《劳动经济学》作者Borjas第五章习题答案.pdf

29 CHAPTER 5 5-1. Suppose the labor supply curve is upward sloping and the labor demand curve is downward sloping. The study of economic trends over a particular time period reveals that the wage recently fell while employment levels rose. Which curve must have shifted and in which direction to produce this effect? If the supply curve does not shift, all wage and employment movements must occur along the supply curve, so that the wage rate and the employment level must move in the same direction. Because the wage went down while employment went up in the situation described in the question, it must have been the case that the supply curve shifted outwards (to the right). We do not have enough information to determine whether the demand curve shifted as well. 5-2. It takes time to produce a new economist, and prospective economists base their career decision by looking only at current wages across various professions. Further, the labor supply curve of economists is much more elastic than the labor demand curve. Suppose the market is now in equilibrium, but that the demand for economists suddenly rises because a new activist government in Washington wants to initiate many new programs that require the input of economists. Illustrate the trend in the employment and wages of economists as the market adjusts to this increase in demand. Initially, the market is in equilibrium at a wage w0 and an employment level of E0. The increase the demand for economists results in a new equilibrium wage of w1 and a new equilibrium employment level of E1. However, the demand for economists in the short-run is inelastic at E0, so the demand increase simply leads to a rise in the wage of economists (as indicated by point 1). In the next period, students believe this wage will persist and oversupply the market so that the cobweb leads to a new wage at point 2. In the next period, students undersupply (because the wage is too low) and the cobweb leads to a new wage at point 3, and so on. Because of the relative elasticities of supply and demand (as drawn), the cobweb is exploding and will never converge to a stable equilibrium. 30 5-3. Suppose the supply curve of physicists is given by w = 10 + 5E, while the demand curve is given by w = 50 3E. Calculate the equilibrium wage and employment level. Suppose now that the demand for physicists increases and the new demand curve is given by w = 70 3E. Assume this market is subject to cobwebs. Calculate the wage and employment level in each round as the wage and employment levels adjust to the demand shock. (Recall that each round occurs on the demand curve when the firm posts a wage and hires workers). What is the new equilibrium wage and employment level? The initial equilibrium is given by 10 + 5E = 50 3E. Solving these two equations simultaneously implies that w = $35 and ES = ED = 5. When demand increases to w = 70 3E, the new equilibrium wage is $47.5 and the equilibrium level of employment is 7.5. Round Wage Employment 1 $55.0 5 2 $43.0 9 3 $50.2 6.6 4 $45.9 8.0 5 $48.4 7.2 6 $46.9 7.7 7 $47.8 7.4 8 $47.2 7.6 The table gives the values for the wage and employment levels in each round. The values in the table are calculated by noting that in any given period the number of physicists is inelastically supplied, so that the wage is determined by the demand curve. Given this wage, the number of economists available in the next period is calculated. By round 7, the market wage rate is within 30 cents of the new equilibrium. 3 1 2 D1 D0 S E0 E1 w1 w0 Employment Wage 31 5-4. The 1986 Immigration Reform and Control Act (IRCA) made it illegal for employers in the United States to knowingly hire illegal aliens. The legislation, however, has not reduced the flow of illegal aliens into the country. As a result, it has been proposed that the penalties against employers who break the law be increased substantially. Suppose that illegal aliens, who tend to be less skilled workers, are complements with native workers. What will happen to the wage of native workers if the penalties for hiring illegal aliens increase? A substantial increase in the penalties associated with hiring illegal aliens will likely reduce the number of illegal aliens entering the United States. The effect of this shift in the size of the illegal alien flow on the marginal product (and hence the demand curve) of native workers hinges on whether illegal aliens are substitutes or complements with natives. As it is assumed that natives and illegal aliens are complements, a cut in the number of illegal aliens reduces the value of the marginal product of natives, shifting down the demand for native labor, and decreasing native wages and employment. 