly. On the other hand, most weeks of unemployment are attributable to the small number of long-term unemployed. By definition, the long-term unemployed do not find jobs quickly, so they appear on unemployment rolls for many weeks or months.

Do Europeans work more or fewer hours than Americans? List three hypotheses that have been suggested to explain the difference.

Europeans work fewer hours than Americans. One explanation is that the higher income tax rates in Europe reduce the incentive to work. A second explanation is a larger underground economy in Europe as a result of more people attempting to evade the high tax rates. A third explanation is the greater importance of unions in Europe and their ability to bargain for reduced work hours. A final explanation is based on preferences, whereby Europeans value leisure more than Americans do, and therefore elect to work fewer hours.

Describe the difference between frictional unemployment and structural unemployment.

Frictional unemployment is the unemployment caused by the time it takes to match workers and jobs. Finding an appropriate job takes time because the flow of information about job candidates and job vacancies is not instantaneous. Because different jobs require different skills and pay different wages, unemployed workers may not accept the first job offer they receive. In contrast, structural unemployment is the unemployment resulting from wage rigidity and job rationing. These workers are unemployed not because they are actively searching for a job that best suits their skills (as in the case of frictional unemployment), but because at the prevailing real wage the quantity of labor supplied exceeds the quantity of labor demanded. If the wage does not adjust to clear the labor market, then these workers must wait for jobs to become available. Structural unemployment thus arises because firms fail to reduce wages despite an excess supply of labor.

When workers' wages rise, their decision about how much time to spend working is affected in two conflicting ways—as you may have learned in courses in microeconomics. The income effect is the impulse to work less, because greater incomes mean workers can afford to consume more leisure. The substitution effect is the impulse to work more, because the reward for working an additional hour has risen (equivalently, the opportunity cost of leisure has gone up). Apply these concepts to Blanchard's hypothesis about American and European tastes for leisure. On which side of the Atlantic do income effects appear larger than substitution effects? On which side do the two effects approximately cancel? Do you think it is a reasonable hypothesis that tastes for leisure vary by geography? Why or why not?

Real wages have risen over time in both the United States and Europe, increasing the reward for working (the substitution effect) but also making people richer, so they want to "buy" more leisure (the income effect). If the income effect dominates, then people want to work less as real wages go up. This could explain the European experience, in which hours worked per employed person have fallen over time. If the income and substitution effects approximately cancel, then this could explain the U.S. experience, in which hours worked per person have stayed about constant. Economists do not have good theories for why tastes might differ, so they disagree on whether it is reasonable to think that Europeans have a larger income effect than do Americans.

What determines the natural rate of unemployment?

The rates of job separation and job finding determine the natural rate of unemployment. The rate of job separation is the fraction of people who lose their job each month. The higher the rate of job separation, the higher the natural rate of unemployment. The rate of job finding is the fraction of unemployed people who find a job each month. The higher the rate of job finding, the lower the natural rate of unemployment.

Give three explanations of why the real wage may remain above the level that equilibrates labor supply and labor demand.

The real wage may remain above the level that equilibrates labor supply and labor demand because of minimum wage laws, the monopoly power of unions, and efficiency wages. Minimum-wage laws cause wage rigidity when they prevent wages from falling to equilibrium levels. Although most workers are paid a wage above the minimum level, for some workers, especially the unskilled and inexperienced, the minimum wage raises their wage above the equilibrium level. It therefore reduces the quantity of their labor that firms demand, and creates an excess supply of workers, which increases unemployment. The monopoly power of unions causes wage rigidity because the wages of unionized workers are determined not by the equilibrium of supply and demand but by collective bargaining between union leaders and firm management. The wage agreement often raises the wage above the equilibrium level and allows the firm to decide how many workers to employ. These high wages cause firms to hire fewer workers than at the market-clearing wage, so structural unemployment increases. Efficiency-wage theories suggest that high wages make workers more productive. The influence of wages on worker efficiency may explain why firms do not cut wages despite an excess supply of labor. Even though a wage reduction decreases the firm's wage bill, it may also lower worker productivity and therefore the firm's profits.

In any city at any time, some of the stock of usable office space is vacant. This vacant office space is unemployed capital. How would you explain this phenomenon? In particular, which approach to explaining unemployed labor applies best to unemployed capital? Do you think unemployed capital is a social problem? Explain your answer.

The vacant office space problem is similar to the unemployment problem; we can apply the same concepts we used in analyzing unemployed labor to analyze why vacant office space exists. There is a rate of office separation: firms that occupy offices leave, either to move to different offices or because they go out of business. There is a rate of office finding: firms that need office space (either to start up or expand) find empty offices. It takes time to match firms with available space. Different types of firms require spaces with different attributes depending on what their specific needs are. Also, because demand for different goods fluctuates, there are "sectoral shifts"—changes in the composition of demand among industries and regions that affect the profitability and office needs of different firms.

