《勞動經(jīng)濟學》(作者Borjas)第十三章習題答案.pdf

89 CHAPTER 13 13 1 Suppose there are 25 000 unemployed persons in the economy You are given the following data about the length of unemployment spells Duration of Spell in months Exit Rate 1 0 60 2 0 20 3 0 20 4 0 20 5 0 20 6 1 00 where the exit rate for month t gives the fraction of unemployed persons who have been unemployed t months and who escape unemployment at the end of the month The data can be used in the problem to calculate the number of workers who have 1 month of unemployment the number who have 2 months of unemployment and so on and how many months of unemployment are associated with workers who get a job after a given duration Duration Months Exit Rate Unemp Start of Month of Exiters of Stayers Months For Duration 1 0 60 25 000 15 000 10 000 15 000 2 0 20 10 000 2 000 8 000 4 000 3 0 20 8 000 1 600 6 400 4 800 4 0 20 6 400 1 280 5 120 5 120 5 0 20 5 120 1 024 4 096 5 120 6 1 00 4 096 4 096 0 24 576 a How many unemployment months will the 25 000 unemployed workers experience The 25 000 workers will experience 58 616 months of unemployment an average of 2 34 months per worker b What fraction of persons who are unemployed are long term unemployed that is are in unemployment spells which last 5 or more months Only 5 120 of the 25 000 workers 20 5 percent are in spells lasting 5 or more months c What fraction of unemployment months can be attributed to persons who are long term unemployed Although only 20 5 percent of workers are unemployed for 5 or more months they account for 29 696 of the 58 616 50 7 percent of months of unemployment 90 d What is the nature of the unemployment problem in this example too many workers losing their jobs or too many long spells Most spells are short lived but workers in long spells account for most of the unemployment observed in this economy Thus the main problem is too many long spells 13 2 Consider Table 599 of the 2002 U S Statistical Abstract a How many workers aged 20 or older were unemployed in the United States during 2001 How many of these were unemployed less than 5 weeks 5 to 14 weeks 15 to 26 weeks and 27 or more weeks In total 5 554 000 workers aged 20 years or older were unemployed in the U S in 2001 Of these 40 percent or 2 221 600 workers were unemployed for less than 5 weeks 32 2 percent or 1 788 388 workers were unemployed between 5 and 14 weeks 15 5 percent or 860 870 workers were unemployed 15 to 26 weeks and 12 9 percent or 716 466 workers were unemployed for 27 or more weeks b Assume that the average spell of unemployment is 2 5 weeks for anyone unemployed for less than 5 weeks Similarly assume the average spell is 10 weeks 20 weeks and 35 weeks for the remaining categories How many weeks did the average unemployed worker remain unemployed What percent of total months of unemployment are attributable to the workers that remained unemployed for at least 15 weeks The total number of weeks of unemployment is calculated as 2 221 600 2 5 1 788 388 10 860 870 20 716 466 35 65 731 590 months of unemployment spread over 5 554 000 unemployed workers implies that the average unemployed worker remained unemployed for 11 835 weeks The percent of total months of unemployment attributable to the workers that remained unemployed for at least 15 weeks is 860 870 20 716 466 35 65 731 590 64 34 percent 13 3 Suppose the marginal revenue from search is MR 50 1 5w where w is the wage offer at hand The marginal cost of search is MC 5 w a Why is the marginal revenue from search a negative function of the wage offer at hand If the offer at hand is relatively low it pays to keep on searching as the next offer is likely higher than the offer at hand If the offer at hand is very high however it does not pay to keep on searching since it is unlikely that the next search will generate a higher wage offer 91 b Can you give an economic interpretation of the intercept in the marginal cost equation in other words what does it mean to say that the intercept equals 5 Similarly what does it mean to say that the slope in the marginal cost equation equals one dollar The 5 indicates the out of pocket search costs Even if the offer at hand is zero so that there is no opportunity cost to search it still costs money to get to the firm and learn about the details of the potential job offer The slope equals 1 because the costs of search also vary directly with the opportunity cost of search which is the wage offer at hand If the wage offer at hand is 10 the opportunity cost from one more search equal 10 if the wage offer at hand is 11 the opportunity cost would be 11 and so on c What is the worker s asking wage Will a worker accept a job offer of 15 The asking wage is obtained by equating the marginal revenue of search to the marginal cost of search or 50 1 5w 5 w Solving for w implies that the asking wage is 18 