chapter: Solution Factor Markets and the Distribution of Income

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1 Factor Markets and the Distribution of Income chapter: In 2010, national income in the United States was $11,722.6 billion. In the same year, 139 million workers were employed, at an average wage of $57,348 per worker per year. a. How much compensation of employees was paid in the United States in 2010? b. Analyze the factor distribution of income. What percentage of national income was received in the form of compensation to employees in 2010? c. Suppose that a huge wave of corpo downsizing leads many terminated employees to open their own businesses. What is the effect on the factor distribution of income? d. Suppose the supply of labor rises due to an increase in the retirement age. What happens to the percentage of national income received in the form of compensation of employees? 1. a. Since 139 million workers were employed at an average yearly wage of $57,348, the total amount of compensation of employees was 139 million $57,348 = $7,791.4 billion. b. Of a total of $11,722.6 billion, the amount received by workers was $7,791.4 billion. In percentage terms, this is ($7,791.4 billion/$11,186.9 billion) 100 = 68.0%. c. The effect of this change is to diminish the share of income going to compensate employees and increase the share going to proprietors income. d. As the supply of labor increases, the equilibrium wage falls, but the equilibrium number of workers employed rises. So it is not clear whether more or less of national income is paid to workers in the form of compensation. 2. Marty s Frozen Yogurt has the production function per day shown in the accompanying table. The equilibrium wage for a worker is $80 per day. Each cup of frozen yogurt sells for $2. (workers) Quantity of frozen yogurt (cups) S-261 KrugWellsECPS3e_Micro_CH19.indd S-261

2 S-262 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker. b. How many workers should Marty employ? 2. a. The accompanying table shows the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL) of each worker. Remember that VMPL = P MPL. Here that means that VMPL = $2 MPL. Quantity of frozen MPL VMPL (workers) yogurt (cups) (cups per worker) (per worker) $ b. Marty should employ 3 workers. The value of the marginal product of the third worker ($140) is above the wage of $80: Marty should hire the third worker. But the fourth worker s value of the marginal product is only $60. This is less than Marty would have to pay this worker, so Marty should not hire a fourth worker. 3. Patty s Pizza Parlor has the production function per hour shown in the accompanying table. The hourly wage for each worker is $10. Each pizza sells for $2. (workers) Quantity of pizza a. Calculate the marginal product of labor for each worker and the value of the marginal product of labor per worker. b. Draw the value of the marginal product of labor curve. Use your diagram to determine how many workers Patty should employ. c. Now the price of pizza increases to $4. Calculate the value of the marginal product of labor per worker, and draw the new value of the marginal product of labor curve in your diagram. Use your diagram to determine how many workers Patty should employ now. KrugWellsECPS3e_Micro_CH19.indd S-262

3 3. a. The accompanying table shows the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL 1 ). VMPL 1 (per worker) VMPL 2 (per worker) Number of Quantity of MPL (price of (price of workers pizza (pizzas per worker) pizza = $2) pizza = $4) CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME S $18 $ b. The accompanying diagram shows the value of the marginal product of labor curve (VMPL 1 ). The value of the marginal product of labor equals the wage at 2 workers. So Patty should employ 2 workers. $ VMPL 2 VMPL (workers) c. The table shows the new value of the marginal product of labor (VMPL 2 ). The value of the marginal product of labor curve is labeled VMPL 2 in the diagram. The new value of the marginal product of labor equals the wage at 4 workers. So Patty should employ 4 workers. 4. The production function for Patty s Pizza Parlor is given in the table in Problem 3. The price of pizza is $2, but the hourly wage rises from $10 to $15. Use a diagram to determine how Patty s demand for workers responds as a result of this wage increase. KrugWellsECPS3e_Micro_CH19.indd S-263

4 S-264 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME 4. The accompanying diagram shows the value of the marginal product of labor curve and the wage s of $10 and $15. As the wage increases from $10 to $15, Patty s demand for workers decreases from 2 workers to 1 worker. So, as the wage increases, Patty should hire fewer workers. New wage Old wage $ VMPL (workers) 5. Patty s Pizza Parlor initially had the production function given in the table in Problem 3. A worker s hourly wage was $10, and pizza sold for $2. Now Patty buys a new high-tech pizza oven that allows her workers to become twice as productive as before. That is, the first worker now produces 18 pizzas per hour instead of 9, and so on. a. Calculate the new marginal product of labor and the new value of the marginal product of labor. b. Use a diagram to determine how Patty s hiring decision responds to this increase in the productivity of her workforce. 5. a. The accompanying table shows the new production function for Patty s Pizza Parlor, the new marginal product of labor (MPL 3 ), and the new value of the marginal product of labor (VMPL 3 ). MPL 3 (pizzas VMPL 3 (per (workers) Quantity of pizza per worker) worker) $ KrugWellsECPS3e_Micro_CH19.indd S-264