In this chapter we saw that the steady-state rate of unemployment is U/L = s/(s + f). Suppose that the unemployment rate does not begin at this level. Show that unemployment will evolve over time and reach this steady state. (Hint: Express the change in the number of unemployed as a function of s, f, and U. Then show that if unemployment is above the natural rate, unemployment falls, and if unemployment is below the natural rate, unemployment rises.)

To show that the unemployment rate evolves over time to the steady-state rate, let's begin by defining how the number of people unemployed changes over time. The change in the number of unemployed equals the number of people losing jobs (sE) minus the number finding jobs (fU). In equation form, we can express this as: Ut + 1 - Ut = ΔUt + 1 = sEt - fUt. Recall from the text that L = Et + Ut, or Et = L - Ut, where L is the total labor force (we will assume that L is constant). Substituting for Et in the above equation, we find ΔUt + 1 = s(L - Ut) - fUt. Dividing by L, we get an expression for the change in the unemployment rate from t to t + 1: ΔUt + 1/L = (Ut + 1/L) - (Ut/L) = Δ[U/L]t + 1 = s(1 - Ut/L) - fUt/L. Rearranging terms on the right side of the equation above, we end up with line 1 below. Now take line 1 below, multiply the right side by (s + f)/(s + f) and rearrange terms to end up with line 2 below: Δ[U/L]t + 1 = s - (s + f)Ut/L = (s + f)[s/(s + f) - Ut/L]. The first point to note about this equation is that in steady state, when the unemployment rate equals its natural rate, the left-hand side of this expression equals zero. This tells us that, as we found in the text, the natural rate of unemployment (U/L) n equals s/(s + f). We can now rewrite the above expression, substituting (U/L) n for s/(s + f), to get an equation that is easier to interpret: Δ[U/L]t + 1 = (s + f)[(U/L)^n - Ut/L]. This expression shows the following: • If Ut/L > (U/L)^n (that is, the unemployment rate is above its natural rate), then Δ[U/L]t + 1 is negative: the unemployment rate falls. • If Ut/L < (U/L)^n (that is, the unemployment rate is below its natural rate), then Δ[U/L]t + 1 is positive: the unemployment rate rises. This process continues until the unemployment rate U/L reaches the steady-state rate (U/L)^n

Consider an economy with two sectors: manufacturing and services. Demand for labor in manufacturing and services are described by these equations: Lm = 200 − 6Wm Ls = 100 − 4Ws where L is labor (in number of workers), W is the wage (in dollars), and the subscripts denote the sectors. The economy has 100 workers who are willing and able to work in either sector. a. If workers are free to move between sectors, what relationship will there be between Wm and Ws? b. Suppose that the condition in part (a) holds and wages adjust to equilibrate labor supply and labor demand. Calculate the wage and employment in each sector. c. Suppose a union establishes itself in manufacturing and pushes the manufacturing wage to $25. Calculate employment in manufacturing. d. In the aftermath of the unionization of manufacturing, all workers who cannot get the highly paid union jobs move to the service sector. Calculate the wage and employment in services. e. Now suppose that workers have a reservation wage of $15—that is, rather than taking a job at a wage below $15, they would rather wait for a $25 union job to open up. Calculate the wage and employment in each sector. What is the economy's unemployment rate?

a. If workers are free to move between sectors, then the wage in each sector will be equal. If the wages were not equal then workers would have an incentive to move to the sector with the higher wage and this would cause the higher wage to fall, and the lower wage to rise until they were equal. b. Since there are 100 workers in total, LS = 100 - LM. We can substitute this expression into the labor demand for services equation, and call the wage w since it is the same in both sectors: Ls =100- Lm = 100 -4w Lm = 4w Now set this equal to the labor demand for manufacturing equation and solve for w: 4w = 200 - 6w w = $20. Substitute the wage into the two labor demand equations to find LM is 80 and LS is 20 c. If the wage in manufacturing is equal to $25 then LM is equal to 50. d. There are now 50 workers employed in the service sector and the wage wS is equal to $12.50. e. The wage in manufacturing will remain at $25 and employment will remain at 50. If the reservation wage for the service sector is $15 then employment in the service sector will be 40. Therefore, 10 people are unemployed and the unemployment rate is 10 percent.

