Ch3_Labor Demand 鲍哈斯劳动经济学
劳动经济学课件(全) 第三章 劳动力需求
劳动经济学
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人力资源管理专业
第三节 企业长期劳动力需求
四、劳动力需求变化
（三）政府的特殊政策
特殊就业促进政策 发放工资补贴 最低工资法
劳动经济学
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人力资源管理专业
第三节 企业长期劳动力需求
五、劳动力需求的调整
（一）生产规模的扩大
L
劳动经济学
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人力资源管理专业
第三节 企业长期劳动力需求
三、最佳生产方法与劳动力需求决定
（一）总成本既定
劳动经济学
25
人力资源管理专业
第三节 企业长期劳动力需求
三、最佳生产方法与劳动力需求决定
（二）总产量既定
劳动经济学
26
人力资源管理专业
第三节 企业长期劳动力需求
三、最佳生产方法与劳动力需求决定
复习思考：
1. 劳动力需求弹性 2. 企业短期劳动力需求 3. 企业长期劳动力需求
劳动经济学
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人力资源管理专业
第一节 劳动力需求概述
劳动力需求曲线 (labor demand curve)
W
0
劳动经济学
D
L
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人力资源管理专业
第三节 企业长期劳动力需求
某企业的产量可以表达为：
Q= f (L,K) = L K
企 业 使 用 机 器 的 成 本 为 750 元 / 周 ， 人 力 成 本 为 300元/周。当企业产量为1000单位时，确定企业最佳 人力与资本组合。
当人力成本下降为225元/周时，确定企业最佳 人力与资本组合，并计算劳动力需求弹性。
劳动经济学
《劳动经济学》(作者Borjas)第五章习题答案
CHAPTER 55-1. 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.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 E S = E D = 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 Employment1 $55.0 52 $43.0 93 $50.2 6.64 $45.9 8.05 $48.4 7.26 $46.9 7.77 $47.8 7.48 $47.2 7.6The 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.01 w 1w 0W age5-4. 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 theemployment level that would be observed in a competitive market (at E *) The imposition of a minimum wage at w MIN leads to the same result as in a competitive market: the firm will only want to hire E D workers as w MIN is now the marginal cost of labor, but E S workers will want to find work at the minimum wage. Thus, the wage increases, but employment falls.DollarsE w w *S D5-6. What happens to wages and employment if the government imposes a payroll tax on amonopsonist? Compare the response in the monopsonistic market to the response that would have been observed in a competitive labor market.Initially, the monopsonist hires E M workers at a wage of w M . 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 labormarket 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 North’s 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.DollarsEmploymentw M w ′(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 by0.71428 percent to roughly $13.60. Thus, the ratio of the Northern to Southern wage after one year is1.09779.(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 ofE = 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 ofMC E = 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 Hut’s hourly profits?First, solve for the labor demand curve: VMP E = P x MP E = $6 x 5 = $30. Thus, every worker is valued at $30 per hour by Chicken Hut. Now, setting VMP E = MC E 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 Hut’s profits are Π = 240(5)($6) –240($18) = $2,880.5-9. Polly’s Pet Store has a local monopoly on the grooming of dogs. The daily inverse demand curve for pet grooming is:P = 20 – 0.1Qwhere P is the price of each grooming and Q is the number of groomings given each day. This implies that Polly’s marginal revenue is:MR = 20 – 0.2Q.Each worker Polly hires can groom 20 dogs each day. What is Polly’s 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 thatVMP E = MR x MP E = ( 20 – 0.2Q ) (20) = (20 – 4E)(20) = 400 – 80E.Thus, as Polly’s demand for labor satisfies VMP E = w, we have that her labor demand curve isE = 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 Qwhere 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 + 5where 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:MC E = 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?First, as Q = 2E, the labor demand curve isVMP E = MR x MP E = (30 – 0.8Q)(2) = 60 – 1.6Q = 60 – 3.2E.Setting VMP E equal to MC E 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 the rental cost of capital. What equipment will Ann rent? How many workers will she employ? How much profit will she earn?Under these conditions, the cost of labor has increased to $6.00 per hour, while the rental costs for a push mower and a riding mower have decreased to $200 and $1,440 respectively. Ann’s profits under the two options, therefore, arePush-Profit = $20,000 – $200(20) – $6(20)(40) = $11,200.Rider-Profit = $20,000 – $1,440(5) – $6(5)(40) = $11,600.Thus, under these conditions, Ann rents riding mowers, hires 5 low-skill workers, and earns a weekly profit of $11,600.5-12. In the United States, some medical procedures can only be administered to a patient by a doctor while other procedures can be administered by a doctor, nurse, or lab technician. What might be the medical reasons for this? What might be the economic reasons for this?The American Medical Association might argue that doctors have more training and experience than nurses, and therefore, are the only professionals who can make certain decisions or perform certain procedures.Economically, the AMA has an incentive to restrict the number of people who can practice medicine (or perform certain procedures) in order to keep doctor wages high. If nurses were allowed to do everything they were capable of, fewer doctors would be demanded, and doctor wages would fall. From an economic viewpoint, therefore, the AMA restricts the supply of doctors, which keeps doctor wages artificially high.WageW restW unrestRestricted Supply ofDoctorsUnrestricted Supplyof DoctorsL rest L unrest Services Provided by DoctorsLabor Market For Medical Services Provided by Doctors。
劳动经济学第四章劳动力需求
劳动经济学第四章劳动力需求劳动经济学是研究劳动市场及其与经济系统相互作用的学科。
在劳动分工和劳动力的需求方面，劳动经济学提供了深入的理论和实证研究。
本文将聚焦于劳动经济学中的第四章——劳动力需求，探讨劳动力需求的决定因素和影响机制。
一、劳动力需求的概念及决定因素劳动力需求是指企业或机构对劳动力数量的需求，涉及到劳动人口的就业。
劳动力需求决定因素复杂多样，主要包括以下几个方面:1. 经济增长率：经济增长率对劳动力需求产生直接影响。
经济增长率高的国家或地区，企业投资扩张、产业发展迅速，因此对劳动力的需求也相对较大。
2. 劳动生产率：劳动生产率是决定劳动力需求的重要因素。
生产力水平高的企业可以通过单位劳动力的数量实现较高的产出，因此对劳动力的需求相对较少。
3. 技术进步与创新：技术进步和创新对劳动力需求产生深远影响。
高新技术行业的发展往往需要更多的技术人才，因此对劳动力的需求也随之增加。
4. 政府政策与法规：政府对劳动力市场的干预也是劳动力需求的决定因素之一。
政府的就业政策、劳动法规等都会直接或间接影响企业对劳动力的需求。
二、劳动力需求的影响机制1. 边际产品与边际成本理论：企业在决定是否雇佣额外劳动力时，会比较劳动力的边际产品与边际成本。
当边际产品大于边际成本时，企业会继续增加劳动力；当边际产品小于边际成本时，企业会减少劳动力。
2. 调整成本与规模效应：调整成本是指企业在改变雇佣劳动力数量时所需要支付的成本，主要包括流动性成本和固定成本。
规模效应是指企业规模对单位产品成本的影响。
当企业规模扩大时，单位产品成本往往会下降。
3. 劳动力替代与辅助技术：某些劳动力可以被机器或技术所替代，特别是一些重复性和繁重的劳动岗位。
而对于一些需要辅助技术或专业技能的职位，劳动力需求相对较高。
4. 资本与劳动力替代：在生产过程中，企业可以通过增加资本投入来替代一部分劳动力。
当资本相对便宜或劳动力相对昂贵时，企业更倾向于选择资本替代劳动力。
劳动经济学(鲍哈斯版)重点复习题总结
1.论述一个存在着两部门的经济中，最低工资对被覆盖的部门和未被覆盖的部门的影响。（P175）
答：（P154）（图）
如果到最低工资仅仅在被覆盖部门的工作岗位上推行，那么被替代的工作者也许就会移动到未被覆盖的部门，以至供给曲线会向右移动，减少为被覆盖部门的工资。如果获得最低工资工作岗位是容易的，那么在未被覆盖部门工作的工作者也许就会辞去他们的工作，在被覆盖的部门等待，直到一个工作岗位出现，将未被覆盖部门的供给曲线移动到左边，并且提高未被覆盖部门的工资。
第三章
1.什么是新增工作者效应？什么是受阻工作者效应？（P107）
答：
（1）新增工作者效应：指在经济衰退时期由于家中主要劳动力失去工作（家庭收入下降），次级劳动者不得不寻找工作弥补家庭收入损失。因此新增工作者效应意味着次级劳动力参与率具有一种逆（反）周期趋势。
（2）受阻工作者效应：a.指很多失业者在衰退时期感觉找不到工作，于是干脆放弃了（暂时退出）；b.隐性失业者——存在受阻工作者效应的结果是劳动参与率具有一种顺应周期趋势。
第十章
1.劳动力市场歧视（论述题）：（P444）
答：
Ⅰ.个人偏好性歧视：
构成
利润
雇佣人数
雇主歧视
纯（黑白分明）
↓
↓
雇员歧视
纯（黑白分明）
不变
↓
顾客歧视
①能藏：不分
不变
不变
②不可藏：纯白人
不变
不变
Ⅱ.统计性歧视：来自于群体
素质越高，越遭歧视；反之—
2.请推倒瓦哈卡歧视测度方法。这种统计方法真的能测度歧视对受影响群体的相对工资的影响吗？（P444）（计算题）
（1）女性真实工资的明显提高；
（2）生育行为的变化：①生育观念变化（不愿生）；②市场工资的提高也使得抚养孩子成为一种昂贵的家庭活动，因而成为家中孩子数减少的原因之一——③致使妇女的保留工资的下降，更愿意进入劳动力市场；
《劳动经济学》（作者Borjas）第四章习题答案
《劳动经济学》（作者Borjas）第四章习题答案CHAPTER 44-1. Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 1 machine to do the work of 3 persons. The firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity of labor demand as the wage falls from $300 to $225?Because labor and capital are perfect substitutes, the isoquants (in bold) are linear and the firm will use only labor or only capital, depending on which is cheaper in producing 100 units of output.The (absolute value of the) slope of the isoquant (MP E / MP K ) is 1/3 because 1 machine does the work of 3 men. When the wage is $900 (left panel), the slope of the isocost is 300/750. The isocost curve,therefore, is steeper than the isoquant, and the firm only hires capital (at point A ). When the weekly wage is $225 (right panel), the isoquant is steeper than the isocost and the firm hires only labor (at point B ).Weekly Salary = $300 Weekly Salary = $225The elasticity of labor demand is defined as the percentage change in labor divided by the percentage change in the wage. Because the demand for labor goes from 0 to a positive quantity when the wagedropped to $225, the (absolute value of the) elasticity of labor demand is infinity.LaborCapitalLaborCapital4-2. (a) What happens to the long-run demand curve for labor if the demand for the firm’s output increases?The labor demand curve is given by VMP E = MR x MP E. As demand for the firm’s output increases, its marginal revenue also increases. Thus, an increase in demand for the firm’s output shifts the labor demand curve to the right.(b) What happens to the long-run demand curve for labor if the price of capital increases?To determine how an increase in the price of capital changes the demand for labor, suppose initially that the firm is producing 200 units of output at point P in the figure. The increase in the price of capital (assuming capital is a normal input) increases the marginal costs of the firm and will reduce the profit-maximizing level of output to say 100 units. The increase in the price of capital also flattens the isocost curve, moving the firm to point R. The move from point P to point R can be decomposed into a substitution effect (P to Q) which reduces the demand for capital, but increases the demand for labor, and a scale effect (Q to R) which reduces the demand for both labor and capital. The direction of the shift in the demand curve for labor, therefore, will depend on which effect is stronger: the scale effect or the substitution effect.4-3. Union A wants to represent workers in a firm that hires 20,000 person workers when the wage rate is $4 and hires 10,000 workers when the wage rate is $5. Union B wants to represent workers in a firm that hires 30,000 workers when the wage is $6 and hires 33,000 workers when the wage is $5. Which union would be more successful in an organizing drive?The union will be more likely to attr act the workers’ support when the elasticity of labor demand (in absolute value) is small. The elasticity of labor demand facing union A is given by: η = percent ?L / percent ?w = (20,000–10,000)/20,000 ÷ (4–5)/4 = –2.The elasticity of labor demand facing union B equals (33,000–30,000)/33,000 ÷ (5–6)/5 = –5/11 ≈ –.45. Union B, therefore, is likely to have a more successful organizing drive as 0.45 < 2.4-4. Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.(a) In which direction will the substitution effect change the firm’s employment and capital stock?Prior to the price shift, the absolute value of the slope of the isocost line (w/r) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect).(b) In which direction will the scale effect change the firm’s employment and capital stock?Because both prices fall, the marginal cost of production falls, and the firm will want to expand. The scale effect, therefore, increases the demand for both labor and capital (as both are normal inputs).(c) Can we say conclusively whether the firm will use more or less labor? More or less capital?The firm will certainly use more capital as the substitution and scale effects reinforce each other in that direction, but the change in labor employed will depend on whether the substitution or the scale effect for labor dominates.4-5. What happens to employment in a competitive firm that experiences a technology shock such that at every level of employment its output is 200 units/hour greater than before?Because output increases by the same amount at every level of employment, the marginal product of labor, and hence the value of the marginal product of labor, does not change. Therefore, as the value of the marginal product of labor will equal the wage rate at the same level of employment as before, the level of employment will not change.4-6. Suppose the market for labor is competitive and the supply curve for labor is backwardbending over part of its range. The government now imposes a minimum wage in this labor market. What is the effect of the minimum wage on employment? Does the answer depend on which of the two curves (supply or demand) is steeper? Why?Equilibrium is attained where the supply curve intersects the demand curve, and the equilibriumemployment and wage levels are E* and w*, respectively . When the minimum wage is set at w MIN , the firm wants to hire E D workers but E S workers are looking for work. As long as the downward-sloping portion of the supply curve is to the right of the demand curve, the fact that the supply curve is downward sloping creates no problems beyond those encountered in the typical competitive model. An interesting extension of the problem would consider the case where the downward-sloping portion of the supply curve recrosses the demand curve at some point above w * and the minimum wage is set above that point.4-7. Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive product market. Thefirm’s elasticity of demand for labor is ?0.4. Suppose the wage increases by 5 percent. What will happen to the number of workers hired by the firm? What will happen to the marginal productivity of the last worker hired by the firm?Given the estimates of the elasticity of labor demand and the change in the wage, we have that4.0%%?=??=w E η => 4.0%5%?=?E=> %2%?=?E .Thus, the firm hires 2 percent fewer workers. Furthermore, because the labor market is competitive, the marginal worker is paid the value of his marginal product. As the product market is also competitive, therefore, we know that the output price does not change so that the marginal productivity of the marginal worker increases by 5 percent.Employment W agesw M INS D4-8. A firm’s technology requires it to combine 5 person-hours of labor with 3 machine-hours to produce 1 unit of output. The firm has 15 machines in place and the wage rate rises from $10 per hour to $20 per hour. What is the firm’s short-run elasticity of labor demand?Unless the firm goes out of business, it will combine 25 persons with the 15 machines it has in place regardless of the wage rate. Therefore, employment will not change in response to the movement of the wage rate, and the short-run elasticity of labor demand is zero.4-9. In a particular industry, labor supply is E S = 10 + w whilelabor demand is E D = 40 ? 4w, where E is the level of employment and w is the hourly wage.(a) What is the equilibrium wage and employment if the labor market is competitive? What is the unemployment rate?In equilibrium, the quantity of labor supplied equals the quantity of labor demanded, so that E S = E D. This implies that 10 + w = 40 – 4w. The wage rate that equates supply and demand is $6. When the wage is $6, 16 persons are employed. There is no unemployment because the number of persons looking for work equals the number of persons employers are willing to hire.(b) Suppose the government sets a minimum hourly wage of $8. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage? What is the unemployment rate?If employers must pay a wage of $8, employers would only want to hire E D = 40 – 4(8) = 8 workers, while E S = 10 + 8 = 18 persons would like to work. Thus, 8 workers lose their job following the minimum wage and 2 additional people enter the labor force. Under the minimum wage, the unemployment rate would be 10/18, or 55.6 percent.4-10. Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function isf(E,K) = E?K ?,so that the marginal product of labor isMP E = (?)(K/E) ? .If the current capital stock is fixed at 1,600 units, how much labor should the firm employ in the short run? How much profit will the firm earn?The firm’s labor demand curve is it marginal revenueproduct of labor curve, VMP E, which equals the marginal productivity of labor, MP E, times the marginal revenue of the firm’s product. Bu t as price is fixed at $50, MR = 50. Thus, we have thatVMP E = MP E× MR = (?)(1,600/E)?(50) = 1,000 / E? .Now, by setting VMP E = w and solving for E, we find that the optimal number of workers for the firm to hire is 10,000 workers. The firm then makes (1600)?(10000)? = 4,000 units of output and earns a profit of 4,000($50) – 1,600($25) – 10,000 ($10) = $60,000.4-11. Table 616 of the 2002 U.S. Statistical Abstract reports data on the nominal and real hourly minimum wage from 1960 through 2000. Under which president did the nominal minimum wage increase by the greatest dollar amount? Under what president did the real minimum wage increase by the greatest percentage?The data are:AdministrationsYear CurrentReal(2000)percentChangeNominalChange President1960 $1.00 $5.821961 $1.15 $6.621962 $1.15 $6.561963 $1.25 $7.03 20.79percent $0.25 Kennedy 1964 $1.25 $6.941965 $1.25 $6.831966 $1.25 $6.641967 $1.40 $7.221968 $1.60 $7.92 14.12percent $0.35 Johnson 1969 $1.60 $7.51 1970 $1.60 $7.101971 $1.60 $6.801972 $1.60 $6.591973 $1.60 $6.211974 $2.00 $6.99 -6.92percent $0.40 Nixon 1975 $2.10 $6.72 1976 $2.30 $6.96 3.57percent $0.20 Ford 1977 $2.30 $6.54 1978 $2.65 $7.001979 $2.90 $6.881980 $3.10 $6.48 -0.92percent $0.80 Carter 1981 $3.35 $6.35 1982 $3.35 $5.981983 $3.35 $5.791984 $3.35 $5.551985 $3.35 $5.361986 $3.35 $5.261987 $3.35 $5.081988 $3.35 $4.88 -23.15percent $0.00 Reagan 1989 $3.35 $4.65 1990 $3.80 $5.011991 $4.25 $5.371992 $4.25 $5.22 12.26percent $0.90 Bush 1993 $4.25 $5.06 1994 $4.25 $4.941995 $4.25 $4.801996 $4.75 $5.211997 $5.15 $5.531998 $5.15 $5.441999 $5.15 $5.322000 $5.15 $5.15 1.78percent $0.90 ClintonThe nominal minimum wage increased by the greatest dollar amount ($0.90) under both President Bush and President Clinton. In percentage terms, however, the real minimum wage increased by 12.26 percent during the Bush presidency, but only by 1.78 percent during the Clinton presidency. The greatest percent increase, however, came during the Kennedy presidency, when the minimum wage increased by over 20 percent.。
