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1、 ...wd... Answers to Textbook Questions and Problems CHAPTER 7Unemployment and the Labor Market Questions for Review 1. The rates of job separation and job finding determine the natural rate of unemployment.The rate of job separation is the f

2、raction 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. 2

3、.Frictional unemployment is the unemployment caused by the time it takes to matchworkers and jobs. Finding an appropriate job takes time because the flow of informationabout job candidates and job vacancies is not instantaneous. Because different jobsrequire different skills and pay different wages,

4、 unemployed workers may not acceptthe first job offer they receive. In contrast, structural unemployment is the unemployment resulting from wagerigidity and job rationing. These workers are unemployed not because they are activelysearching for a job that best suits their skills (as in the case of f

5、rictional 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 forjobs to become available. Structural unemployment thus arises because firms fai

6、l toreduce wages despite an excess supply of labor. 3.The real wage may remain above the level that equilibrates labor supply and labordemand because of minimum wage laws, the monopoly power of unions, and efficiencywages. Minimum-wage laws cause wage rigidity when they prevent wages from falling

7、toequilibrium levels. Although most workers are paid a wage above the minimum level,for some workers, especially the unskilled and inexperienced, the minimum wage raisestheir wage above the equilibrium level. It therefore reduces the quantity of their laborthat firms demand, and creates an excess su

8、pply of workers, which increases unemployment. The monopoly power of unions causes wage rigidity because the wages of unionizedworkers are determined not by the equilibrium of supply and demand but by collectivebargaining between union leaders and firm management. The wage agreementoften raises the

9、 wage above the equilibrium level and allows the firm to decide howmany workers to employ. These high wages cause firms to hire fewer workers than atthe market-clearing wage, so structural unemployment increases. Efficiency-wage theories suggest that high wages make workers more productive.The infl

10、uence of wages on worker efficiency may explain why firms do not cut wagesdespite an excess supply of labor. Even though a wage reduction decreases the firm’swage bill, it may also lower worker productivity and therefore the firm’s profits. 4. Depending on how one looks at the data, most unemployme

11、nt can appear to be eithershort term or long term. Most spells of unemployment are short; that is, most of thosewho became unemployed find jobs quickly. On the other hand, most weeks of unemploymentare attributable to the small number of long-term unemployed. By definition,the long-term unemployed d

12、o not find jobs quickly, so they appear on unemploymentrolls for many weeks or months. 5.Europeans work fewer hours than Americans. One explanation is that the higherincome tax rates in Europe reduce the incentive to work. A second explanation is alarger underground economy in Europe as a result of

13、 more people attempting to evadethe high tax rates. A third explanation is the greater importance of unions in Europeand their ability to bargain for reduced work hours. A final explanation is based onpreferences, whereby Europeans value leisure more than Americans do, and thereforeelect to work few

14、er hours. Problems and Applications 1. a.In the example that follows, we assume that during the school year you look for apart-time job, and that, on average, it takes 2 weeks to find one. We also assumethat the typical job lasts 1 semester, or 12 weeks. b.If it takes 2 weeks to find a job, then

15、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 )], whe

16、re U is the number of people unemployed, and L is the number of people in thelabor 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 naturalrate of u

17、nemployment for this population of college students seeking part-timeemployment is 14 percent. 2. Call the number of residents of the dorm who are involved I, the number who are uninvolvedU, and the total number of students T = I + U. In steady state the total numberof involved students is constant

18、. For this to happen we need the number of newly uninvolvedstudents, (0.10)I, to be equal to the number of students who just becameinvolved, (0.05)U. Following a few substitutions: (0.05)U= (0.10)I = (0.10)(T – U), so We find that two-thirds of the students are uninvolved. 3. To show that the u

19、nemployment rate evolves over time to the steady-state rate, let’sbegin by defining how the number of people unemployed changes over time. The changein the number of unemployed equals the number of people losing jobs (sE) minus thenumber finding jobs (fU). In equation form, we can express this as:

20、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 (wewill assume that L is constant). Substituting forEtin the above equation, we find ΔUt+1 = s(L – Ut) – fUt. Dividing by L, we get an expression for the change in the unemployme

21、nt rate from t tot + 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 1below. Now take line 1 below, multiply the right side by (s + f)/(s + f) andrearrange terms to end up with line 2 below: Δ[U

22、/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 unemploymentrate equals its natural rate, the left-hand side of this expression equals zero. Thistells us that, as we found in the text, the natural rate of unemploy