The worker therefore would not accept a job offer of 15 d Suppose UI benefits are reduced causing the marginal cost of search to increase to MC 20 w What is the new asking wage Will the worker accept a job offer of 15 If we equate the new marginal cost equation to the marginal revenue equation we find that the asking wage drops to 12 The worker will now accept a wage offer of 15 13 4 a How does the exclusion of non working welfare recipients affect the calculation of the unemployment rate Use the 2002 U S Statistical Abstract to estimate what the 2000 unemployment rate would have been if welfare recipients had been included in the calculation Excluding non working welfare recipients from the unemployment rate biases the unemployment rate downward Table 560 of the Statistical Abstract shows that the labor force in 2000 totaled 140 863 000 while the number employed totaled 135 208 000 Thus the unemployment rate was 4 0 percent Table 513 of the Statistical Abstract shows that 2 253 000 people received public assistance in 2000 Assuming all of these were non working and out of the labor force their inclusion in the calculation of the unemployment rate would increase the unemployment rate to 140 863 000 2 253 000 135 208 000 140 863 000 2 253 000 5 5 b How does the exclusion of black market workers affect the calculation of the unemployment rate Estimate the best you can what the 2000 unemployment rate would have been if workers in the underground economy had been included in the calculation Excluding black market workers from the calculation of the unemployment rate keeps the unemployment rate artificially high At the best black market workers are not counted in the labor force but at the worst the black market workers claim to be in the labor force and without a job The problem is that there is no or very little data on the black market by definition Some researchers have estimated the underground economy to be on the order of 10 to 20 percent of activity in the U S Suppose half of underground economy workers have regular market jobs as well Suppose further that of the remaining half one half claim to be unemployed while the other half is out of the labor force Thus 10 percent of the unemployed workers are the number of underground economy workers in the labor force without a job 10 percent of 92 140 863 000 135 208 000 565 500 An equal number say they are not in the labor force And twice this number is already reporting having a legitimate job Using these estimates therefore the labor force should be 140 863 000 565 500 141 428 500 while the number employed should be 135 208 000 565 500 565 500 136 339 000 Thus the unemployment rate would be 141 428 500 136 339 000 141 428 500 3 6 13 5 Compare two unemployed workers the first is 25 years old and the second is 55 years old Both workers have similar skills and face the same wage offer distribution Suppose that both workers also incur similar search costs Which worker will have a higher asking wage Why Can search theory explain why the unemployment rate of young workers differs from that of older workers The marginal revenue of search depends on the length of the payoff period Younger workers have the most to gain from obtaining higher paying jobs since they can then collect the returns from their search investment over a longer expected work life As a result it pays for younger workers to set their asking wage at a relatively high level This implies that younger workers will tend to have higher unemployment rates and longer spells of unemployment than older workers 13 6 Suppose the government proposes to increase the level of UI benefits for unemployed workers A particular industry is now paying efficiency wages to its workers in order to discourage them from shirking What is the effect of the proposed legislation on the wage and on the unemployment rate for workers in that industry The introduction of UI benefits shifts the no shirking supply curve upwards from NS to NS because a higher wage would have to be paid in order to attract the same number of workers who do not shirk As a result the new equilibrium point Q entails a higher efficiency wage and leads to a larger number of unemployed workers Dollars Employment S NS NS Q Q P D E 93 13 7 It is well known that more educated workers are less likely to be unemployed and have shorter unemployment spells than less educated workers Which theory ies the job search model the sectoral shifts hypothesis or the efficiency wage model can explain this empirical correlation Two of the theories in question can be formulated in such a way that they each predict that more educated workers will have less unemployment and shorter spells of unemployment than less educated workers The job search model suggests that highly educated workers would have a lower unemployment rate either if they