劳动经济学(作者Borjas)第十章习题答案
CHAPTER 1010-1. Suppose blacks and whites are not perfect substitutes in production. The firm would like to minimize the costs of producing 100 units of output. Show that employers who discriminate against blacks earn lower profits. Does your conclusion depend on whether the market-determined black wage is lower than the white wage?As drawn in the figure below, the profit-maximizing position for a non-discriminating employer occurs at point P where the 100-unit isoquant is tangent to the lowest possible isocost line given by X. Discrimination against blacks implies that the utility-adjusted black wage is relatively high, and hence employers would move to a point like A, which is tangent to the utility-adjusted isocost given by line Y. Note, however, that at point A the true costs of production are given by isocost line Z, which is clearly higher than isocost line X. As a result, discrimination is costly. It is worth noting that this analysis assumes nothing about which wage, the black or the white, is higher.Capital10-2. Suppose black and white workers are complements in the sense that the marginal product of whites increases when more blacks are hired. Suppose also that white workers do not like working alongside black workers. Does employee discrimination lead to complete segregation? Does it create a wage differential between black and white workers?If blacks and whites are perfect substitutes, employee discrimination leads to complete segregation. If, however, blacks and whites are complements as in this problem, then there is an incentive for employers to employ blacks and whites together in the work place if the increase in productivity achieved by integrating the work force is higher than the extra wages employers must pay white workers to compensate them for working alongside blacks. The interpretation of the wage differential between black and white workers is more difficult. The wage differential between the two groups will reflect not only the effect of discrimination (a higher wage for whites to encourage them to work alongside blacks), but also the effect of differences in productivity. Overall, however, it is clear that whites must be paid a compensating differential.10-3. In 1960, the proportion of blacks in Southern states was higher than the proportion of blacks in Northern states. The black-white wage ratio in Southern states was also much lower than in Northern states. Does the difference in the relative black-white wage ratios across regions indicate that Southern employers discriminated more than Northern employers?Suppose employers in neither region discriminate, so that the equilibrium black-white wage differential in both regions is determined by the (relative) demand for and supply of black workers. If there arerelatively many more black workers in the South than in the North, then the black-white wage ratio will be lower in the South than in the North, as the marginal black hired in the South is less valuable than the marginal black hired in the North. Thus, the fact that blacks earn relatively less in the South need not indicate that Southern employers discriminate more than Northern employers. Rather, the large differential may simply reflect the relatively large number of black workers in the South. (This does assume that blacks and whites are not perfect substitutes.)10-4. Suppose years of schooling, s , is the only variable that affects earnings. The equations for the weekly salaries of male and female workers are given by:w m = 500 + 100sandw f = 300 + 75s .On average, men have 14 years of schooling and women have 12 years of schooling.(a) What is the male-female wage differential in the labor market?The wage differential can be written as:∆w − = w −m – w − f = 500 + 100 s −m – ( 300 + 75 s −f ) = 500 + 100(14) – 300 – 75(12) = $700(b) Using the Oaxaca decomposition, calculate how much of this wage differential is due to discrimination?The raw wage differential is4342144443444421Skills in Difference to Due al Differenti tion Discrimina to Due al Differenti )()()(f m m f f m f m s s s w −+−+−=∆βββαα700$200$500$)1214(10012)75100()300500(Skills in Difference to Due al Differenti tion Discrimina to Due al Differenti =+=−+−+−=4342144443444421.The wage differential that is due to discrimination equals $500, or 5/7ths of the raw differential.(c) Can you think of an alternative Oaxaca decomposition that would lead to a different measure of discrimination? Which measure is better?Suppose instead of adding and subtracting βm f s to the expression giving the raw wage differential, βf m s had been added and subtracted to the expression. The Oaxaca decomposition would then be given by ∆w s s s m f m f m f m f =−+−+−()()()ααβββDifferential Due to Discrimination Differential Due to Difference in Skills 1244443444412434 700150$550$)1214(7514)75100()300500(Skills in Difference to Due al Differenti tion Discrimina to Due al Differenti =+=−+−+−=4342144443444421.Under this method, $550 of the $700 wage differential is due to discrimination. The difference between methods arises because of the way in which discrimination is defined. In one, discrimination is measured by calculating how much a woman would earn if she were treated like a man (as in the text), and in the second it is measured by calculating how much a man would earn if he were treated like a woman. On the surface, neither is a better measure. It can be shown, however, that the second approach (as in part c) attributes more variation to discrimination.10-5. Suppose the firm’s production function is given byq E E w b =+10,where E w and E b are the number of whites and blacks employed by the firm respectively. It can be shown that the marginal product of labor is thenMP E E E w b=+5.Suppose the market wage for black workers is $10, the market wage for whites is $20, and the price of each unit of output is $100.(a) How many workers would a firm hire if it does not discriminate? How much profit does this non-discriminatory firm earn if there are no other costs?There are no complementarities between the types of labor as the quantity of labor enters the production function as a sum, E w + E b . Further, the market-determined wage of black labor is less than the market-determined wage of white labor. Thus, a profit-maximizing firm will not hire any white workers and will hire black workers up to the point where the black wage equals the value of their marginal product:w p MP E b E b=×=1005()which yields E b = 2,500. The 2,500 black workers produce q = 10(sqrt(2,500)) = 500 units of output, and profits are:Π = pq – w b E b = 100(500) – 10(2,500) = $25,000.(b) Consider a firm that discriminates against blacks with a discrimination coefficient of .25. How many workers does this firm hire? How much profit does it earn?The firm acts as if the black wage is w b (1 + d ), where d is the discrimination coefficient. The employer’s hiring decision, therefore, is based on a comparison of w w and w b (1 + d ). The employer will then hire whichever input has a lower utility-adjusted price. As d = 0.25, the employer is comparing a white wage of $20 to a black (adjusted) wage of $12.50. As $12.50 < $20, the firm will hire only blacks.As before, the firm hires black workers up to the point where the utility-adjusted price of a black worker equals the value of marginal product, orbE )5(10050.12=so that E b = 1,600 workers. The 1,600 workers produces 400 units of output, and profits areΠ = 100(400) – 10(1,600) = $24,000.(c) Finally, consider a firm that has a discrimination coefficient equal to 1.25. How many workers does this firm hire? How much profit does it earn?As d = 1.25, the employer compares a white wage of $20 against a black wage of $22.50. Thus, the firm hires only whites. The firm hires white workers up to the point where the price of a white worker equals the value of marginal product:wE )5(10020=so the firm hires 625 whites, produces 250 units of output, and earns profits ofΠ = 100(250) – 20(625) = $12,500.10-6. Suppose a restaurant hires only women to wait on tables, and only men to cook the food and clean the dishes. Is this most likely to be indicative of employer, employee, consumer, or statistical discrimination?If this hiring pattern is due to discrimination at all, it is most likely due to customer discrimination. It is not employer discrimination as the employer is hiring both men and women. It is further unlikely to be statistical discrimination as an employer would likely be able to determine in a short time what would happen if women became chefs or men waited on tables. The hiring pattern could result from employee discrimination as well, but this seems unlikely as wait staff and chefs/dishwashers interact on the job.10-7. Suppose that an additional year of schooling raised wages by 7 percent in 1970, regardless of the worker’s race or ethnicity. Suppose also that the wage differential between the average white and the average Hispanic was 36 percent. Finally, assume education is the only factor that affects productivity, and the average white worker had 12 years of schooling in 1970, while the average Hispanic worker had 9 years. By 1980, the average white worker had 13 years of education, while the average Hispanic had 11 years. A year of schooling still increased earnings by 7 percent, regardless of the worker’s ethnic background, and the wage differential between the average white worker and the average Hispanic fell to 24 percent. Was there a decrease in wage discrimination during the decade? Was there a decrease in the share of the wage differential between whites and Hispanics that can be attributed to discrimination?On the basis of their education, the average white worker should have earned 21 percent more in 1970 and 14 percent more in 1980 than the average Hispanic worker. The average Hispanic worker actually received 36 percent less in 1970 and 24 percent less in 1980. Thus, in 1970, 15 percentage points can be attributed to wage discrimination, while 10 percentage points can be attributed to wage discrimination in 1980. Hence, the degree of discrimination declined from 15 to 10 percent from 1970 to 1980. On the other hand, discrimination accounted for (15/36)×100 = 41.7 percent of the 1970 differential and(10/24)×100 = 41.7 percent of the 1980 differential. Thus, there was no change in the portion due to discrimination. The two findings are not contradictory. The wage differential decreased for two reasons – less discrimination and smaller educational differences – and the two channels were equally important. Hence, despite its absolute decrease, the importance of discrimination relative to other factors was unchanged.10-8. Use Table 211 of the 2002 U.S. Statistical Abstract.(a) How much does the average female worker earn for every 1 dollar earned by the average male worker?$23,551 / $40,257 = $0.59(b) How much does the average black worker earn for every 1 dollar earned by the average white worker?$24,979 / $33,326 = $0.75.(c) How much does the average Hispanic worker earn for every 1 dollar earned by the average white worker?$22,096 / $33,326 = $0.66.10-9. Repeat each of the three comparisons in Problem 8, except now condition on education level. In other words, calculate the wage ratios separately for all workers who have not graduated high school, have only a high school degree, have a Bachelor’s degree, and have a Master’s degree. Does the degree of labor market inequality decrease or increase after conditioning on education? Why? Men & Women:No High School Degree: $12,145 / $18,855 = $0.64.High School Degree: $18,092 / $30,414 = $0.59.Bachelor’s Degree: $32,546 / $57,706 = $0.56.Master’s Degree: $42,378 / $68,367 = $0.62.Whites & Blacks:No High School Degree: $13,569 / $16,620 = $0.82.High School Degree: $20,991 / $25,270 = $0.83.Bachelor’s Degree: $37,422 / $46,894 = $0.80.Master’s Degree: $48,777 / $55,622 = $0.88.Whites & Hispanics:No High School Degree: $16,106 / $16,620 = $0.97.High School Degree: $20,704 / $25,270 = $0.82.Bachelor’s Degree: $36,212 / $46,894 = $0.77.Master’s Degree: $50,576 / $55,622 = $0.91.In every case, the wage gap closes when education attainment is taken into account except the gap stays the same between men and women with a high school degree and the gap worsens between men and women with a Bachelor’s degree.10-10. After controlling for age and education, it is found that the average woman earns $0.80 for every $1.00 earned by the average man. After controlling for occupation to control for compensating differentials (i.e., maybe men accept riskier or more stressful jobs than women, and therefore are paid more), the average woman earns $0.92 for every $1.00 earned by the average man. The conclusion is made that occupational choice reduces the wage gap 12 cents and discrimination is left to explain the remaining 8 cents.(a) Explain why discrimination may explain more than 8 cents of the 20 cent differential (and occupational choice may explain less than 12 cents of the differential).Discrimination may occur during the process of choosing an occupation (i.e., occupational crowding). As students, for example, girls may be encouraged to take a different set of courses than boys. Later, discrimination may preclude women from being hired into the higher paying occupations. Put differently, accepting the statistics at face value requires there to be wage discrimination but no employment discrimination.(b) Explain why discrimination may explain less than 8 cents of the 20 cent differential.The labor supply curve of women and men could be different, because they have different preferences when it comes to leisure and consumption. Thus, wage differences might come about to account for gender-based preferences and not discrimination. Put differently, other factors chosen by the employee, such as hours worked or work experience, have yet to be controlled for and could explain at least some of the remaining 8 cent differential.10-11. Consider a town with 10 percent blacks (and the remainder is white). Because blacks are more likely to work the night shifts, 20 percent of all cars driven in that town at night are driven by blacks. One out of every twenty people driving at night is drunk, regardless of race. Persons who are not drunk never swerve their car, but 10 percent of all drunk drivers, regardless of race, swerve their cars. On a typical night, 5,000 cars are observed by the police force.(a) What percent of blacks driving at night are driving drunk? What percent of whites driving at night are driving drunk?The percent of drivers who are drunk is identical across races – 5 percent of all drivers regardless of race are drunk.(b) Of the 5,000 cars observed, how many are driven by blacks? How many of these cars are driven by a drunk? Of the 5,000 cars observed at night, how many are driven by whites? How many of these cars are driven by a drunk? What percent of nighttime drunk drivers are black?Of the 5,000 cars driven at night, 20 percent (or 1,000) are driven by blacks. As one out of every twenty people are drunk, there are 50 black drunk drivers. Similarly, 4,000 of the cars are driven by whites, and there are 200 drunk white drivers. Thus 20 percent (50 out of 250) of the drunk drivers are black, just like20 percent of all drivers are black.