23、ment (U/L)n equalss/(s + f). We can now rewrite the above expression, substituting (U/L)n for s/(s + f), toget 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 natur

24、al rate), thenΔ[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), thenΔ[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. 4

25、.Consider the formula for the natural rate of unemployment, If the new law lowers the chance of separation s, but has no effect on the rate of jobfinding f, then the natural rate of unemployment falls. For several reasons, however, the new law might tend to reduce f. First, raisingthe cost of firi

26、ng might make firms more careful about hiring workers, since firms havea harder time firing workers who turn out to be a poor match. Second, if job searchersthink that the new legislation will lead them to spend a longer period of time on a particularjob, then they might weigh more carefully whether

27、 or not to take that job. If thereduction in f is large enough, then the new policy may even increase the natural rateof unemployment. 5.a.The demand for labor is determined by the amount of labor that a profit-maximizingfirm wants to hire at a given real wage. The profit-maximizing condition istha

28、t the firm hire labor until the marginal product of labor equals the real wage, The marginal product of labor is found by differentiating the production functionwith respect to labor (see Chapter 3 for more discussion), In order to solve for labor demand, we set the MPL equal to the real wage ands

29、olve for L: Notice that this expression has the intuitively desirable feature that increases inthe real wage reduce the demand for labor. b.We assume that the 27,000 units of capital and the 1,000 units of labor are suppliedinelastically (i.e., they will work at any price). In this case we know th

30、at all 1,000units of labor and 27,000 units of capital will be used in equilibrium, so we can substitute these values into the abovelabor demand function and solve for . In equilibrium, employment will be 1,000, and multiplying this by 10 we find thatthe workers earn 10,000 units of output. The tot

31、al output is given by the productionfunction: Notice that workers get two-thirds of output, which is consistent with what weknow 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 labo

32、r demand function to decide how many workers to hire atthe given real wage of 11 and capital stock of 27,000: So 751 workers will be hired for a total compensation of 8,261 units of output. Tofind the new level of output, plug the new value for labor and the value for capitalinto the production fun

33、ction and you will find Y = 12,393. d.The policy redistributes output from the 249 workers who become involuntarilyunemployed to the 751 workers who get paid more than before. The lucky workersbenefit less than the losers lose as the total compensation to the working classfalls from 10,000 to 8,26

34、1 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 labordemand reduces the total number of jobs. Note, however, that if labor demand isless elastic than in this example, then the loss of e

35、mployment may be smaller, andthe change in worker income might be positive. 6.a.The labor demand curve is given by the marginal product of labor schedule facedby firms. If a country experiences a reduction in productivity, then the labordemand curve shifts to the left as in Figure 7-1. If labor bec

36、omes 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 effecton employment or unemployment, as in Figure 7-2. c.If uni

37、ons constrain real wages to remain unaltered, then as illustrated in Figure7-3, employment falls to L1 and unemployment equalsL – L1. This example shows that the effect of a productivity shock on an economy dependson the role of unions and the response of collective bargaining to such a change.

38、7. 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 eq

39、ual. 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 equatio

40、n and solve for w: 4w = 200 – 6w w = $20. Substitute the wage into the two labor demand equations to find LM is 80 and LSis 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.

41、 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. 8.Real wages have risen over tim

42、e in both the United States and Europe, increasing thereward for working (the substitution effect) but also making people richer, so they wantto “buy〞 more leisure (the income effect). If the income effect dominates, then peoplewant to work less as real wages go up. This could explain the European e

43、xperience, inwhich hours worked per employed person have fallen over time. If the income and substitutioneffects approximately cancel, then this could explain the U.S. experience, inwhich hours worked per person have stayed about constant. Economists do not havegood theories for why tastes might dif

44、fer, so they disagree on whether it is reasonableto think that Europeans have a larger income effect than do Americans. 9.The vacant office space problem is similar to the unemployment problem; we can applythe same concepts we used in analyzing unemployed labor to analyze why vacant officespace exi

45、sts. There is a rate of office separation: firms that occupy offices leave, eitherto move to different offices or because they go out of business. There is a rate of officefinding: firms that need office space (either to start up or expand) find empty offices. Ittakes time to match firms with availa

46、ble space. Different types of firms require spaceswith different attributes depending on what their specific needs are. Also, becausedemand for different goods fluctuates, there are “sectoral shifts〞—changes in the compositionof demand among industries and regionsthat affect the profitability andoffice needs of different firms.