have relatively higher search costs or relatively lower gains from search It could then be argued for example that search costs are relatively higher for highly educated workers than for less educated workers perhaps because the nature of the job match between a highly educated worker and a firm is much more complex than the type of job match required between the firm and a worker who does repetitive tasks Similarly it is plausible to argue that it is easier to retool a highly educated worker than a less educated worker The decline in demand in particular industries then leads to sectoral shift that can be better weathered by highly educated workers The efficiency wage model however has a harder time explaining the correlation Presumably the output of highly educated workers is more difficult to measure than the output of less educated workers As a result efficiency wages are more likely to arise in industries that employ highly educated workers and these industries which pay above market wages would have to maintain a pool of unemployed workers in order to keep the employed workers in line 13 8 Suppose a country has 100 million inhabitants The population can be divided into the employed the unemployed and the persons who are out of the labor force OLF In any given year the transition probabilities among the various categories are given by Moving Into Employed Unemployed OLF Employed 0 94 0 02 0 04 Unemployed 0 20 0 65 0 15 Moving From OLF 0 05 0 03 0 92 These transition probabilities are interpreted as follows In any given year 2 percent of the workers who are employed become unemployed 20 percent of the workers who are unemployed find jobs and so on What will be the steady state unemployment rate Use E for the number of employed people U for the number of unemployed and N for the number not participating The flows of people among the three categories can be found by multiplying these numbers with respective probabilities in the table In the steady state the flows into each category must exactly balance the outflows This produces the following equations Employed E 94E 20U 05N Unemployed U 02E 65U 03N OLF N 04E 15U 92N 94 Only two of the three equations can be used however as E U N 100 million The steady state solutions for E U and N can now be found with brute force algebra The solution is that 54 273 million are employed 6 466 million are unemployed and 39 261 million are not in the labor force The steady state unemployment rate is then 646 10 739 60 466 6 100100 EU U u 13 9 Consider an economy with 250 000 adults of which 40 000 are retired senior citizens 20 000 are college students 120 000 are employed 8 000 are looking for work and 62 000 stay at home What is the labor force participation rate What is the unemployment rate The labor force participation rate 120 000 8 000 250 000 51 2 percent The unemployment rate 8 000 120 000 8 000 6 25 percent 13 10 Consider an economy with 3 types of jobs The table below shows the jobs the frequency with which vacancies open up on a yearly basis and the income associated with each job Searching for a job costs C per year and generates at most 1 job offer There is a 20 percent chance of not generating any offer in a year Note the expected search duration for a job with probability p of appearing is 1 p years Job Type Frequency Income A 30 percent 60 000 B 20 percent 100 000 C 30 percent 80 000 As a function of C specify the optimal job search strategy if the worker maximizes her expected income net of search costs There are four possible strategies for the worker accept any job paying at least 100 000 accept any job paying at least 80 000 accept any job paying at least 60 000 or do not search for a job Under the first strategy the worker will only accept a B job The expected search time for a B job is 5 years Thus the expected value of this strategy is 100 000 5C Under the second strategy the worker will accept a B or a C job The expected search time therefore is 2 years i e there is a 50 percent chance of receiving a B or a C job in a year so the search time is 1 0 5 2 Thus the expected value of this strategy is CC2000 88 2 000 80 3 02 0 3 0 000 100 3 02 0 2 0 95 Under the third strategy the worker will accept any of the three jobs The expected search time therefore is 1 25 years and the expected value of this strategy is CC25 1500 77 25 1 000 60 8 0 3 0 000 80 8 0 3 0 000 100 8 0 2 0 Under the fourth strategy the worker does not search and therefore does not find a job or incur search costs for an expected payoff of 0 One can now compare the four expected payoffs to determine that the optimal search strategy is Accept the first B job if C 4 000 Accept the first B or C job if 4 000 C 14 000 Accept the first job of any kind if 14 000 C 62 000 Don t search if 62 000 C 13 11 a A country is debating whether to fund a national data