(c) The police chief believes the drunk-driving problem is mainly due to black drunk drivers. He orders his policemen to pull over all swerving cars and one in every two non-swerving cars that is driven by a black person. The driver of a non-swerving car is then given a breathalyzer test that is 100 percent accurate in diagnosing drunk driving. Under this enforcement scheme, what percent of people arrested for drunk driving will be black?One-tenth of white drunk drivers will be arrested as they were swerving. This totals 20 drivers. Likewise one-tenth of black drunk drivers will be arrested as they were seen swerving. This totals 5 drivers.Of the remaining 4,975 drivers, 995 are black with 45 being drunk. As one in every two blacks is pulled over on suspicion, 22.5 additional blacks will be arrested for drunk driving as they will fail the breathalyzer test. Therefore, at the end of the night, 47.5 people will be arrested for drunk driving, 27.5 of which are black. Therefore, even though only 20 percent of all drunks are black, the percent of drunks arrested who are black is almost 50 percent (27.5/47.5).10-12. Suppose 100 men and 100 women graduate from high school. After high school, each can work in a low-skill job and earn $200,000 over his or her lifetime, or each can pay $50,000 and go to college. College graduates are given a test. If someone passes the test, he or she is hired for a high-skill job paying lifetime earnings of $300,000. Any college graduate who fails the test, however, is relegated to a low-skill job. Academic performance in high school gives each person some idea of how he or she will do on the test if they go to college. In particular, each person’s GPA, call it x, is an “ability score” ranging from 0.01 to 1.00. With probability x, the person will pass the test if he or she attends college. Upon graduating high school, there is one man with x = .01, one with x = .02, and so on up to x = 1.00. Likewise, there is one woman with x = .01, one with x = .02, and so on up to x = 1.00.(a) Persons attend college only if the expected lifetime payoff from attending college is higher than that of not attending college. Which men and which women will attend college? What is the expected pass rate of men who take the test? What is the expected pass rate of women who take the test?Both groups are identical, so the answers are identical. The expected value requirement for attending college is:$300,000 x + $200,000 (1 – x) – $50,000 > $200,000$100,000 x > $50,000x > 0.50.Thus, the 50 men and 50 women with x = .51 to x = 1.00 all go to college and take the test. The number of test takers expected to pass is then the sum of expected pass rates: .51 + .52 + … + 1.00 = 37.75. Thus, 75.5 percent (37.75 of the 50) of men and 75.5 percent of the women who take the test are expected to pass the test.(b) Suppose policymakers feel not enough women are attending college, so they take actions that reduce the cost of college for women to $10,000. Which women will now attend college? What is the expected pass rate of women who take the test?The expected value requirement for attending college for women has changed to:$300,000 x + $200,000 (1 – x) – $10,000 > $200,000$100,000 x > $10,000x > 0.10.Thus, the 90 women with x = .11 to x = 1.00 attend college and take the test. The number of female test takers expected to pass is the sum of expected pass rates: .11 + .12 + … + 1.00 = 49.95. Thus, 55.5 percent (49.95 of the 90) of the women who take the test are expected to pass the test.。
劳动经济学(全) 第二章 劳动力供给
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失业者（U）：从某一工作岗位暂时下岗，或是没有工作， 但在参照周的前4周里一直在积极地寻找工作。
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《劳动经济学》(作者Borjas)第十二章习题答案
CHAPTER 1212-1. Suppose there are 100 workers in an economy with two firms. All workers are worth $35 per hour to firm A but differ in their productivity at firm B. Worker 1 has a value of marginal product of $1 per hour at firm B; worker 2 has a value of marginal product of $2 per hour at firm B, and so on. Firm A pays its workers a time-rate of $35 per hour, while firm B pays its workers a piece rate. How will the workers sort themselves across firms? Suppose a decrease in demand for both firms’ output reduces the value of every worker to either firm by half. How will workers now sort themselves across firms?Workers 1 to 34 work for firm A as a time rate of $35 is more than their value to firm B, while workers 36 to 100 work for firm B. Worker 35 is indifferent. More productive workers, therefore, flock to the piece rate firm. After the price of output falls, firm A values all workers at $17.50 per hour, while worker 1’s value at firm B falls to 50 cents, worker 2’s value falls to $1 at firm B, etc. The key question is what happens to the wage in the time-rate firm. Presumably this wage will also fall by half to $17.50 per hour. If it falls by half, then the sorting of workers to the two firms remains unchanged.12-2. Taxicab companies in the United States typically own a large number of cabs and licenses; taxicab drivers then pay a daily fee to the owner to lease a cab for the day. In return, the drivers keep their fares (so that, in essence, they receive a 100 percent commission on their sales). Why did this type of compensation system develop in the taxicab industry?Imagine what would happen if the cab company paid a 50 percent commission on fares. The cab drivers would have an incentive to misinform the company about the amount of fares they generated in order to pocket most of the receipts. Because cab companies find it almost impossible to monitor their workers, they have developed a compensation scheme that leaves the monitoring to the drivers. By charging drivers a rental fee and letting the drivers keep all the fares, each driver has an incentive to not shirk on the job.12-3. A firm hires two workers to assemble bicycles. The firm values each assembly at $12. Charlie’s marginal cost of allocating effort to the production process is MC = 4N, where N is the number of bicycles assembled per hour. Donna’s marginal cost is MC = 6N.(a) If the firm pays piece rates, what will be each worker’s hourly wage?As the firm values each assembly at $12, it will pay $12 for 1 assembly, $24 for 2 assembly’s, etc. when offering piece rates. As Charlie’s marginal cost of the first assembly is $4, the second is $8, the third is $12, and the fourth is $16; Charlie assembles 3 bicycles each hour and is paid an hourly wage of $36. Likewise, as Donna’s marginal cost of the first assembly is $6, the second is $12, and the third is $18; Donna assembles 2 bicycles each hour and is paid an hourly wage of $24.(b) Suppose the firm pays a time rate of $15 per hour and fires any worker who does not assemble at least 1.5 bicycles per hour. How many bicycles will each worker assemble in an 8 hour day?As working is painful to workers, each will work as hard as necessary to prevent being fired, but that is all. Thus, each worker assembles 1.5 bicycles each hour, for a total of 12 bicycles in an eight hour day. 12-4. All workers start working for a particular firm when they are 20 years old. The value of each worker’s marginal product is $18 per hour. In order to prevent shirking on the job, a delayed-compensation scheme is imposed. In particular, the wage level at every level of seniority is determined by:Wage = $10 + (.4 × Years in the firm).Suppose also that the discount rate is zero for all workers. What will be the mandatory retirement age under the compensation scheme? (Hint: Use a spreadsheet.)To simplify the problem, suppose the workers works 1 hour per year. (The answer would be the same regardless of how many hours are worked, as long as the number of hours worked does not change over time). Some of the relevant quantities required to determine the optimal length of the contract are:Age Yearson theJob VMPAccumulatedVMPContractWageAccumulatedContractWage21 1 $18 $18 $10.00 $10.0022 2 $18$36 $10.40 $20.4023 3 $18$54 $10.80 $31.2024 4 $18$72 $11.20 $42.4040 20 $18$360 $17.60 $276.0041 21 $18$378 $18.00 $294.0042 22 $18$396 $18.40 $312.4043 23 $18$414 $18.80 $331.2060 40 $18$720 $25.60 $712.0061 41 $18$738 $26.00 $738.0062 42 $18$756 $26.40 $764.40The VMP is constant at $18 per year. The accumulated VMP gives the total product the worker has contributed to the firm up to that point in the contract. The wage in the contract follows from the equation, and the accumulated wage is the total wage payments received by the worker up to that point. Until the 20th year in the firm, the worker receives a wage lower than her VMP; after the 21st year the worker’s wage exceeds the VMP. The contract will be terminated when the total accumulated VMP equals the total accumulated wage under the delayed compensation contract, which occurs on the worker’s 41st year on the job. So the optimal retirement age is age 61.12-5. Suppose a firm’s technology requires it to hire 100 workers regardless of the wage level. The firm, however, has found that worker productivity is greatly affected by its wage. The historical relationship between the wage level and the firm’s output is given by:Wage Rate Units of Output$8.00 65$10.00 80$11.25 90$12.00 97$12.50 102What wage level should a profit-maximizing firm choose? What happens to the efficiency wage if there is an increase in the demand for the firm’s output?The data in the problem can be used to calculate the elasticity of the change in output with respect to the change in the wage. The efficiency wage is determined by the condition that this elasticity must equal 1. This elasticity is 1 when the firm raises the wage from $10 to $11.25 an hour: (90-80)/80 ÷ (11.25-10)/10 = 1. The efficiency wage, therefore, is $11.25. Note that this efficiency wage is independent of any labor market conditions, and particularly does not depend on the demand for the firm’s output.12-6. Consider three firms identical in all aspects except their monitoring efficiency, which cannot be changed. Even though the cost of monitoring is the same across the three firms, shirkers at Firm A are identified almost for certain; shirkers at Firm B have a slightly greater chance of not being found out; and shirkers at Firm C have the greatest chance of not being identified as a shirker. If all three firms pay efficiency wages to keep their workers from shirking, which firm will pay the greatest efficiency wage? Which firm will pay the smallest efficiency wage?In this example, there is no connection between the cost of monitoring and the efficiency of monitoring. Moreover, the value of unemployment is the same for workers regardless of their employer. Focusing just on the probability of being caught shirking, therefore, workers in Firm A have the least incentive to shirk (as they are most likely to get caught) while workers in Firm C have the greatest incentive to shirk (as they are least likely to get caught). The idea of efficiency wages is to use wages to buy-off the incentive to shirk. Therefore, Firm A will pay the lowest efficiency wage, while Firm C will pay the greatest efficiency wage.12-7. Consider three firms identical in all aspects (including the probability with which they discover a shirker), except that monitoring costs vary across the firms. Monitoring workers is very expensive at Firm A, less expensive at Firm B, and cheapest at Firm C. If all three firms pay efficiency wages to keep their workers from shirking, which firm will pay the greatest efficiency wage? Which firm will pay the smallest efficiency wage?In this example, there is no connection between the cost of monitoring and the efficiency of monitoring. The efficiency wage, therefore, is determined by the incentives of the workers, not the costs of the firms. (The decision of whether to monitor workers, of course, will depend on the cost of monitoring.) Thus, all three firms will offer the same efficiency wage.12-8. Why will a firm be more likely to pay its factory workers according to a time rate, but be more likely to pay its sales people a piece rate?Each factory worker has a place on an assembly line and must do a certain task for each unit of theproduct made. Thus, the production process requires very little monitoring of workers, as they are more or less forced to do their job or else the assembly line will breakdown, with the factory manager knowing who is at fault. This is the ideal situation in which to pay a time rate.In comparison, sales persons are likely paid a piece rate, because monitoring their efforts is much more difficult. By paying a piece rate, the sales people have an incentive to work hard to make as many sales as possible.12-9. Suppose a worker only cares about her wage (a “good”) and how much effort she exerts on the job (a “bad”). Graph some indifference curves over these two goods for the worker.With the wage on the horizontal axis, any shaped indifference curves as long as they are upward sloping and increasing in the direction of higher wages and less effort fulfill the requirements that wages are a good thing and effort is a bad thing.12-10. Why would a firm ever choose to offer profit-sharing to its employees in place of paying piece rates?Piece rates can be very difficult to pay in some situations. For example, in a situation in which a group of workers is responsible for producing the good, determining who made what may be impossible. Consider Southwest Airlines, which is known to have a wonderful profit sharing program. To pay a flight attendant a piece rate, the airline would have to survey passengers as they depart the plane, and then, from the passengers’ opinions, pay the appropriate piece rates. Clearly this is unreasonable. Profit sharing, on the other hand, is a convenient way to approximate the piece rate system. Since all workers are covered by profit sharing at Southwest Airlines, all workers have a continuous incentive to do their job very well. EffortWageIndifference Curves: Wages and Effort12-11. Describe the free riding problem in a profit-sharing compensation scheme. How might the workers of a firm “solve” the free riding problem?When all workers are covered by a profit sharing plan, an individual worker has the incentive to shirk his responsibilities as his direct effect on profits is tiny. If all workers do this, however, the total profit created by the firm will be much smaller than it would be if workers were paid a piece rate.One way to “solve” the free rider problem is with social pressure. If the atmosphere of the workers is that everyone works and shirkers will be punished somehow – socially, annual reviews, being fired, etc. – then the incentive to shirk is diminished.。
劳动经济学鲍哈斯7e答案
劳动经济学鲍哈斯7e答案一、单项选择题:本大题共20小题，每小題1分，共20分。
在每小题列出的备选项中只有一项是最符合题目要求的，请将其选出。
1.劳动经济学是经济学的重要分支，主要研究A.劳动生产率B.劳动的人C.劳动资料D.劳动要素2.当劳动力供给弹生等于1时，该劳动力供给弹性为A.供给无限弹性B.单位供给弹性C.供给无弹性D.供给缺乏弹性3.妻子选择就业还是闲暇的尺度是A.家庭人口B.爱好C.家务的多少D.工资率的高低4.在工资率保持不变的情况下，由于收入的变化引起的工作时间的变化称为A.替代效应B.收入效应C.规模效应D.均衡效应5.在市场经济中，劳动力供给的决策主体是A.劳动者家庭或个人B.政府或公共部门C行业工会D.企业或雇主6.衡量社会劳动力供给总量的主要指标是A.就业率B.失业率C.劳动力供给弹性D.劳动力参与率7.如果企业雇工水平变动的百分比大于工资率变动的百分比，则此时劳动力需求弹性A.等于0B.小于1C.等于1D.大于18.如果劳动力市场上的工资率无论如何变化都不会对劳动力需求量产生任何影响，则该劳动力需求曲线(工资率为纵轴，劳动力需求量为横轴)是一条A.与横轴垂直的线B.与横轴平行的线C.向右上倾斜且较为平坦的曲线D.向右上倾斜且较为能峭的曲线9.劳动力资源能实现最优分配是在A.劳动力市场实现均衡时B.劳动力市场偏离均衡时C.当生产效率高的行业向生产效率低的行业转移劳动力时D.不同行业出现不同的工资率时10.下列选项中，关于劳动力流动说法不正确的是A.年龄越大，流动的意愿越少B.未婚比已婚容易流动C.学历越高，越可能流动D.流动的可能性与迁移距离成同方向变动11.以下属于教育间接成本的是A.老师工资B.书本费用C.学费D.不上学参加工作所得的收入12.劳动报酬的基本形式是A.直接工资和间接工资B.超额工资和累计工资C.计时工资和计件工资D.包工工资和提成工资13.工资既可以反映劳动者向社会提供的劳动贡献，也可以反映出劳动者的清费水平，这是工资的A.保障职能B.调节职能C.增值职能D.统计和监督职能14.影响宏观工资水平的主要因素是A经济效益B.劳动力分配C.工资分配形式D.物价变动15.将工人工资按照形组或个人营业额、毛利或纯收入等的定比例提取进行计发的工资形式称为A.超额计件工资B.提成工资C.集体计件工资D.累计计件工资16.知识员工通过技术股份获得收益的具体模式不包括A.技术骨干股模式B.分红回填模式C.分红股模式D.一揽子型模式17.绝大多数经济学家认为，充分就业的数量标准是失业率控制在A0-1%之间B.3-4%之间C.8-10%之间D.10-15%之间18.现在我国对女性失业者的年龄上限规定为A60B.50C.65D.5519.因为产品需求下降使厂商销售发生困难，从而对劳动供给的数量产生限制而造成的劳动者失业的现象称为A.非自愿失业B.摩擦性失业C.自愿失业D.结构性失业20.社会保障的资金来源于各要素所有名的贡献，体现了社会保障的A.保证性B.福利性C.普遍性D.互济性二、填空题:本大题共5小题，每小题2分，共10分。
《劳动经济学》(作者Borjas)第四章习题答案