5-5. Suppose a firm is a perfectly discriminating monopsonist. The government imposes a minimum wage on this market. What happens to wages and employment? A perfectly discriminating monopsonist faces a marginal cost of labor curve that is identical to the supply curve. As a result, the employment level of a perfectly discriminating monopsonist equals the employment level that would be observed in a competitive market (at E*) The imposition of a minimum wage at wMIN leads to the same result as in a competitive market: the firm will only want to hire ED workers as wMIN is now the marginal cost of labor, but ES workers will want to find work at the minimum wage. Thus, the wage increases, but employment falls. Dollars S A VMPE Employment wMIN w* ES ED E* 32 5-6. What happens to wages and employment if the government imposes a payroll tax on a monopsonist? Compare the response in the monopsonistic market to the response that would have been observed in a competitive labor market. Initially, the monopsonist hires EM workers at a wage of wM. The imposition of a payroll tax shifts the demand curve to VMP, and lowers employment to E and the wage to w. Thus, the effect of imposing a payroll tax on a monopsonist is qualitatively the same as imposing a payroll tax in a competitive labor market: lower wages and employment. (It is interesting to note that the same result comes about if the payroll tax is placed on workers, so that the labor supply and marginal cost of labor curves shift as opposed to labor demand.) 5-7. An economy consists of two regions, the North and the South. The short-run elasticity of labor demand in each region is 0.5. The within-region labor supply is perfectly inelastic. The labor market is initially in an economy-wide equilibrium, with 600,000 people employed in the North and 400,000 in the South at the wage of $15 per hour. Suddenly, 20,000 people immigrate from abroad and initially settle in the South. They possess the same skills as the native residents and also supply their labor inelastically. (a) What will be the effect of this immigration on wages in each of the regions in the short run (before any migration between the North and the South occurs)? There will be no effect on the Norths labor supply in the short run, so the wage rate will not change there. In the South, labor supply will have increased by 5 percent, so the wage rate must fall by 5/(0.5) = 10 percent (recall that the elasticity of labor demand is -0.5, so a one percent decrease in wages would have been generated by a 0.5 percent expansion of the labor supply). The new hourly wage in the South, therefore, is $13.50 and total employment in the South is 420,000. Dollars Employment VMP VMPE w M MC E S EM w E B A 33 (b) Suppose 1,000 native-born persons per year migrate from the South to the North in response to every dollar differential in the hourly wage between the two regions. What will be the ratio of wages in the two regions after the first year native labor responds to the entry of the immigrants? After the initial migration, we have seen that wages in the South are $13.50 while wages in the North are $15. This difference leads 1,500 natives migrating from the South to the North in the first year. Employment in the North after one year, therefore is 601,500. Moreover, as the elasticity of labor demand in the North is -0.5 and employment has increased by 0.25 percent, the Northern wage falls by 0.5 percent to roughly $14.93. Likewise, employment in the South after one year is 418,500. As the elasticity of labor demand is -0.5 and employment has decreased by 0.3571 percent, the Southern wage increases by 0.71428 percent to roughly $13.60. Thus, the ratio of the Northern to Southern wage after one year is 1.09779. (c) What will be the effect of this immigration on wages and employment in each of the regions in the long run (after native workers respond by moving across regions to take advantage of whatever wage differentials may exist)? Assume labor demand does not change in either region. In the long run, people must move from the South to the North to equalize the wage rates in the two regions. Since the wages were equal in the two regions before the influx of immigrants, and they also must be equal after things settle down, the proportional decrease in the wage rate should be the same in the North and in the South. Because the elasticity of labor demand is the same in the two regions, this last observation implies that the percentage increase in employment in the North must be the same as the percentage increase in employment in the South. Thus, as 60 percent of the original workers were employed in the North, 60 percent of the 20,000 increase in Southern employment will eventually migrate to the North. In the long run, therefore, total Northern employment will be 612,000 while total Southern employment will be 408,000. (Note: there is no presumption that only immigrants further migrate to the North.) In each region, therefore, employment increases by 2 percent in the long run, i.e., 12,000 is 2 percent of 600,000 and 8,000 is 2 percent of 400,000. (This can also be seen immediately as 20,000 is 2 percent of the 1 million workers.) Now, given that the elasticity of labor demand is -0.5, the 2 percent increase in employment will cause the wage rate to fall by 4 percent. Hence, the long-run equilibrium hourly wage will be $14.40. 