Answer the following questions about your own experience in the labor force. a. When you or one of your friends is looking for a part-time job, how many weeks does it typically take? After you find a job, how many weeks does it typically last? b. From your estimates, calculate (in a rate per week) your rate of job finding f and your rate of job separation s. (Hint: If f is the rate of job finding, then the average spell of unemployment is 1/f.) c. What is the natural rate of unemployment for the population you represent?

a. In the example that follows, we assume that during the school year you look for a part-time job, and that, on average, it takes 2 weeks to find one. We also assume that the typical job lasts 1 semester, or 12 weeks. b. If it takes 2 weeks to find a job, then the rate of job finding in weeks is f = (1 job/2 weeks) = 0.5 jobs/week. If the job lasts for 12 weeks, then the rate of job separation in weeks is s = (1 job/12 weeks) = 0.083 jobs/week. c. From the text, we know that the formula for the natural rate of unemployment is (U/L) = [s/(s + f )], where U is the number of people unemployed, and L is the number of people in the labor force. Plugging in the values for f and s that were calculated in part (b), we find (U/L) = [0.083/(0.083 + 0.5)] = 0.14. Thus, if on average it takes 2 weeks to find a job that lasts 12 weeks, the natural rate of unemployment for this population of college students seeking part-time employment is 14 percent.

Consider an economy with the following Cobb-Douglas production function: Y = 5K^1/3XL^2/3. a. Derive the equation describing labor demand in this economy as a function of the real wage and the capital stock. (Hint: Review Chapter 3.) b. The economy has 27,000 units of capital and a labor force of 1,000 workers. Assuming that factor prices adjust to equilibrate supply and demand, calculate the real wage, total output, and the total amount earned by workers. c. Now suppose that Congress, concerned about the welfare of the working class, passes a law setting a minimum wage that is 10 percent above the equilibrium wage you derived in part (b). Assuming that Congress cannot dictate how many workers are hired at the mandated wage, what are the effects of this law? Specifically, calculate what happens to the real wage, employment, output, and the total amount earned by workers. d. Does Congress succeed in its goal of helping the working class? Explain. e. Do you think that this analysis provides a good way of thinking about a minimum-wage law? Why or why not?

a. The demand for labor is determined by the amount of labor that a profit-maximizing firm wants to hire at a given real wage. The profit-maximizing condition is that the firm hire labor until the marginal product of labor equals the real wage, MPL = W/P The marginal product of labor is found by differentiating the production function with respect to labor (see Chapter 3 for more discussion), MPL = Dy/DL =d(5k^1/3 XL^2/3)/dL = 10/3K^1/3 X L^-1/3 In order to solve for labor demand, we set the MPL equal to the real wage and solve for L: 10/3K^1/3 X L ^-1/3 =w/p L= 1000/27K(w/p)^-3 Notice that this expression has the intuitively desirable feature that increases in the real wage reduce the demand for labor. We assume that the 27,000 units of capital and the 1,000 units of labor are supplied inelastically (i.e., they will work at any price). In this case we know that all 1,000 units of labor and 27,000 units of capital will be used in equilibrium, so we can substitute these values into the above labor demand function and solve for W/P 1000 = 1000/27(27000)(w/p)^-3 w/p =10 In equilibrium, employment will be 1,000, and multiplying this by 10 we find that the workers earn 10,000 units of output. The total output is given by the production function: Y= 5k^1/3 X L^2/3 y= 5 (27,000^1/3)(1,000^2/3) y = 15,000. Notice that workers get two-thirds of output, which is consistent with what we know about the Cobb-Douglas production function from Chapter 3. c. The real wage is now equal to 11 (10% above the equilibrium level of 10). Firms will use their labor demand function to decide how many workers to hire at the given real wage of 11 and capital stock of 27,000: L = 1000/27 X27000(11)^-3 L = 751 So 751 workers will be hired for a total compensation of 8,261 units of output. To find the new level of output, plug the new value for labor and the value for capital into the production function and you will find Y = 12,393. d. The policy redistributes output from the 249 workers who become involuntarily unemployed to the 751 workers who get paid more than before. The lucky workers benefit less than the losers lose as the total compensation to the working class falls from 10,000 to 8,261 units of output. e. This problem does focus on the analysis of two effects of the minimum-wage laws: they raise the wage for some workers while downward-sloping labor demand reduces the total number of jobs. Note, however, that if labor demand is less elastic than in this example, then the loss of employment may be smaller, and the change in worker income might be positive.

Suppose that a country experiences a reduction in productivity—that is, an adverse shock to the production function. a. What happens to the labor demand curve? b. How would this change in productivity affect the labor market—that is, employment, unemployment, and real wages—if the labor market is always in equilibrium? c. How would this change in productivity affect the labor market if unions prevent real wages from falling?

a. The labor demand curve is given by the marginal product of labor schedule faced by firms. If a country experiences a reduction in productivity, then the labor demand curve shifts to the left as in Figure 7-1. If labor becomes less productive, then at any given real wage, firms demand less labor. b. If the labor market is always in equilibrium, then, assuming a fixed labor supply, an adverse productivity shock causes a decrease in the real wage but has no effect on employment or unemployment, as in Figure 7-2. c. If unions constrain real wages to remain unaltered, then as illustrated in Figure 7-3, employment falls to L1 and unemployment equals L - L1. This example shows that the effect of a productivity shock on an economy depends on the role of unions and the response of collective bargaining to such a change.