CHAPTER 44-1. Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 1 machine to do the work of 3 persons. The firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week. What combination of inputs will the firm use if the weekly salary of each worker is $300? What combination of inputs will the firm use if the weekly salary of each worker is $225? What is the elasticity of labor demand as the wage falls from $300 to $225?Because labor and capital are perfect substitutes, the isoquants (in bold) are linear and the firm will use only labor or only capital, depending on which is cheaper in producing 100 units of output.The (absolute value of the) slope of the isoquant (MP E / MP K ) is 1/3 because 1 machine does the work of 3 men. When the wage is $900 (left panel), the slope of the isocost is 300/750. The isocost curve,therefore, is steeper than the isoquant, and the firm only hires capital (at point A ). When the weekly wage is $225 (right panel), the isoquant is steeper than the isocost and the firm hires only labor (at point B ).Weekly Salary = $300 Weekly Salary = $225The elasticity of labor demand is defined as the percentage change in labor divided by the percentage change in the wage. Because the demand for labor goes from 0 to a positive quantity when the wagedropped to $225, the (absolute value of the) elasticity of labor demand is infinity.LaborCapitalLaborCapital4-2. (a) What happens to the long-run demand curve for labor if the demand for the firm’s output increases?The labor demand curve is given by VMP E = MR x MP E. As demand for the firm’s output increases, its marginal revenue also increases. Thus, an increase in demand for the firm’s output shifts the labor demand curve to the right.(b) What happens to the long-run demand curve for labor if the price of capital increases?To determine how an increase in the price of capital changes the demand for labor, suppose initially that the firm is producing 200 units of output at point P in the figure. The increase in the price of capital (assuming capital is a normal input) increases the marginal costs of the firm and will reduce the profit-maximizing level of output to say 100 units. The increase in the price of capital also flattens the isocost curve, moving the firm to point R. The move from point P to point R can be decomposed into a substitution effect (P to Q) which reduces the demand for capital, but increases the demand for labor, and a scale effect (Q to R) which reduces the demand for both labor and capital. The direction of the shift in the demand curve for labor, therefore, will depend on which effect is stronger: the scale effect or the substitution effect.4-3. Union A wants to represent workers in a firm that hires 20,000 person workers when the wage rate is $4 and hires 10,000 workers when the wage rate is $5. Union B wants to represent workers in a firm that hires 30,000 workers when the wage is $6 and hires 33,000 workers when the wage is $5. Which union would be more successful in an organizing drive?The union will be more likely to attract the workers’ support when the elasticity of labor demand (in absolute value) is small. The elasticity of labor demand facing union A is given by:η = percent ∆L / percent ∆w = (20,000–10,000)/20,000 ÷ (4–5)/4 = –2.The elasticity of labor demand facing union B equals (33,000–30,000)/33,000 ÷ (5–6)/5 = –5/11 ≈ –.45. Union B, therefore, is likely to have a more successful organizing drive as 0.45 < 2.4-4. Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially the firm faces market prices of w = 6 and r = 4. These prices then shift to w = 4 and r = 2.(a) In which direction will the substitution effect change the firm’s employment and capital stock?Prior to the price shift, the absolute value of the slope of the isocost line (w/r) was 1.5. After the price shift, the slope is 2. In other words, labor has become relatively more expensive than capital. As a result, there will be a substitution away from labor and towards capital (the substitution effect).(b) In which direction will the scale effect change the firm’s employment and capital stock?Because both prices fall, the marginal cost of production falls, and the firm will want to expand. The scale effect, therefore, increases the demand for both labor and capital (as both are normal inputs).(c) Can we say conclusively whether the firm will use more or less labor? More or less capital?The firm will certainly use more capital as the substitution and scale effects reinforce each other in that direction, but the change in labor employed will depend on whether the substitution or the scale effect for labor dominates.4-5. What happens to employment in a competitive firm that experiences a technology shock such that at every level of employment its output is 200 units/hour greater than before?Because output increases by the same amount at every level of employment, the marginal product of labor, and hence the value of the marginal product of labor, does not change. Therefore, as the value of the marginal product of labor will equal the wage rate at the same level of employment as before, the level of employment will not change.4-6. Suppose the market for labor is competitive and the supply curve for labor is backwardbending over part of its range. The government now imposes a minimum wage in this labor market. What is the effect of the minimum wage on employment? Does the answer depend on which of the two curves (supply or demand) is steeper? Why?Equilibrium is attained where the supply curve intersects the demand curve, and the equilibriumemployment and wage levels are E* and w*, respectively . When the minimum wage is set at w MIN , the firm wants to hire E D workers but E S workers are looking for work. As long as the downward-sloping portion of the supply curve is to the right of the demand curve, the fact that the supply curve is downward sloping creates no problems beyond those encountered in the typical competitive model. An interesting extension of the problem would consider the case where the downward-sloping portion of the supply curve recrosses the demand curve at some point above w * and the minimum wage is set above that point.4-7. Suppose a firm purchases labor in a competitive labor market and sells its product in a competitive product market. The firm’s elasticity of demand for labor is −0.4. Suppose the wage increases by 5 percent. What will happen to the number of workers hired by the firm? What will happen to the marginal productivity of the last worker hired by the firm?Given the estimates of the elasticity of labor demand and the change in the wage, we have that4.0%%−=∆∆=w E η => 4.0%5%−=∆E=> %2%−=∆E .Thus, the firm hires 2 percent fewer workers. Furthermore, because the labor market is competitive, the marginal worker is paid the value of his marginal product. As the product market is also competitive, therefore, we know that the output price does not change so that the marginal productivity of the marginal worker increases by 5 percent.Employment W agesw M INS D4-8. A firm’s technology requires it to combine 5 person-hours of labor with 3 machine-hours to produce 1 unit of output. The firm has 15 machines in place and the wage rate rises from $10 per hour to $20 per hour. What is the firm’s short-run elasticity of labor demand?Unless the firm goes out of business, it will combine 25 persons with the 15 machines it has in place regardless of the wage rate. Therefore, employment will not change in response to the movement of the wage rate, and the short-run elasticity of labor demand is zero.4-9. In a particular industry, labor supply is E S = 10 + w while labor demand is E D = 40 − 4w, where E is the level of employment and w is the hourly wage.(a) What is the equilibrium wage and employment if the labor market is competitive? What is the unemployment rate?In equilibrium, the quantity of labor supplied equals the quantity of labor demanded, so that E S = E D. This implies that 10 + w = 40 – 4w. The wage rate that equates supply and demand is $6. When the wage is $6, 16 persons are employed. There is no unemployment because the number of persons looking for work equals the number of persons employers are willing to hire.(b) Suppose the government sets a minimum hourly wage of $8. How many workers would lose their jobs? How many additional workers would want a job at the minimum wage? What is the unemployment rate?If employers must pay a wage of $8, employers would only want to hire E D = 40 – 4(8) = 8 workers, while E S = 10 + 8 = 18 persons would like to work. Thus, 8 workers lose their job following the minimum wage and 2 additional people enter the labor force. Under the minimum wage, the unemployment rate would be 10/18, or 55.6 percent.4-10. Suppose the hourly wage is $10 and the price of each unit of capital is $25. The price of output is constant at $50 per unit. The production function isf(E,K) = E½K ½,so that the marginal product of labor isMP E = (½)(K/E) ½ .If the current capital stock is fixed at 1,600 units, how much labor should the firm employ in the short run? How much profit will the firm earn?The firm’s labor demand curve is it marginal revenue product of labor curve, VMP E, which equals the marginal productivity of labor, MP E, times the marginal revenue of the firm’s product. But as price is fixed at $50, MR = 50. Thus, we have thatVMP E = MP E× MR = (½)(1,600/E)½(50) = 1,000 / E½ .Now, by setting VMP E = w and solving for E, we find that the optimal number of workers for the firm to hire is 10,000 workers. The firm then makes (1600)½(10000)½ = 4,000 units of output and earns a profit of 4,000($50) – 1,600($25) – 10,000 ($10) = $60,000.4-11. Table 616 of the 2002 U.S. Statistical Abstract reports data on the nominal and real hourly minimum wage from 1960 through 2000. Under which president did the nominal minimum wage increase by the greatest dollar amount? Under what president did the real minimum wage increase by the greatest percentage?The data are:AdministrationsYear CurrentReal(2000)percentChangeNominalChange President1960 $1.00 $5.821961 $1.15 $6.621962 $1.15 $6.561963 $1.25 $7.03 20.79percent $0.25 Kennedy 1964 $1.25 $6.941965 $1.25 $6.831966 $1.25 $6.641967 $1.40 $7.221968 $1.60 $7.92 14.12percent $0.35 Johnson 1969 $1.60 $7.511970 $1.60 $7.101971 $1.60 $6.801972 $1.60 $6.591973 $1.60 $6.211974 $2.00 $6.99 -6.92percent $0.40 Nixon 1975 $2.10 $6.721976 $2.30 $6.96 3.57percent $0.20 Ford 1977 $2.30 $6.541978 $2.65 $7.001979 $2.90 $6.881980 $3.10 $6.48 -0.92percent $0.80 Carter 1981 $3.35 $6.351982 $3.35 $5.981983 $3.35 $5.791984 $3.35 $5.551985 $3.35 $5.361986 $3.35 $5.261987 $3.35 $5.081988 $3.35 $4.88 -23.15percent $0.00 Reagan 1989 $3.35 $4.651990 $3.80 $5.011991 $4.25 $5.371992 $4.25 $5.22 12.26percent $0.90 Bush 1993 $4.25 $5.061994 $4.25 $4.941995 $4.25 $4.801996 $4.75 $5.211997 $5.15 $5.531998 $5.15 $5.441999 $5.15 $5.322000 $5.15 $5.15 1.78percent $0.90 ClintonThe nominal minimum wage increased by the greatest dollar amount ($0.90) under both President Bush and President Clinton. In percentage terms, however, the real minimum wage increased by 12.26 percent during the Bush presidency, but only by 1.78 percent during the Clinton presidency. The greatest percent increase, however, came during the Kennedy presidency, when the minimum wage increased by over 20 percent.。
《劳动经济学》 作者Borjas 习题答案
CHAPTER 66-1. Politicians who support the green movement often argue that it is profitable for firms to pursue a strategy that is “environmentally correct” (for example, by building factories that do not pollute and are not noisy), because workers will be willing to work in environmentally correct factories at a lower wage rate. Evaluate the validity of this claim.If it is profitable for firms to build factories that do not pollute and are not noisy, they would have been built already. After all, firms could build these profit-maximizing factories and attract persons to work at these factories at lower wages because no compensating differential would be needed. The fact that compensating differentials exist and that governments attempt to regulate the quality of the workplace implies that providing these amenities to workers is more costly than cost-saving.6-2. Suppose wages and health insurance are the only two job characteristics workers care about. Describe the relationship between the wage level in a particular job and whether the job offers health insurance if the government does not require employers to offer health insurance to their workers. What happens to the wage structure if the government requires all firms to provide a standard package of health insurance to their workers?When the government does not require employers to offer health insurance, workers would prefer to work in those firms that offer health insurance and would be willing to pay for the right to work in such firms (assuming that all workers prefer to have health insurance). In other words, jobs that offered health insurance would pay less than jobs that did not offer such plans. When the government mandates that all employers offer health insurance to workers, the wage in those firms that had provided either no health insurance or a “substandard” package would fall and the wage would eventually be the same in all jobs. 6-3. Workers choose to work a risky or a safe job. Suppose there are 100 workers in the economy. Worker 1’s reservation price (for accepting the risky job) is $1; worker 2’s reservation price is $2, and so on. Because of technological reasons, there are only 10 risky jobs. What is the equilibrium wage differential between safe and risky jobs? Which workers will be employed at the risky firm? Suppose now that an advertising campaign paid for by the employers who offer risky jobs stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of -$10 (that is, she is willing to pay $10 for the right to work in the risky job); worker 2’s reservation price is -$9, and so on. There are still only 10 risky jobs. What is the new equilibrium wage differential? The supply curve to the risky job is given by the fact that worker 1 has a reservation price of $1, worker 2 has a reservation price of $2, and so on. As the figure below illustrates, this supply curve (given by S) is upward sloping, and has a slope of 1. The demand curve (D) for risky jobs is perfectly inelastic at 10 jobs. Market equilibrium is attained where supply equals demand so that 10 workers are employed in risky jobs; the market compensating wage differential is $10 since this is what it takes to entice the marginal (tenth) worker to accept a job offer from a risky firm. Note that the firm employs those workers who least mind being exposed to risk.If tastes towards risk change, the supply curve shifts down to S′ and the market equilibrium is attained when the compensating wage differential is -$1. This is the compensating differential required to hire the marginal worker (that is, the 10th worker). Note that this compensating differential implies that eventhough most workers (from worker 12 onwards) dislike risk, the market determines that risky jobs will pay less than safe jobs.6-4. Suppose all workers have the same preferences represented byU w x ,=−2where w is the wage and x is the proportion of the firm’s air that is composed of toxic pollutants. There are only two types of jobs in the economy, a clean job (x = 0) and a dirty job (x = 1). Let w 0 be the wage paid by the clean job and w 1 be the wage paid by the polluted job. If the clean job pays $16 per hour, what is the wage in dirty jobs? What is the compensating wage differential?If all persons have the same preferences regarding working in a job with polluted air, market equilibrium requires that the utility offered by the clean job be the same as the utility offered by the dirty job, otherwise all workers would move to the job that offers the higher utility. This implies that:)1(2)0(210−=−w w => .2161−=wSolving for w 1 implies that w 1 = $36. The compensating wage differential, therefore, is $20.C om pensatin gDm ent6-5. Suppose a drop in the compensating wage differential between risky jobs and safe jobs has been observed. Two explanations have been put forward:• Engineering advances have made it less costly to create a safe working environment.• The phenomenal success of a new action serial “Die On The Job!” has imbued millions ofviewers with a romantic perception of work-related risks.Using supply and demand diagrams show how each of the two developments can explain the drop in the compensating wage differential. Can information on the number of workers employed in the risky occupation help determine which explanation is the right one?The engineering advances make it cheaper for firms to offer safe jobs, and hence reduce the gain from switching from a safe environment to a risky one. This will shift the demand curve for risky jobs in and reduce the compensating wage differential (Figure 1). Note that the equilibrium number of workers in risky jobs goes down.The glamorization of job-related risks may make people more willing to take these risks. This shiftssupply to the right and reduces the compensating differential (Figure 2). Note that the equilibrium number of workers in risky jobs goes up.Thus, information on whether employment in the risky sector increased or decreased can help discern between the two competing explanations.Figure 1. Labor Market for Risky JobsCompensatingDifferentialE new E old Number of Workers in Risky Jobs(w 1 – w 0 )old (w 1 – w 0 )Figure 2. Labor Market for Risky Jobs6-6. Consider a competitive economy that has four different jobs that vary by their wage and risk level. The table below describes each of the four jobs.Job Risk ( r ) Wage ( w )A 1/5 $3B 1/4 $12C 1/3 $23D 1/2 $25All workers are equally productive, but workers vary in their preferences. Consider a worker who values his wage and the risk level according to the following utility function:u w r w r (,)=+12.Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation?Calculate the utility level for each job by using the wage and the risk level: U(A) = 28, U(B) = 28, U(C) = 32, and U(D) = 29. Therefore, the worker chooses a type C job and receives 32 units of happiness. If she is forced to work a type A job, the worker needs to receive a wage of $7 in order to maintain her 32 unitsof happiness as 7 + 25 = 32.CompensatingDifferential E old E new Number of Workers in Risky Jobs(w 1 – w 0 )old (w 1 – w 0 )6-7. Consider Table 6-1 and compare the fatality rate of workers in the agricultural, mining, construction, and manufacturing industries?(a) What would the distribution of wages look like across these four industries given the compensating differential they might have to pay to compensate workers for risk?Mining would pay the highest compensating differential, followed by agriculture, then construction, and finally manufacturing.(b) Now look at the median weekly earnings by industry as reported in Table 629 of the 2002 U.S. Statistical Abstract. Does the actual distribution of wages reinforce your answer to part (a)? If not, what else might enter the determination of median weekly earnings?Median weekly earnings by industry are:$795Mining$371Agriculture$609Construction$613ManufacturingThus, the distribution of wages does not perfectly reflect the compensating differential story, though mining is the best paid and the most dangerous. It is also the unhealthiest, which workers would supposedly take into account as well. Many other factors, however, probably explain the wage structure just as much if not more than compensating differentials, including preferences (family farmers), unions (manufacturing), required skills, and the length of the average work week.6-8. The EPA wants to investigate the value workers place on being able to work in “clean” mines over “dirty” mines. The EPA conducts a study and finds the average wage in clean mines to be $42,250 and the average wage in dirty mines to be $47,250.(a) According to the EPA, how much does the average worker value working in a clean mine?The average value is $47,250 - $42,250 = $5,000.(b) Suppose the EPA could mandate that all dirty mines become clean mines and that all workers who were in a dirty mine must therefore accept a $5,000 pay decrease. Are these workers helped by the intervention, hurt by the intervention, or indifferent to the intervention?All except the marginal worker are hurt by the intervention. The workers who sort themselves into the dirty jobs are those workers that do not mind dirt, and therefore do not value working in a clean job at $5,000. (Similarly, if all of the workers in the clean jobs were forced to accept dirty jobs for $5,000 more, all of them except the marginal worker would be hurt as they all value working in a clean job at more than $5,000.)6-9. There are two types of farming tractors on the market, the FT250 and the FT500. The only difference between the two is that the FT250 is more prone to accidents than the FT500. Over their lifetime, one in ten FT250s is expected to result in an accident, as compared to one in twenty-five FT500s. Further, one in one-thousand FT250s is expected to result in a fatal accident, as compared to only one in five-thousand FT500s. The FT250 sells for $125,000 while the FT500 sells for $137,000. At these prices, 2,000 of each model are purchased each year. What is the statistical value farmers place on avoiding a tractor accident? What is the statistical value of a life of a farmer? The FT500 is associated with an extra cost of $12,000, but its accident rate is only 0.04 compared to the 0.10 accident rate of the FT250. Also, each farmer that buys the FT250 is willing to accept the additional risk in order to save $12,000. Thus, these workers are willing to receive $24 million ($12,000 x 2,000) in exchange for 200 – 80 = 120 accidents. Thus, the value placed on each accident is $200,000. Likewise, the 2,000 farmers who buy the FT250 are willing to receive $24 million in exchange for 2 – .4 = 1.6 fatal accidents. Thus, the value placed on each life is $15 million.6-10. Consider the labor market for public school teachers. Teachers have preferences over their job characteristics and amenities.(a) One would reasonably expect that high-crime school districts pay higher wages than low-crime school districts. But the data consistently reveal that high-crime school districts pay lower wages than low-crime school districts. Why?The likely reason for this is not that teachers do not care about crime – they almost certainly do – but rather that school funding is determined in large part by local property taxes. If high crime schools are located in low income cities, there is nothing (or at least very little) the local school board can do to raise more money to pay the compensating differential.(b) Does your discussion suggest anything about the relation between teacher salaries and school quality?In the end, because high crime schools cannot offer the necessary compensating differential, they will not be able to attract the highest quality workers. Therefore, one would expect that the worst schools (with the worst teachers) are located in the poorest communities with the most crime. This is the typical story of proponents of replacing the property tax scheme to fund public education with a federal program.6–11. Many employers willingly offer their employees certain benefits such as health insurance, a retirement plan, gym memberships, or even an on-site subsidized cafeteria. Why?Offering job benefits is identical to offering a job with bad characteristics such as risk. When offering a risky job, for example, the employer must buy-off the risk from the worker. The employer chooses to do this because it is profitable, i.e., because the cost of buying-off the risk is less costly than transforming the job into a safe one. The same (but opposite) argument holds for job benefits. By offering a job with benefits, the employer can pay the worker less as the worker values the benefits. The employer will find it profitable to continue to offer benefits as long as the employer can save more in reducing the wage than it costs to provide the benefits.One reason health insurance benefits are fairly popular is that firms can usually negotiate lower prices and better packages of care than individuals can do by themselves. Also, firms can deduct the cost of their benefits from their net revenue, whereas individuals cannot deduct the full amount of their healthcare expenses.。
《劳动经济学》(作者Borjas)第六章习题答案
CHAPTER 66-1. Politicians who support the green movement often argue that it is profitable for firms to pursue a strategy that is “environmentally correct” (for example, by building factories that do not pollute and are not noisy), because workers will be willing to work in environmentally correct factories at a lower wage rate. Evaluate the validity of this claim.If it is profitable for firms to build factories that do not pollute and are not noisy, they would have been built already. After all, firms could build these profit-maximizing factories and attract persons to work at these factories at lower wages because no compensating differential would be needed. The fact that compensating differentials exist and that governments attempt to regulate the quality of the workplace implies that providing these amenities to workers is more costly than cost-saving.6-2. Suppose wages and health insurance are the only two job characteristics workers care about. Describe the relationship between the wage level in a particular job and whether the job offers health insurance if the government does not require employers to offer health insurance to their workers. What happens to the wage structure if the government requires all firms to provide a standard package of health insurance to their workers?When the government does not require employers to offer health insurance, workers would prefer to work in those firms that offer health insurance and would be willing to pay for the right to work in such firms (assuming that all workers prefer to have health insurance). In other words, jobs that offered health insurance would pay less than jobs that did not offer such plans. When the government mandates that all employers offer health insurance to workers, the wage in those firms that had provided either no health insurance or a “substandard” package would fall and the wage would eventually be the same in all jobs. 6-3. Workers choose to work a risky or a safe job. Suppose there are 100 workers in the economy. Worker 1’s reservation price (for accepting the risky job) is $1; worker 2’s reservation price is $2, and so on. Because of technological reasons, there are only 10 risky jobs. What is the equilibrium wage differential between safe and risky jobs? Which workers will be employed at the risky firm? Suppose now that an advertising campaign paid for by the employers who offer risky jobs stresses the excitement associated with “the thrill of injury,” and this campaign changes the attitudes of the work force toward being employed in a risky job. Worker 1 now has a reservation price of -$10 (that is, she is willing to pay $10 for the right to work in the risky job); worker 2’s reservation price is -$9, and so on. There are still only 10 risky jobs. What is the new equilibrium wage differential? The supply curve to the risky job is given by the fact that worker 1 has a reservation price of $1, worker 2 has a reservation price of $2, and so on. As the figure below illustrates, this supply curve (given by S) is upward sloping, and has a slope of 1. The demand curve (D) for risky jobs is perfectly inelastic at 10 jobs. Market equilibrium is attained where supply equals demand so that 10 workers are employed in risky jobs; the market compensating wage differential is $10 since this is what it takes to entice the marginal (tenth) worker to accept a job offer from a risky firm. Note that the firm employs those workers who least mind being exposed to risk.If tastes towards risk change, the supply curve shifts down to S′ and the market equilibrium is attained when the compensating wage differential is -$1. This is the compensating differential required to hire the marginal worker (that is, the 10th worker). Note that this compensating differential implies that eventhough most workers (from worker 12 onwards) dislike risk, the market determines that risky jobs will pay less than safe jobs.6-4. Suppose all workers have the same preferences represented byU w x ,=−2where w is the wage and x is the proportion of the firm’s air that is composed of toxic pollutants. There are only two types of jobs in the economy, a clean job (x = 0) and a dirty job (x = 1). Let w 0 be the wage paid by the clean job and w 1 be the wage paid by the polluted job. If the clean job pays $16 per hour, what is the wage in dirty jobs? What is the compensating wage differential?If all persons have the same preferences regarding working in a job with polluted air, market equilibrium requires that the utility offered by the clean job be the same as the utility offered by the dirty job, otherwise all workers would move to the job that offers the higher utility. This implies that:)1(2)0(210−=−w w => .2161−=wSolving for w 1 implies that w 1 = $36. The compensating wage differential, therefore, is $20.C om pensatin gDm ent6-5. Suppose a drop in the compensating wage differential between risky jobs and safe jobs has been observed. Two explanations have been put forward:• Engineering advances have made it less costly to create a safe working environment.• The phenomenal success of a new action serial “Die On The Job!” has imbued millions ofviewers with a romantic perception of work-related risks.Using supply and demand diagrams show how each of the two developments can explain the drop in the compensating wage differential. Can information on the number of workers employed in the risky occupation help determine which explanation is the right one?The engineering advances make it cheaper for firms to offer safe jobs, and hence reduce the gain from switching from a safe environment to a risky one. This will shift the demand curve for risky jobs in and reduce the compensating wage differential (Figure 1). Note that the equilibrium number of workers in risky jobs goes down.The glamorization of job-related risks may make people more willing to take these risks. This shiftssupply to the right and reduces the compensating differential (Figure 2). Note that the equilibrium number of workers in risky jobs goes up.Thus, information on whether employment in the risky sector increased or decreased can help discern between the two competing explanations.Figure 1. Labor Market for Risky JobsCompensatingDifferentialE new E old Number of Workers in Risky Jobs(w 1 – w 0 )old (w 1 – w 0 )Figure 2. Labor Market for Risky Jobs6-6. Consider a competitive economy that has four different jobs that vary by their wage and risk level. The table below describes each of the four jobs.Job Risk ( r ) Wage ( w )A 1/5 $3B 1/4 $12C 1/3 $23D 1/2 $25All workers are equally productive, but workers vary in their preferences. Consider a worker who values his wage and the risk level according to the following utility function:u w r w r (,)=+12.Where does the worker choose to work? Suppose the government regulated the workplace and required all jobs to have a risk factor of 1/5 (that is, all jobs become A jobs). What wage would the worker now need to earn in the A job to be equally happy following the regulation?Calculate the utility level for each job by using the wage and the risk level: U(A) = 28, U(B) = 28, U(C) = 32, and U(D) = 29. Therefore, the worker chooses a type C job and receives 32 units of happiness. If she is forced to work a type A job, the worker needs to receive a wage of $7 in order to maintain her 32 unitsof happiness as 7 + 25 = 32.CompensatingDifferential E old E new Number of Workers in Risky Jobs(w 1 – w 0 )old (w 1 – w 0 )6-7. Consider Table 6-1 and compare the fatality rate of workers in the agricultural, mining, construction, and manufacturing industries?(a) What would the distribution of wages look like across these four industries given the compensating differential they might have to pay to compensate workers for risk?Mining would pay the highest compensating differential, followed by agriculture, then construction, and finally manufacturing.(b) Now look at the median weekly earnings by industry as reported in Table 629 of the 2002 U.S. Statistical Abstract. Does the actual distribution of wages reinforce your answer to part (a)? If not, what else might enter the determination of median weekly earnings?Median weekly earnings by industry are:$795Mining$371Agriculture$609Construction$613ManufacturingThus, the distribution of wages does not perfectly reflect the compensating differential story, though mining is the best paid and the most dangerous. It is also the unhealthiest, which workers would supposedly take into account as well. Many other factors, however, probably explain the wage structure just as much if not more than compensating differentials, including preferences (family farmers), unions (manufacturing), required skills, and the length of the average work week.6-8. The EPA wants to investigate the value workers place on being able to work in “clean” mines over “dirty” mines. The EPA conducts a study and finds the average wage in clean mines to be $42,250 and the average wage in dirty mines to be $47,250.(a) According to the EPA, how much does the average worker value working in a clean mine?The average value is $47,250 - $42,250 = $5,000.