5-8. Chicken Hut faces perfectly elastic demand for chicken dinners at a price of $6 per dinner. The Hut also faces an upward sloped labor supply curve of E = 20w 120, where E is the number of workers hired each hour and w is the hourly wage rate. Thus, the Hut faces an upward sloped marginal cost of labor curve of MCE = 6 + 0.1E. Each hour of labor produces 5 dinners. (The cost of each chicken is $0 as the Hut receives two-day old chickens from Hormel for free.) How many workers should Chicken Hut hire each hour to maximize profits? What wage will Chicken Hut pay? What are Chicken Huts hourly profits? 34 First, solve for the labor demand curve: VMPE = P x MPE = $6 x 5 = $30. Thus, every worker is valued at $30 per hour by Chicken Hut. Now, setting VMPE = MCE yields 30 = 6 + .1E which implies E* = 240. Thus, Chicken Hut will hire 240 workers every hour. Further, according to the labor supply curve, 240 workers can be hired at an hourly wage of $18. Finally, Chicken Huts profits are = 240(5)($6) 240($18) = $2,880. 5-9. Pollys Pet Store has a local monopoly on the grooming of dogs. The daily inverse demand curve for pet grooming is: P = 20 0.1Q where P is the price of each grooming and Q is the number of groomings given each day. This implies that Pollys marginal revenue is: MR = 20 0.2Q. Each worker Polly hires can groom 20 dogs each day. What is Pollys labor demand curve as a function of w, the daily wage that Polly takes as given? As each worker can groom 20 dogs each day, and using Q = 20E, we have that VMPE = MR x MPE = ( 20 0.2Q ) (20) = (20 4E)(20) = 400 80E. Thus, as Pollys demand for labor satisfies VMPE = w, we have that her labor demand curve is E = 5 0.0125w. 5-10. The Key West Parrot Shop has a monopoly on the sale of parrot souvenir caps in Key West. The inverse demand curve for caps is: P = 30 0.4 Q where P is the price of a cap and Q is the number of caps sold per hour. Thus, the marginal revenue for the Parrot Shop is: MR = 30 0.8Q. The Parrot Shop is the only employer in town, and faces an hourly supply of labor given by: w = 0.9E + 5 where w is the hourly wage rate and E is the number of workers hired each hour. The marginal cost associated with hiring E workers, therefore, is: MCE = 1.8E + 5. Each worker produces two caps per hour. How many workers should the Parrot Shop hire each hour to maximize its profit? What wage will it pay? How much will it charge for each cap? 35 First, as Q = 2E, the labor demand curve is VMPE = MR x MPE = (30 0.8Q)(2) = 60 1.6Q = 60 3.2E. Setting VMPE equal to MCE and solving for E yields E = 11. Eleven workers can be hired at a wage of .9(11) + 5 = $14.99 per hour. The 11 workers make 22 caps each hour, and the 22 caps can be sold at a price of 30 0.4(22) = $21.20 each. 5-11. Ann owns a lawn mowing company. She has 400 lawns she needs to cut each week. Her weekly revenue from these 400 lawns is $20,000. If given an 18-inch deck push mower, a low-skill worker can cut each lawn in two hours. If given a 60-inch deck riding mower, a low-skill worker can cut the lawn in 30 minutes. Low-skilled labor is supplied inelastically at $5.00 per hour. Each laborer works 8 hours a day and 5 days each week. (a) If Ann decides to have her workers use push mowers, how many push mowers will Ann rent and how many workers will she hire? As each worker can cut a lawn in 2 hours, it follows that each worker can cut 4 lawns in a day or 20 lawns in a week. Therefore, Ann would need to rent 20 push mowers and hire 20 workers in order to cut all 400 lawns each week. (b) If she decides to have her workers use riding mowers, how many riding mowers will Ann rent and how many workers will she hire? As each worker can cut a lawn in 30 minutes, it follows that each worker can cut 16 lawns in a day or 80 lawns in a week. Therefore, Ann would need to rent 5 riding mowers and hire 5 workers in order to cut all 400 lawns each week. (c) Suppose the weekly rental cost (including gas and maintenance) for each push mower is $250 and the weekly rental cost (including gas and maintenance) of each riding mower is $1,800. What equipment will Ann rent? How many workers will she employ? How much profit will she earn? If Ann uses push mowers, her weekly cost of mowers is $250(20) = $5,000 while her weekly labor cost is $5(20)(40) = $4,000. Under this scenario, her weekly profit is $11,000. If Ann uses riding mowers, her weekly cost of mowers is $1,800(5) = $9,000 while her weekly labor cost is $5(5)(40) = $1,000. Thus, under this scenario, her weekly profit is $10,000. Therefore, under these conditions, Ann will rent 20 push mowers and employ 20 low-skill workers. (d) Suppose the government imposes a 20 percent payroll tax (paid by employers) on all labor and offers a 20 percent subsidy on t