(b) Suppose the EPA could mandate that all dirty mines become clean mines and that all workers who were in a dirty mine must therefore accept a $5,000 pay decrease. Are these workers helped by the intervention, hurt by the intervention, or indifferent to the intervention?All except the marginal worker are hurt by the intervention. The workers who sort themselves into the dirty jobs are those workers that do not mind dirt, and therefore do not value working in a clean job at $5,000. (Similarly, if all of the workers in the clean jobs were forced to accept dirty jobs for $5,000 more, all of them except the marginal worker would be hurt as they all value working in a clean job at more than $5,000.)6-9. There are two types of farming tractors on the market, the FT250 and the FT500. The only difference between the two is that the FT250 is more prone to accidents than the FT500. Over their lifetime, one in ten FT250s is expected to result in an accident, as compared to one in twenty-five FT500s. Further, one in one-thousand FT250s is expected to result in a fatal accident, as compared to only one in five-thousand FT500s. The FT250 sells for $125,000 while the FT500 sells for $137,000. At these prices, 2,000 of each model are purchased each year. What is the statistical value farmers place on avoiding a tractor accident? What is the statistical value of a life of a farmer? The FT500 is associated with an extra cost of $12,000, but its accident rate is only 0.04 compared to the 0.10 accident rate of the FT250. Also, each farmer that buys the FT250 is willing to accept the additional risk in order to save $12,000. Thus, these workers are willing to receive $24 million ($12,000 x 2,000) in exchange for 200 – 80 = 120 accidents. Thus, the value placed on each accident is $200,000. Likewise, the 2,000 farmers who buy the FT250 are willing to receive $24 million in exchange for 2 – .4 = 1.6 fatal accidents. Thus, the value placed on each life is $15 million.6-10. Consider the labor market for public school teachers. Teachers have preferences over their job characteristics and amenities.(a) One would reasonably expect that high-crime school districts pay higher wages than low-crime school districts. But the data consistently reveal that high-crime school districts pay lower wages than low-crime school districts. Why?The likely reason for this is not that teachers do not care about crime – they almost certainly do – but rather that school funding is determined in large part by local property taxes. If high crime schools are located in low income cities, there is nothing (or at least very little) the local school board can do to raise more money to pay the compensating differential.(b) Does your discussion suggest anything about the relation between teacher salaries and school quality?In the end, because high crime schools cannot offer the necessary compensating differential, they will not be able to attract the highest quality workers. Therefore, one would expect that the worst schools (with the worst teachers) are located in the poorest communities with the most crime. This is the typical story of proponents of replacing the property tax scheme to fund public education with a federal program.6–11. Many employers willingly offer their employees certain benefits such as health insurance, a retirement plan, gym memberships, or even an on-site subsidized cafeteria. Why?Offering job benefits is identical to offering a job with bad characteristics such as risk. When offering a risky job, for example, the employer must buy-off the risk from the worker. The employer chooses to do this because it is profitable, i.e., because the cost of buying-off the risk is less costly than transforming the job into a safe one. The same (but opposite) argument holds for job benefits. By offering a job with benefits, the employer can pay the worker less as the worker values the benefits. The employer will find it profitable to continue to offer benefits as long as the employer can save more in reducing the wage than it costs to provide the benefits.One reason health insurance benefits are fairly popular is that firms can usually negotiate lower prices and better packages of care than individuals can do by themselves. Also, firms can deduct the cost of their benefits from their net revenue, whereas individuals cannot deduct the full amount of their healthcare expenses.。
劳动经济学概念共58页word资料
劳动力:马克思在《资本论》中定义：“我们把劳动力或劳动能力,理解为人的身体即活的人体中存在的,每当人生产某种使用价值时就运用的体力和智力的总和.”包含以下几个方面：A．劳动力是人所特有的一种能力B.劳动力是存在于活的人体中的能力C．劳动力是人在劳动中所运用的能力D.劳动是人在劳动中运用的体力和智力的总和.劳动力资源: 指从事各类工作的劳动力人口,它是劳动力人口的数量和其平均素质的乘积.劳动力需求: 指一个时期内,在某种工资率下雇主愿意并能够雇用到的劳动力的数量.区分劳动力资源与社会劳动力？劳动力资源不同于社会劳动力,社会劳动力指一个国家或地区实际从事社会劳动的人口,劳动力资源较广泛,而社会劳动力的范围较窄.劳动力流动的类型:工作岗位之间的流动；地域之间的流动；地域和职业之间同时流动.劳动力供应：从本质上说,是指劳动力的供给主体在一定的劳动条件自愿对存在于主体之中的劳动力使用权的出让；从量的角度说,是指一个经济体在某一段时期中,可以获得的劳动者愿意并能够提供的劳动能力的总和.劳动力参与率：研究劳动就业状态的重要统计指标,反映一定范围内的人口参与市场性劳动的程度.劳动力供给弹性：劳动力供给量变动对工资率变动的反映程度定义为劳动力供给的工资弹性,简称劳动力供给弹性.劳动力需求弹性:劳动力需求弹性是一般需求弹性概念的属概念,也具有一般需求弹性的各种性质.按绝对值的大小,劳动力需求弹性可以呈现五种状态:1.劳动力需求弹性等于零.2.劳动力需求弹性小于1.3.劳动力需求弹性等于1.4.劳动力需求弹性大于1.5.劳动力需求弹性无穷大.均衡：它所描述的是一个系统的特殊状态,即运动的物体在受到方向各异,但作用相互抵消,合力等于零的外力作用时,受力的物体所处的相对静止的状态,即为均衡.一般均衡分析：是经济学中用来考察市场上所有市场.所有商品的价格和供求关系变化的一种分析方法.静态均衡分析：抽象调整时间因素,设定变量的调整能够在可以忽略的瞬时内完成,其调整时间设为零.U-V分析: 是从失业与职业空位,也就是劳动力过剩和劳动力短缺的关系出发,研究劳动力市场资源分配功能效率问题的分析方法.内部劳动力市场：内部劳动力市场是作为外部劳动力市场的对立概念出现的.在这里,内部是指企业组织内部,外部则指企业之外.因而,有人将内部劳动力市场称为企业内劳动力市场.非自愿失业:是一种市场非均衡现象,它不是由实际工资太高而引起的,而是因为产品需求下降时厂商销售发生困难,对劳动力供给造成数量限制情形发生的失业.自愿失业: 由于存在工资刚性,市场工资率不能随劳动力供给和劳动力需求的变化而变化,或者由于存在有关方面的法律规定如最低工资法,使工资率不能下降到法定最低工资率下.总之是由于实际工资率太高而引起劳动力供给大于劳动力需求而造成的劳动者失业的现象.超时工作:指在法定劳动时间以外继续劳动,俗称“加班加点”；兼职工作实际上也是一种超时工作.帕金森定律: 增加劳动时间可能不会啬工作量,也不会提高工作效率；减少工作时间可能不会减少工作量,也不会降低工作效率.换句话说,劳动时间的增长和产量的增加并不总是成正比,而呈现单峰形曲线,增加劳动时间有一个限度,超过这个限度,产量反而会下降,这一规律被称为“帕金森定律”.就业: 指达成法定劳动年龄,具有劳动能力的劳动者,运用生产资料依法从事某种社会劳动,并获得赖以生存的报酬收入或经营收入的经济活动,简称就业.登记失业人员: 指有非农业户口,在一定的劳动年龄内,有劳动能力,无业而要求就业,并在当地就业服务机构进行登记求职的人员.自然失业率: 又叫均衡失业率,是指在整个劳动力市场既不存在过多的劳动力供给,也不存在过多劳动力需求的失业率.奥肯法则: 20世纪60年代奥肯担任肯尼迪总统经济顾问委员会顾问时,通过实证考察得出的结论是,实际国民生产总值每降低3%,失业率就会升高1%,这就是著名的奥肯法则.菲利普斯曲线: 西方经济学家把表示失业率与货币工资变动率之间此消彼长.相互交替关系的曲线称做菲利浦斯曲线.菲利浦斯曲线说明,失业率与货币工资增长率彼此是逆相关或负相关的.配第—克拉克定理: 该定理以若干国家在时间的推移中发生的变化为依据,这种时间毓是和不断提高的人均国民收入水平相适应的.其主要结论是：随着经济发展水平的提高,劳动力首先由第一产业向第二产业移动,当人均国民收水平进一步提高时,劳动力便向第三产业移动.摩擦性失业: 指在生产过程中由于难以避免的摩擦造成的暂时的局部的失业.结构性失业：是由于劳动者的技能结构与现有的就业岗位技能结构错位,造成失业与岗位并存的一种失业现象,表现在技能.文化.区域和年龄结构失衡等许多方面.隐性失业：指经济部门中存在着边际生产率等于或小于零的现象.即如果3个人的活安排5个人去干,那么其中2个人是隐性失业.间接成本:又称机会成本,是指高中毕业就参加工作所获得的.大学生如果不上大学而直接参加工作也同样能够获得的收入.劳动力需求曲线:是用几何图形的形式表述劳动力需求的概念,劳动力需求曲线是一条从左上向右下倾斜的曲线,它充分说明了在其他条件不变的情况下,劳动力需求量与工资率之间的反向联系.劳动力供给曲线:供给曲线是一条平滑的曲线而不是一条折线,原因是假定工资率和劳动力供给量无限可分.这种假设虽然不完全符合实际,但为了分析方便（同时它也确实反映供给变化的大致趋势和一般规律）,劳动经济学家仍然这样假设.短期劳动力需求:所谓短期劳动力需求是指在资本存量不变,惟一可变的因素是劳动投入量时,即在资本投入量不会变化.技术条件也不变的条件下对劳动力的需求.长期劳动力需求:长期劳动力需求则是指在企业的一切生产要素,不论是资本.技术,还是劳动力要素都是可变的,即任何条件都可能变化时对劳动力的需求.人力资本投资：人力资本的形成,特别是人力资本存量的增加,主要依靠人力资本投资.凡是有利于形成与增强劳动力因素结构的行为.费用与时间都是人力资本投资.劳动力流动：劳动者相对于劳动力市场条件的差别,在地区之间.行业之间.产业之间.职业之间和岗位之间的自愿选择和迁移.工资收入歧视：指从事相同工作的员工,一部分人由于非经济个人特征而导致所获工资收低于另一部分人.效用理论:所谓效用是指商品或劳务存在于消费者心目中的满足欲望或需要的能力,它表示商品或劳务同消费者的愉快或痛苦之间的关系.换句话说,效用就是消费者在消费商品或劳务时的满足程度.一种商品或劳务对消费者是否有效用,取决于消费者对这种商品或劳务是否有欲望以及这种商品或劳务是否有满足消费者欲望的能力.收入约束线:收入约束线是个人在时间和劳动能力状况约束下,所能消费余暇和获得收入的最大组合线.人力资本：是一种与物质资本相对应的资本形式,它表现为能为任何个人带来永久性经济收的能力和知识等.年龄歧视：在一些招聘广告中,经常看到有关年龄的限制性条件.人力资本投资歧视：是指某些劳动力因非经济个人特征导致较少获得能够提高劳动生产率的正规教育.在职培训以及较好的健康照顾等的机会.最低劳动标准：最低劳动标准包括多方面的内容,从劳动经济学的角度看,最低劳动标准包括最低工资标准.最长劳动时间标准和其它劳动条件标准.其它劳动条件标准包括最低就业年龄标准.保护劳动者在生产中的安全和健康所应采取措施的各种法律规范以及关于女工与未成年工的特殊保护等等.人力政策：人力政策,又称积极的劳动力市场政策,是指政府通过对劳动力进行重新教育和培训,提高其就业适应能力,达到改善劳动力供给结构,提高劳动力市场运行效率等目的的政策.统计性歧视理论:是将一个群体的典型特征看做该群体中每一个个体所具有的特征,并利用这个群体的典型特征作为雇用标准而产生的歧视.主体均衡:约束条件下的最大效用.所谓主体均衡,就是在资源约束的条件下余暇与收入的组合能使主体获得最大效用的状态.收入效应:是从一条无差异曲线移向更高效用的无差异曲线所引起的.一般情况下,纯收入效应使余暇增加,劳动时间减少.工资水平:是指在一定时期和一定统计范围内劳动者平均工资的数额.替代效应:在个人实现相同效用水平的情况下,劳动供给的决策主体改变其时间分配结构,必定由于工资率的变化所引起.相对价格提高的商品必然引起较小的需求,价格提高的商品必然增加其供给,这就是替代效应.劳动力市场的均衡:在劳动力市场,劳动力供给和劳动力需求相互作用,当供给等于需求时,即实现了劳动力市场的均衡.劳动力市场的非均衡:需求与供给数量虽不相等,但市场上已没有改变这种不相等格局的力量,市场价格也因此而稳定下来.这种不稳定状态实际上也是一种均衡状态,但与传统均衡理论的解释不同,所以被称之为“非均衡”.雇用调整:雇用活动实际上是以企业组织为前提并将其机能当做媒介来开展的.雇用活动意味着以它对企业内各个部门和环节施加影响来体现其自身和组织的调整.因此,一般可以说企业的雇用活动就是雇用调整.劳动时间:劳动时间又称工作时间,是指劳动者从事有酬性社会劳动所花费的时间.劳动投入量:某一时点受雇劳动者的人数是存量,一定时间内的总劳动时间是流量.既然产量是在一定时间内发生的流量,与此相应的劳动投入量应该是以“人员·时间”为单位的流量.准固定成本:为了区别于随时变化而变化的可变成本,这些成本被称为准固定成本.集体作业:现实中,企业的工作方式在很多情况下是集体作业.因为在生产过程中的流水作业,如果只考虑到每个人的具体情况而选择分散的劳动时间,就会给工作带来很大的障碍.为了有效利用分工的优势,提高生产效率,必须统一规定集体作业时间,就是说是一个集体,不是分散的个体.制度劳动时间:劳动时间由企业规定,即使工资率相同,随着劳动时间的不同劳动力参与率也会变化,而且缩短劳动时间会使劳动力参与率上升的可能性增强.既由企业制度劳动时间相关内容.余暇时间:除劳动时间以外的时间就称为余暇时间.生命周期（何谓生命周期）:本书所说的生命周期系指与就业密切相关的人生各重要阶段,因此也可能称为劳动力供给的生命周期.结婚育儿决策:结婚和生育年龄的变化对女性劳动参与决策的影响远大于它对男性劳动参与决策的影响程度,尤其总和生育率大幅度下降对中国女性劳动时间的增加起到了很大的推动作用.在参加就业的时间延长了,结婚育儿的时间就推后,这样劳动参与率就会增加.家庭生产函数:对理解家庭经济行为有益的概念,即家庭生产函数.与企业生产财富.提供服务一样,在家庭中也存在着供自家消费的财富和服务的创造以及提高效用的考虑.就业与转换工作决策:在做出就业还是不就业.换工作还是不换工作（本节把转换工作界定为脱离原单位的工作变换,转换工作是劳动力流动的一种现象）的决定时,是什么样的经济性动机左右当事者？是期望总工资收入.期望工资总额是影响人们选择的重要因素.期望工资总收入:人们在选择就业单位时,除了要考虑自己的工作兴趣之外,就是工资.劳动时间.劳保福利等雇用（劳动）条件.此时考虑的劳动条件不仅是当时的状态,还包括未来是什么样子,即准备去就业的企业将来会怎么样,自己升职.升薪的可能性等.求职:在考虑转换工作时,必然要开展求职活动.求职即从劳动力需求市场上寻求适应自己工作的职位,同时要掌握更多的信息,从多方面了解社会劳动力的需求与供给,以寻求自己理想中的职业.退休决策:达到规定的年龄,看是否退休还是继续就业,从方面因素去考虑这个问题.工资形式:按要素类别分配社会总产品或收入,称为功能性收入分配,作为劳动要素均衡价格的工资,亦称之为劳动报酬.在明确工资等同于劳动报酬后,工资形式即劳动报酬获取的形式.1.基本工资2.计时工资与计件工资3.福利.工资职能:工资职能即由本质属性所决定的作用.工资具有补偿职能.激励职能.调节职能和效益职能.工资变动规律:劳动供给影响工资高低,当劳动力的市场价格超过共自然价格时,劳动者的景况是繁荣而幸福的,能够得到更多生活必需品和享受品,从而可以供应更多的人口.但是随着工人人口增加又会引起劳动的供给超过需求,于是劳动的市场价格又会降低到其自然价格以下.当市场价格低于自然价格时,工人的生活状况就会急剧恶化,于是劳动的市场价格又会再提高到自然价格上来.把工人人口的自然增长率的变化看成会自动调节工资水平,使工资必然只等于工人维持最低限度生产资料的价格.从劳动的需求方面来看,知道工人人数只能决定劳动的供给一面,而劳动的需求则决定于资本数量的增减.如果资本积累的速度大于工人人口增长的速度,则对劳动的需求便会在于供给,工资就会上涨.资本积累的速度赶不上工人人数的增长速度,加之人口的增长必然使粮食等生活资料的价格上涨,即使货币工资随之增加,但其速度比不上生活必需品涨价的速度,因此工资有下降的趋势.相对工资:工资水平决定于维持工人自身及其家属生存所必需的生活资料的总价值或价格.工资刚性:是指劳动力市场上的货币工资水平向下浮动的可能性或工资向下变动的弹性非常低.效率工资:效率工资是劳动经济学中最新的一个研究成果.这一理论中最主要的一个假设条件是,员工的有效劳动供给量,或者说工作努力程度.工作绩效与工资水平的高低成正比,即企业支付的工资越高,员工们的工作效率就越高.按要素分配:该理论认为各种报酬取决于各种相应的投入,凭投入取得报酬,投入了什么要素就按一定的标准取得相应的报酬.社会各阶层.居民之所以有资格取得报酬收入,是因为他们为生产这些“收入”提供了生产要素,即有所“投入”,这些投入才是收入的来源.按劳分配:在收入工资分配中实行按劳分配与按要素分配相结合的调控原则,是在中国社会主义市场经济体制下,配合“公有制为主体,多种所有制经济共同发展”的所有制结构改革而提出的.集体谈判制度:集体谈判制度,是协调劳资关系的一种主要形式,也是工会维护工人权益的重要手段,甚至被称为工会运动的“基石”.工资水平控制:一是通过建立最低工资制度等方式,对最低工资水平进行控制；二是通过个人或企业累进税制,对最高工资水平进行控制；三是通过个人收入政策对社会工资总水平进行控制.工资水平变动:决定微观工资水平的因素可以分为外部因素少内部因素两大方面.企业外部影响工资水平的因素,主要有市场劳动力供求状况.政府对宏观工资水平的决策以及物价水平的变动等.企业内部因素对工资水平的影响,主要表现为员工之间的劳动差别.分配形式和企业经济效益三个方面.工资指导线制度:所谓“工资指导线”,是在市场经济条件下,政府为保证宏观经济目标的实现,根据社会经济发展相关经济指标的现状与变动,提出的关于年度工资水平增长标准的权威性建议.工资谈判制度:所谓工资谈判,是指在市场经济条件下,以企业.雇主或其组织为一方,以雇员或工会组织为另一方,双方在政府的指导协调下,就企业工资分配问题进行协商的制度.工资差别:所谓工资差别,是指劳动要素供给者之间在要素服务收入数量方面的差异和相互关系.职业间工资差别:现代经济学一般用职业的非货币（或职业的非金钱）特征来解释为什么相同素质的劳动者之间工资会有差别.也就是说,对某些职业必须支付较高的工资以补偿不同职业的非金钱差异,从而形成职业间工资差别.劳动负效用补偿工资差别:劳动者的能力相同,贡献也一样,工资应该是无差别的,但事实上往往是存在差别的.这是因为有些职业的劳动环境恶劣（危险.不愉快.紧张.枯燥.劳累.肮脏等）,给劳动者带来精神损失.健康损失.这种由于“劳动负效用”造成的“非货币损失”需要在工资中给予补偿；否则,就雇用不到劳动者.风险补偿性工资差别:亦称职业收入的变动性差别.稳定性差别）有些职业的工资较稳定,有的则变动大；有的职业较稳定,有的则不稳定甚至有失业风险.因此,虽然其他条件相同,工资却会有差别,这种差别称为风险性补偿工资.人力资本补偿性工资差别:人力资本理论指出,人们对人力资本进行投资是要取得回报的,劳动者进行了教育费用等的投资后,在工资上就应有所回报.因此,不同职业之间工资就会有差别,甚至在同一职业中的不同劳动者,其工资也可能会有差别.竞争性差别工资:这种工资由于劳动力素质（劳动技能）差异产生的工资差别称为竞争性工资差别或技能性工资差别.垄断性工资差别:垄断性工资差别既非补偿工资差别,也非竞争性工资差别,它是由于劳动者的特殊素质或特殊阶层而产生的.垄断性工资收入是由于劳动力供给几乎无弹性,使工资中含有很高的“租金”部分,所以又称“租金性工资收入”.地区间工资差别:地区工资差别是一种普遍存在的工资差别,形成地区间工资差别的原因方面看,地区间经济发展的不平衡具体反映在以下方面:1.地区劳动力市场劳动力供求差异；2.人均物质资本差异；3.人均人力资本差异；4.市场竞争程度差异；等等.上述差别的存在,造成了地区间的工资差别.年龄间工资差别:很多国家往往是年龄越大,工资越高,工资与年龄成正比,直到工资升到顶点后再逐步下降.为什么会出现这一现象？有两种原因在起作用:1.人力资本理论（这里不再做分析）；2.随着年龄增长,受教育程度逐渐提高,知识和经验也在不断积累,而且和企业的关系在加深,受到雇主的信任,由于劳动者自身原因和雇主的原因,因此工资随着年龄不断增长（在这里年龄实际上应理解为工龄）.性别间工资差别:从理论上讲,工资分配实行同工同酬,不应该存在男女工资差别.但是事实上男性劳动者工资比女性高（从总体上讲）.造成差别的原因包括:1.传统观念中轻视妇女,妇女升职与受培养的机会少于男性,致使有的妇女受压抑,得不到重用,积极性下降；2.由于受教育少而能力低,因此女性平均工资低于男性；3.由于生理.必理等自然原因,使女性进入高收入劳动者行列的机会受到限制.洛伦茨曲线:为了描述社会收入分配差异状况,美国统计学家M·洛伦茨提出了判断分配均等程度的方法,以发明者命名,称为洛伦茨曲线.基尼系数:设洛伦茨曲线与绝对均等曲线围成的面积为a,与绝对不均等曲线围成的面积为b,则可用a除以（a+b）的商表示分配的均等程度.这个数值称为基尼系数,亦称为洛伦茨系数.基尼系数介于0和1之间.失业:失业是指有劳动能力并愿意就业的劳动者找不到工作的一种社会现象.其实质是劳动者与生产资料相分离,劳动者不能与生产资料相结合进行社会财富的创造,从而也失去了获得劳动报酬的机会.充分就业:充分就业就是“在某一工资水平下,所有愿意接受这种工资的人都能得到工作”.失业率:衡量一个国家宏观经济中失业状况最基本的指标是失业率.失业率是指失业人数占劳动力总数的百分比.就业失业理论:就业理论产生于解决失业问题的实践中.失业现象最初产生于18世纪,19世纪以后日益严重,迫使经济学家们对其展开研究,就业理论成了经济学说的重要内容之一.就业结构:一般是指社会劳动力在国民经济各部门.各行业.各地区.各领域的分布.构成和联系.摩擦性失业:是由于劳动者在要求就业和获得工作岗位之间存在时间。
《劳动经济学》(作者Borjas)第十一章习题答案
CHAPTER 1111-1. Suppose the firm’s labor demand curve is given by:w = 20 - 0.01 E ,where w is the hourly wage and E is the level of employment. Suppose also that the union’s utility function is given byU = w × E .It is easy to show that the marginal utility of the wage for the union is E and the marginal utility of employment is w . What wage would a monopoly union demand? How many workers will be employed under the union contract?Utility maximization requires the absolute value of the slope of the indifference curve equal the absolute value of the slope of the labor demand curve. For the indifference curve, we have thatEw MU MU w E =.The absolute value of the slope of the labor demand function is 0.01. Thus, utility maximization requires that01.=Ew .Substituting for E with the labor demand function, the wage that maximizes utility must solve01.0100000,2=−ww ,which implies that the union sets a wage of $10, at which price the firm hires 1,000 workers.11-2. Suppose the union in problem 1 has a different utility function. In particular, its utility function is given by:U = (w - w *) × Ewhere w * is the competitive wage. The marginal utility of a wage increase is still E , but the marginal utility of employment is now w – w *. Suppose the competitive wage is $10 per hour. What wage would a monopoly union demand? How many workers will be employed under the union contract? Contrast your answers to those in problem 1. Can you explain why they are different?Again equate the absolute value of the slope of the indifference curve to the absolute value of the slope of the labor demand curve:01.0*=−=Ew w MU MU w E .Setting w* = $10 and using the labor demand equation yields:01.0100000,210=−−ww .Thus, the union demands a wage of $15, at which price the firm hires 500 workers.In problem 1, the union maximized the total wage bill. In problem 2 the utility function depends on the difference between the union wage and the competitive wage. That is, the union maximizes its rent. Since the alternative employment pays $10, the union is willing to suffer a cut in employment in order to obtain a greater rent.11-3. Using the model of monopoly unionism, present examples of economic or political activities that the union can pursue to manipulate the firm’s elasticity of labor demand. Relate your examples to Marshall’s rules of derived demand.Marshall’s rules state that the elasticity of labor demand is lower the1. lower is the elasticity of substitution;2. lower is the elasticity of demand for the output;3. lower is labor’s share of total costs; and4. lower is the supply elasticity of other factors of production.Consider two examples: innovations and picket lines. Unions are notoriously bad at allowing firms to introduce (labor saving) innovations in their factories. The long shoremen on the west coast recently struck, because they were unwilling to let cargo crates be identified with bar codes. (The union wanted a union worker to record all movements of crates with pencil and paper.) Thus, the union was pursuing a policy of limiting the supply of other factors of production (rule 4). In a similar vein, when on strike, unions picket the firm in order to decrease the ability of the firm to hire scabs (rule 1).11-4. Suppose the union only cares about the wage and not about the level of employment. Derive the contract curve and discuss the implications of this contract curve.The utility function U = U(w) implies that the union’s indifference curves are horizontal lines, so that the contract curve coincides exactly with the firm’s labor demand curve (D).11-5. A bank has $5 million in capital that it can invest at a 5 percent annual interest rate. A group of 50 workers comes to the bank wishing to borrow the $5 million. Each worker in the group has an outside job available to him or her paying $50,000 per year. If the group of workers borrows the $5 million from the bank, however, they can set up a business (in place of working their outside jobs) that returns $3 million in addition to maintaining the original investment.(a) If the bank has all of the bargaining power (that is, the bank can make a take-it or leave-it offer), what annual interest rate will be associated with the repayment of the loan? What will be each worker’s income for the year?If the bank has all of the bargaining power, it will pay each worker exactly their reservation wage, i.e., $25,000. The total cost of this is $2.5 million. Thus, the firm will claim the remaining $500,000 by imposing a 10 percent interest rate as $500,000 is 10 percent of the original $5 million.(b) If the workers have all of the bargaining power (that is, the workers can make a take-it or leave-it offer), what annual interest rate will be associated with the repayment of the loan? What will be each worker’s income for the year?If the workers have all of the bargaining power, they will pay the bank its reservation value, i.e., an interest rate of 5 percent. When it does this, the 50 workers receive $3 million less the 5 percent interest of $250,000 for a total of $2.75 million. Split evenly among the 50 workers, this leaves each worker with a yearly income of $55,000.11-6. Consider a firm that faces a constant per unit price of $1,200 for its output. The firm hires workers, E, from a union at a daily wage of w, to produce output, q, whereq = 2E½.Given the production function, the marginal product of labor is 1/E½. There are 225 workers in the union. Any union worker who does not work for the firm can find a non-union job paying $96 per day.(a) What is the firm’s labor demand function?The labor demand function, or the marginal revenue product of labor, isMRP E = MR × MP E = 1200 / E ½.(b) If the firm is allowed to specify w and the union is then allowed to provide as many workers as it wants (up to 225) at the daily wage of w, what wage will the firm set? How many workers will the union provide? How much output will be produced? How much profit will the firm earn? What is the total income of the 225 union workers?If the firm offers w < $96, no workers will be provided. This would leave the firm with no output and no profit. The workers would all receive $96 per day, making their total daily income $21,600.If the firm offers a wage of w > $96, all 225 workers will be provided. These 225 workers would produce 30 units of output. The firm would then earn a profit of 30($1,200) – 225w. Profit, therefore, is maximized when w is minimized subject to the constraint. If the union would supply all 225 workers at a wage of $96, for example, the firm would offer w = $96 and earn a daily profit of $14,400. The total daily income of the 225 workers would remain at $21,600.If the firm needs to offer strictly more than $96 per day to attract workers, it would offer a daily wage of $96.01. All 225 workers would work for the firm, making 30 units of output. The firm’s daily profit would be $14,397.75. And the total daily income of the 225 workers would be $21,602.25.(c) If the union is allowed to specify w and the firm is then allowed to hire as many workers as it wants (up to 225) at the daily wage of w, what wage will the union set in order to maximize the total income of all 225 workers? How many workers will the firm hire? How much output will be produced? How much profit will the firm earn? What is the total income of the 225 union workers?The spreadsheet looks like the following, where the union specifies the wage, labor demand comes from part (a), and everything else follows naturally:wageLaborDemandLaborCosts Output Price Revenue ProfitUnionDaily Income$96 156.25 $15,000.00 25.00 $1,200 $30,000.00 $15,000.00 $19,200.00$97 153.04 $14,845.36 24.74 $1,200 $29,690.72 $14,845.36 $19,353.04$98 149.94 $14,693.88 24.49 $1,200 $29,387.76 $14,693.88 $19,499.88$99 146.92 $14,545.45 24.24 $1,200 $29,090.91 $14,545.45 $19,640.77$100 144.00 $14,400.00 24.00 $1,200 $28,800.00 $14,400.00 $19,776.00…… ……… … … …$190 39.89 $7,578.95 12.63 $1,200 $15,157.89 $7,578.95 $22,949.58$191 39.47 $7,539.27 12.57 $1,200 $15,078.53 $7,539.27 $22,949.90$192 39.06 $7,500.00 12.50 $1,200 $15,000.00 $7,500.00 $22,950.00$193 38.66 $7,461.14 12.44 $1,200 $14,922.28 $7,461.14 $22,949.90$194 38.26 $7,422.68 12.37 $1,200 $14,845.36 $7,422.68 $22,949.60$195 37.87 $7,384.62 12.31 $1,200 $14,769.23 $7,384.62 $22,949.11 Thus, the union sets a daily wage of $192. The firm responds by hiring 39.06 workers, who produce 12.5 units of output. The firm earns a daily profit of $7,500, while the 225 union workers earn a total of $25,297.92 each day.11-7. Suppose the union’s resistance curve is summarized by the following data. The union’s initial wage demand is $10 per hour. If a strike occurs, the wage demands change as follows:Length of Strike: Hourly Wage Demanded1 month 92 months 83 months 74 months 65 or more months 5Consider the following changes to the union resistance curve and state whether the proposed change makes a strike more likely to occur, and whether, if a strike occurs, it is a longer strike. (a) The drop in the wage demand from $10 to $5 per hour occurs within the span of 2 months, as opposed to 5 months.If the union is willing to drop its demands very fast, the firm will find it profitable to delay agreement until the wage demand drops to $5. A strike, therefore, is more likely to occur. If $5 is the lowest wage the union is willing to accept, the strike would probably last 2 months.(b) The union is willing to moderate its wage demands further after the strike has lasted for 6 months. In particular, the wage demand keeps dropping to $4 in the 6th month, $3 in the 7th month, etc.If the union is willing to accept even lower wages in the future, some firms will find it optimal to wait the union out. Thus, strikes will be more likely and last longer.(c) The union’s initial wage demand is $20 per hour, which then drops to $9 after the strike lasts one month, $8 after 2 months, and so on.Conditioning on a strike occurring, the length of strike will be unchanged as the resistance curve after the initial demand stays the same. Of course, the probability of a strike occurring increases when the initial demand increases.11-8. (a) Would you expect unions to be more willing to call a strike during good economic times or bad economics times? Explain.This is an open question – much empirical evidence suggests that strikes are procyclical – a conclusion that the model of job search supports. During good economic times, there are many good jobs available, searching for jobs is relatively easy, and the probability of securing a job is quite high. In short, the non-union option is quite attractive. During such times, therefore, the union may be a tough negotiator, and this tough stance may lead to more strikes being called. (This doesn’t explain, though, why the firms are also tough negotiators during such times.)The opposite happens during bad economic times. Namely, jobs are scarce, they are difficult to find, and searching is costly. The non-union option, therefore, is not very attractive. Consequently, the union leadership may be more willing to accept a deal. This softer stance, therefore, may lead to fewer strikes being called.(b) Does Table 627 of the 2002 U.S. Statistical Abstract provide evidence to support your answer to part (a)? What is the single overriding pattern in this table?There is some evidence that strikes are more prevalent in good times than bad (compare the 1960s to the early 1970s), but there was much more strike activity in the late 1970s and early 1980s than in the mid to late 1980s.The single most obvious pattern in the table, however, is that as union membership steadily fell over this time period, the level of strike activity also fell. The average percent or working time lost to a strike was about 12 percent, 10 percent, 4 percent, and 2 percent for the 1960s, 1970s, 1980s, and 1990s respectively.11-9. Suppose the value of the marginal product of labor in the steel industry is VMP E = 100,000 – E dollars per year, where E is the number of steel workers. The competitive wage for the workers with the skills needed in steel production is $30,000 a year, but the industry is unionized so that steel workers earn $35,000 a year. The steelworkers’ union is a monopoly union. What is the efficiency cost of the union contract in this industry?If the steel industry were to pay the competitive wage to its workers, it would employ 70,000 workers, because at this level the VMP of the last employee equals the competitive wage. Under the union wage, however, the industry only hires 65,000 workers. The efficiency cost of the union, therefore, is(½)($35,000 – $30,000)($70,000 – $65,000) = $125 million per year.11-10. Suppose the economy consists of a union and a non-union sector. The labor demand curve in each sector is given by L = 1,000,000 – 20w. The total (economy-wide) supply of labor is 1,000,000, and it does not depend upon the wage. All workers are equally skilled and equally suited for work in either sector. A monopoly union sets the wage at $30,000 in the union sector. What is the union wage gap? What is the effect of the union on the wage in the non-union sector?In a competitive economy, the wage would be the same in the two sectors, and its value would be such that the total labor demand L D = 2 × (1,000,000 – 20w C) equaled total labor supply. The solution to the equation 2 (1,000,000 – 20w C) = 1,000,000 is w C = $25,000.If the union wage is set at $30,000, the union sector employs 400,000 workers. The remaining 600,000 must be employed in the non-union sector, which will happen if the wage in the non-union sector is (1,000,000 – 600,000)/20 = $20,000.Hence, the wage gap between the union and the non-union sectors equals $10,000, or 50 percent of the non-union wage.11-11. Consider Table 628 of the 2002 U.S. Statistical Abstract.(a) How many workers were covered by a union contract in 1983? What percent of the workforce was unionized?In 1983, 20.532 million workers (23.3 percent of all workers) were covered by a union contract in the U.S.(b) How many workers were covered by a union contract in 2001? What percent of the workforce was unionized?In 2001, 17.878 million workers (14.8 percent of all workers) were covered by a union contract in the U.S.(c) Decompose the changes from part (a) to part (b) in terms of public- and private-sector workers and unions.This dramatic change in union coverage masks an even deeper pattern in union coverage – namely that public-sector unions have been growing in absolute numbers and holding their own in percent coverage, while the private-sector unions have experienced sharp decreases in their enrollments.The number of public-sector workers covered by a union contract, for example, increased from just over 7 million in 1983 to almost 8 million in 2001. The percent of public-sector workers who were members of a union held constant over this time span at roughly 37 percent, while the percent of public-sector workers covered by a union contract fell slightly from 45.5 percent in 1983 to 41.7 percent in 2001.On the other hand, the number of private-sector workers covered by a union contract decreased from 13.4 million in 1983 to only 9.9 million in 2001. The percent of private-sector workers covered by a union contract also fell drastically, from 18.5 percent in 1983 to just 9.7 percent in 2001.11-12. Consider table 618 in the 2002 U.S. Statistical Abstract.(a) Calculate the union wage effect. Calculate the union effect on total benefits. Calculate the union effect on total compensation.The union effects are simply the ratio of the union amount divided by the non-union amount:Wage effect: $19.33 / $15.38 = 1.257 percent.Benefit effect: $10.09 / $5.41 = 1.865 percentTotal compensation effect: $29.42 / $20.79 = 1.415 percent.(b) Note that for most categories, retirement and savings increases total compensation by about 60 to 80 cents per hour, with roughly two-thirds of this expense coming in defined contribution retirement plans. In contrast, retirement and savings adds $1.64 to the hourly compensation of union workers, and over 70 percent of this comes in the form of defined benefit pension plans, not defined contribution. What is the difference between defined benefit and defined contribution plans? Why might a union prefer (and be able to negotiate) more compensation in defined benefit plans than defined contribution plans?A defined benefit plan specifies the retirement benefit as a fixed dollar amount. For example, if someone receives 50 percent of their last annual income as their annual pension, this is a defined benefit plan. In contrast, a defined contribution plan specifies the amount of savings into a retirement plan the firm will make. The amount of benefit eventually received by the worker depends on how well the money is invested until retirement.It is generally thought the workers prefer DB plans (though this doesn’t need to be the case). DB plans put the risk on the part of the firm, while DC plans put the financial risk on the part of the worker. (The workers at Enron, for example, lost huge amounts of retirement savings not only because they were in a DC plan but also because they were forced to keep most of their contributions as Enron stock.) As unions tend to work in large firms, they may be more able than other workers to negotiate a DB plan.。
《劳动经济学》(作者Borjas)第二章习题答案
CHAPTER 22-1. How many hours will a person allocate to leisure activities if her indifference curves between consumption and goods are concave to the origin?A worker will either work all available time or will not work at all. As drawn in Figure A, pointB is preferred to points A andC . Thus, the worker chooses not to enter the labor market. As drawn in Figure B, point C is preferred to both points A and B . Thus, the worker chooses not to consume any leisure and work all available time.Figure A Figure B2-2. What is the effect of a rise in the price of market goods on a worker’s reservation wage, probability of entering the labor force, and hours of work?Suppose the price of market goods increases from p to p ′ and the person’s non-labor income is V . If she chooses not to work, she can purchase V/p ′ units of consumption after the price change, whereas she could have consumed V/p units of consumption prior to the price increase. Thus, her endowment point has moved from E to E ′ in Figure A. As long as leisure is a normal good, the indifference curve is steeper as we move up a vertical line, indicating that the slope of the indifference curve is steeper at E than at E ′. Thus, an increase in the price of goods lowers the reservation wage and makes the person more likely to work.Hours of LeisureHours of LeisureGoods GoodsBCA ABCU 1U 1U 0U 0Figure A.To simplify the illustration of the effect on hours of work, assume for simplicity that V = 0. The increase in the price of goods shifts the budget line from FE to GE , moving the worker from P to point R . This shift induces both an income effect and a substitution effect. The price increase in effect lowers the person’s real wage rate, increasing the demand for leisure and leading to fewer hours of work. Thissubstitution effect is illustrated by the move from point P to point Q in Figure B. The price increase also reduces the worker’s wealth, lowering the demand for leisure and leading to more hours of work. This income effect is illustrated by the move from Q to R . As drawn the income effect dominates thesubstitution effect and the price increase lowers the demand for leisure and increases hours of work. It is, of course, possible for the substitution effect to dominate the income effect (not pictured), so that hours of work decreases. Thus, without further restrictions on preferences, an increase in the price of market goods has an ambiguous effect on hours worked.Figure B.GoodsV /p ′V /LeisureHours of Leisure2-3. Sally can work up to 3,120 hours each year (a busy social life and sleep take up the remaining time). She earns a fixed hourly wage of $25. Sally owes a 10 percent payroll tax on the first $40,000 of income. Above $40,000 of income, there is no payroll tax. Sally also faces a progressive income tax rate. There is no income tax on the first $10,000 of income. From $10,000 up to $60,000, the marginal income tax rate is 25 percent. Above $60,000, the marginal income tax rate is 50 percent. Graph Sally’s budget line.Sally’s budget line will have kinks at gross income levels of $10,000, $40,000, and $60,000. As her wage is $25 per hour, these kinks occur after 400 hours, 1,600 hours, and 2,400 hours of work respectively, or, similarly, at 2,720, 1,520, and 720 hours of leisure.•From 0 to 400 hours, Sally’s after-tax wage is $22.50 (90 percent of $25). If she works exactly 400 hours, her after-tax income is $9,000.•From 400 to 1,600 hours, Sally’s after-tax wage is $16.25 (65 percent of $25). If she works exactly 1,600 hours, her after-tax income is $9,000 + $16.25 (1600-400) = $28,500.•From 1,600 to 2,400 hours, Sally’s after-tax wage is $18.75 (75 percent of $25). If she works exactly 2,400 hours, her after-tax income is $28,500 + $18.75 (2400-1600) = $43,500.•From 2,400 to 3,120 hours, Sally’s after-tax wage is $12.50 (50 percent of $25). If she works exactly 3,120 hours, her after-tax income is $43,500 + $12.50 (3120-2400) = $52,500.2-4. Tom earns $15 per hour for up to 40 hours of work each week. He is paid $30 per hour for every hour in excess of 40. Tom faces a 20 percent tax rate and pays $4 per hour in child care expenses for each hour he works. Tom receives $80 in child support payments each week. There are 168 hour in the week. Graph Tom’s weekly budget line.•If Tom does not work, he leisures for 168 hours and consumes $80.•For all hours Tom works up to his first 40, his after-tax and after-child care wage equals (80 percent of $15) – $4 = $8 per hour. Thus, if he works for 40 hours, he will be able to leisure for 128 hours and consume $80 + $8(40) = $400.•For all hours Tom works over 40, his after-tax and after-child care wage equals (80 percent of $30) – $4 = $20. Thus, if he works for 168 hours (128 hours at the overtime wage), he will notleisure at all, but he will consume $80 + $8(40) + $20(128) = $2,960.2-5. What happens to a worker’s desired hours of work if employers pay an overtime premium equal to “time and a half”(that is, 1.5 times the straight-time wage) for any hours worked in excess of 40 hours? What would happen to hours of work if the overtime premium were raised to double the straight-time wage?The availability of overtime pay generates a new (steeper) segment of the budget line originating at the point where the person works 40 hours per week. The figure below illustrates three different possibilities. If the person works 40 hours per week (person B), he or she will be better off by moving to the tangency point labeled X. This person, therefore, will take advantage of the overtime pay and work more hours. If the person is working more than 40 hours per week initially (as is the case for person C), the move from C to X involves both income and substitution effects, and hence we cannot determine which effect dominates. If the person works many fewer than 40 hours per week (person A) he or she will not be affected by the possibility of overtime pay. If the overtime pay were increased to double-pay, it would steepen the line segment originating at 40 hours of work, and perhaps induce some of the persons like A to take advantage of the overtime pay. Person B would continue to work more than 40 hours under a double-time rate, while the double-time rate would have an ambiguous effect on the hours worked of person C.Dollars of Consumption$2,960$400 $80128 168 Hours of LeisureTom’s Weekly Budget Line2-6. A person owns a small farm near a large city and must decide whether to work on that small farm or take a job in the city. Her utility depends on her income per day, Y , and the number of hours allocated to leisure activities, L . Daily income from farm work is:220f f f h h Y −=,where h f is hours of work on the farm; and daily income from the city job is:Y C = 14h C ,where h C is hours of work in the city.To calculate the budget lines associated with each of the opportunities, it is easiest to work through a numerical calculation of what a worker’s earnings would be if he or she allocated 1 hour, 2 hours, 3 hours, etc., to each of the sectors and worked in that sector exclusively. This calculation leads to:Total Earnings Marginal EarningsHours of Work Farm City Farm City1 19 14 19 142 36 28 17 143 51 42 15 14 4 64 56 13 145 75 70 11 146 84 84 9 147 91 98 7 14 8 96 112 5 14Consumption ($)Leisure(a) If she can work on the farm or in the city, but not both, which sector would she choose?The table above suggests the budget line associated with working exclusively in the city is given by CE and on the farm is the parabola FE . As a result, if a worker can only work in either the city or on the farm, a worker with indifference curves like person A is better off working on the farm, while a worker with indifference curves like person B is better off in the city.(b) If she can work both on the farm and in the city, how would she allocate her time?If a worker can allocate her time to both the city and the farm, the worker is then better off allocating the first few hours of work to the farm sector. As the table indicates, the first hour allocated to the farm sector generates $19 worth of income, the second hour generates $17, the third hour generates $15, the fourth hour generates $13, and so on. The worker is thus best off by allocating the first three hours to the farm sector and working any remaining hours she wishes in the city where each additional hour of work generates a constant $14.2-7. Cindy gains utility from consumption C and leisure L . The most leisure she can consume in any given week is 168 hours. Her utility function is U(C,L) = C × L . This functional form implies that Cindy’s marginal rate of substitution is C / L . Cindy receives $630 each week from her great-grandmother – regardless of how much Cindy works. What is Cindy’s reservation wage?The reservation wage is the MRS when not working at all. Thus, w RES = MRS at maximum leisure = C / L = $630 / 168 = $3.75.Leisure2-8. The utility function of a worker is represented by U(C, L) = C ×L, so that the marginal utility of leisure is C and the marginal utility of consumption is L. Suppose this person currently has a weekly income of $600 and chooses to enjoy 70 hours of leisure per week. How many additional dollars of income would it take to entice the worker to work 10 more hours?Initially the person’s utility is U(C,L) = U(600,70) = 600 × 70 = 42,000. She would agree to work 10 more hours (i.e., give up 10 hours of leisure) if the increase in consumption would allow her to achieve at least the same level of utility. Letting Y be her new total income, therefore, Y must solve 60Y = 42,000, which requires Y = $700. Thus, the person’s income would have to rise by $100 to compensate her for the loss of 10 hours of leisure.2-9. You can either take a bus or drive your car to work. A bus pass costs $5 per week, whereas driving your car to work costs $60 weekly (parking, tolls, gas, etc.). You spend half-an-hour less on a one-way trip in your car than on a bus. How would you prefer to travel to work if your wage rate is $10 per hour? Will you change your preferred mode of transportation if your wage rate rises to $20 per hour? Assume you work five days a week and time spent riding on a bus or driving a car does not directly enter your utility.Taking a bus will save you $55 a week, but it will cost you 5 hours of leisure time due to the longer commute. Since the price of leisure is equal to the wage rate, the monetary value of the time lost is $50 when the hourly wage is $10 and $100 when the hourly wage is $20. Therefore, it makes sense for you to take a bus to work if you are paid $10 per hour, but you will switch to driving your car if your wage increases to $20 per hour.2-10. Shelly’s preferences for consumption and leisure can be expressed asU(C,L) = ( C – 200 )× ( L – 80 ).This utility function implies that Shelly’s marginal utility of leisure is C – 200 and her marginal utility of consumption is L – 80. There are 168 hours in the week available to split between work and leisure. Shelly earns $5 per hour after taxes. She also receives $320 worth of welfare benefits each week regardless of how much she works.(a) Graph Shelly’s budget line.If Shelly does not work, she leisures for 168 hours and consumes $320. If she does not leisure at all, she consumes $320 + $5(168) = $1,160.(b) What is Shelly’s marginal rate of substitution when L = 100 and she is on her budget line?If Shelly leisures for 100 hours, she works for 68 hours and consumes $320 + $5(68) = $660. Thus, her MRS when doing this is:23$204608010020066080200==−−=−−==L C MUcMU MRS L .(c) What is Shelly’s reservation wage?The reservation wage is defined as the MRS when working no hours. When working no hours, Shelly leisures for 168 hours and consumes $320. Thus,36.1$8812080168200320≈=−−=RES w .Dollars of Consumption$1,160$320168 Hours of LeisureShelly’s Weekly Budget Line(d) Find Shelly’s optimal amount of consumption and leisure.Her optimal mix of consumption and leisure is found by setting her MRS equal to her wage and solving for hours of leisure given the budget line: C = 320 + 5(168–L )..1365960400580200)168(53205802005=−=−−−−+=−−==L LL L L L C MRSwThus, Shelly will choose to leisure 136 hours, work 32 hours, and consume $320 + $5(32) = $480 each week.2-10. Among single, college-educated women aged 22 – 25, average annual hours worked is 2,160 and the average wage is $22.50. If the average wage increases to $25 per hour, average annual hours worked increases to 2,340. What is the elasticity of labor supply for this group of workers?The elasticity of labor supply is75.09112150.2250.2200.25160,2160,2340,2%%==−−=∆∆=wL S σ.2-11. Mike’s utility for consumption and leisure is U(C,L) = C × L so that his marginal rate ofsubstitution between leisure and consumption is C/L . There are 168 hours in the week and he earns $10 per hour.(a) What is Mike’s optimal amount of consumption and leisure?Mike’s optimal mix of consumption and leisure is found by setting his MRS equal to his wage and solving for hours of leisure given that the budget line is C = 10(168–L ).. 84101680 1010=−== =L LLLCMRS wThus, Mike will choose to leisure 184 hours, work 84 hours, and consume $10(84) = $840 each week. (b) If the government starts a welfare policy that pays B to all non-workers and pays $0 to all workers, at what value of B will Mike opt out of the labor force in order to go on welfare?Given our answer in part (a), we know that if Mike opts to work, his utility will be u work(840,84) =840(84) = 70,560. If he opts out of the labor market, his utility will be u welfare(B,168) = 168B. Mike will not work, therefore, as long as u welfare≥ u work, which requires that B≥ $420.2-12. Explain why a lump sum government transfer can entice some workers to stop working (and entices no one to start working) while the earned income tax credit can entice some people who otherwise would not work to start working (and entices no one to stop working).A lump sum transfer is associated with an income effect but not a substitution effect, because it doesn’t affect the wage rate. Thus, if leisure is a normal good, a lump sum transfer will likely cause workers to work fewer hours (and certainly not cause them to work more hours) while possibly enticing some workers to exit the labor force. On the other hand, the Earned Income Tax Credit raises the effective wage of low-income workers by 20 percent (at least for the poorest workers). Thus, someone who had not been working faces a wage that is 20 percent higher than it otherwise was. This increase may be enough to encourage the person to start working. For example, if a worker’s reservation wage is $6.50 per hour but the only job she can find pays $6.00 per hour, she will not work. Under the earned income tax credit, however, the worker views this same job as paying $7.20 per hour, which exceeds her reservation wage. Furthermore, the EITC cannot encourage a worker to exit the labor force, as the benefits of the EITC are received only by workers.2-13. In 1999, 4,860 TANF recipients were asked how many hours they worked in the previous week. In 2000, 4,392 of these recipients were again subject to the same TANF rules and were again asked their hours of work during the previous week. The remaining 468 individuals were randomly assigned to a “Negative Income Tax” (NIT) experiment which gave out financial incentives for welfare recipients to work and were subject to its rules. Like the other group, they were asked about their hours of work during the previous week. The data from the experiment are contained in the table below.TotalNumber OfRecipients Number ofRecipients Who Worked At Some Time in the SurveyWeek Total Hours Of Work By All Recipients in the Survey Week1999 2000 1999 2000TANF 4,392 1,217 1,568 15,578 20,698NIT 468 131 213 1,6382,535Total 4,860 1,348 1,781 17,21623,233(a) What effect did the NIT experiment have on the employment rate of public assistance recipients? Develop a standard difference-in-differences table to support your answer.EmploymentRate1999 2000 Diff Diff-in-DiffTANF 27.7% 35.7% 8.0%NIT 28.0% 45.5% 17.5% 9.5%The NIT increased the probability of employment by 9.5 percentage points.(b) What effect did the NIT experiment have on the weekly hours worked of public assistance recipients who worked positive hours during the survey week? Develop a standard difference-in-differences table to support your answer.Weekly Hours Worked Per Working Person1999 2000 Diff Diff-in-DiffTANF 12.8 13.2 0.4NIT 12.5 11.9 -0.6 -1.0The NIT decreased weekly hours worked, of those working, by 1 hour.11。
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������ ������������ = ������ Assumption of diminishing returns also implies that the AP will eventually decline.
Profit Maximization
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Objective of the firm is to maximize profits.
(a)
Compare the life cycle path of hours of work between the two workers if Bill receives a one-time, unexpected inheritance at the age of 35. Compare the life cycle path of hours of work between the two workers if Bill had always known he would receive (and, in fact, does receive) a one-time inheritance at the age of 35.
Value of Average Product of Labor (VAPL): the dollar value of output per worker ������������������������ = ������ × ������������������
Suppose p=$2
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18
Employment Decision in the Short-Run
Short-Run Hiring Decision
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Value of Marginal Product of Labor (VMPL): the dollar benefit derived from hiring an additional worker, holding capital constant ������������������������ = ������ × ������������������
Added worker effect Discouraged worker effect
Review Question (#2-9)
7
Consider two workers with identical preferences, Phil and Bill. Both workers have the same life cycle wage path in that they face the same wage at every age, and they know what their future wages will be. Leisure and consumption are both normal goods.12 Nhomakorabea
Marginal product of capital (MPK): the change in output resulting from employing one additional unit of capital, holding constant the quantities of other inputs. Marginal product of labor (MPL): the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs.
The Firm’s Production Function
10
Firm’s production function: describes the technology that the firm uses to produce goods and services.
The firm’s output can be produced by a variety of capital– labor combinations.
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• MP > AP when AP is rising → MP < AP when AP is decreasing • MP and AP intersect when AP peaks.
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The Firm’s Production Function
15
Marginal product of labor (MPL): the change in output resulting from hiring an additional worker, holding constant the quantities of other inputs.
MPL is the slope of the total product curve, holding capital fixed. Law of diminishing returns: eventually, MPL declines
Average product (AP): the amount of output produced by the typical worker
Utility function, indifference curve, budget constraint
Intensive margin: hours of work decision
Change in nonlabor income, wage Income effect, substitution effect
1. 2. 3.
Graph budget line. Find ������������������ and ������������������ . Use tangency condition ������������������ = ������.
Labor Supply
5
Labor Supply of Women
1.
2.
L: number of workers hired × average number of hours worked per person Different types of workers can be aggregated to a single input “labor”
The Firm’s Production Function
Last Week
Labor Supply
2
Employed, Unemployed, Out of Labor Force
Labor Force Participation Rate Employment Rate Unemployment Rate
Labor Supply
3
Labor-leisure model
Extensive margin: whether to work decision
Reservation wage
Labor supply curve
Labor supply elasticity
Review Question (#2-6)
4
Shlley’s preferences for consumption and leisure: ������ ������, ������ = ������ − 200 × ������ − 80
Perfectly competitive firm: a firm that cannot influence prices of output or inputs (p, w, r constant). A perfectly competitive firm maximizes profits by hiring the “right” amount of labor and capital.
q: output L: labor (total hours hired by firm) K: capital ������ = ������(������, ������)
The Firm’s Production Function
11
Two assumptions about L
If VMPL kept rising, the firm would maximize profits by expanding indefinitely. The law of diminishing returns sets limits on the size of the firm.
������������������������������������������ = ������������ – ������������ – ������������
p: price of output, w: wage rate, r: price of capital Total Revenue = ������������ Total Costs = (������������ + ������������)
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Short-Run Hiring Decision
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How many workers should the firm hire?
1. 2.
3.
������������������������ = ������ ������������������������ is declining ������������������������ ≤ ������������������������ The marginal gain from hiring an additional worker equals the cost of that hire. It does not pay to further expand the firm because the value of hiring more workers is falling.