5 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME S-265 b. The accompanying diagram shows the original value of the marginal product of labor curve from Problem 3 (VMPL 1 ) and the new value of the marginal product of labor curve (VMPL 3 ). The value of the marginal product of labor now equals the wage at 4 workers. So Patty should employ 4 workers. As the value of the marginal product of labor increases in this case as a result of a technological innovation (the new pizza oven) Patty should hire more workers. $ VMPL 3 VMPL (workers) 6. Jameel runs a driver education school. The more driving instructors he hires, the more driving lessons he can sell. But because he owns a limited number of training automobiles, each additional driving instructor adds less to Jameel s output of driving lessons. The accompanying table shows Jameel s production function per day. Each driving lesson can be sold at $35 per hour. (driving instructors) Quantity of driving lessons (hours) Determine Jameel s labor demand schedule (his demand schedule for driving instructors) for each of the following daily wage s for driving instructors: $160, $180, $200, $220, $240, and $260. KrugWellsECPS3e_Micro_CH19.indd S-265

6 S-266 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME 6. The accompanying table calculates the marginal product of labor (MPL) and the value of the marginal product of labor (VMPL). MPL VMPL (hours per (per (driving Quantity of driving driving driving instructors) lessons (hours) instructor) instructor) $ If the daily wage of driving instructors is $160, Jameel should hire 4 instructors: the fourth instructor has a value of the marginal product of $175, which is greater than the wage ; but the fifth instructor would have a value of the marginal product of only $140, which is less than the wage. By similar reasoning for the other wage s, Jameel s demand schedule for labor is as shown in the accompanying table. Daily wage demanded (driving instructors) $ Dale and Dana work at a self-service gas station and convenience store. Dale opens up every day, and Dana arrives later to help stock the store. They are both paid the current market wage of $9.50 per hour. But Dale feels he should be paid much more because the revenue gened from the gas pumps he turns on every morning is much higher than the revenue gened by the items that Dana stocks. Assess this argument. 7. Dale s argument is incorrect because the owner of the business will hire workers until the hourly value of the marginal product of the last person hired equals $9.50. This implies that all other workers hired will have an hourly value of the marginal product higher than $9.50 but will be paid a wage of $9.50. Or to put it a slightly different way, any worker who opens the station, regardless of whether it is Dale or Dana, will have a higher value of the marginal product than the second person to report for work. 8. A New York Times article published in 2007 observed that the wage of farmworkers in Mexico was $11 an hour but the wage of immigrant Mexican farmworkers in California was $9 an hour. KrugWellsECPS3e_Micro_CH19.indd S-266

7 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME S-267 a. Assume that the output sells for the same price in the two countries. Does this imply that the marginal product of labor of farmworkers is higher in Mexico or in California? Explain your answer, and illust with a diagram that shows the demand and supply curves for labor in the respective markets. In your diagram, assume that the quantity supplied of labor for any given wage is the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California. b. Now suppose that farmwork in Mexico is more arduous and more dangerous than farmwork in California. As a result, the quantity supplied of labor for any given wage is not the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California. How does this change your answer to part a? What concept best accounts for the difference between wage s for Mexican farmworkers and immigrant Mexican farmworkers in California? c. Illust your answer to part b with a diagram. In this diagram, assume that the quantity of labor demanded for any given wage is the same for Mexican employers as it is for Californian employers. 8. a. We know that farmworkers are employed up to the point where the value of the marginal product of labor is just equal to the wage: VMPL = P MPL = W. In Mexico, this means that P MPL Mexico = $11 and in California P MPL California = $9. Since the price, P, is the same in Mexico and in California, this means that the marginal product of labor in Mexico has to be higher than in California. Assuming that the quantity supplied for any given wage is the same for Mexican farmworkers as it is for immigrant Mexican farmworkers in California implies that the two groups have equivalent supply curves. Therefore, one supply curve can be drawn to illust the supply responses of both types of workers. The different wage s received by the two groups of workers is a result of differences in the demand curves for labor. Because Mexican farmworkers have a higher marginal product of labor, the demand curve for their labor lies above and to the right of the demand curve for their peers in California, as shown in the accompanying diagram. Supply $ Higher MPL of Mexican farmworkers in Mexico Demand for Mexican farmworkers in Mexico Demand for immigrant Mexican farmworkers in California b. Because farmwork in Mexico is more arduous and dangerous than farmwork in California, we can no longer infer that the higher wages paid to Mexican farmworkers is evidence that they have a higher marginal product of labor than their peers in California. Rather, the difference in wages is a compensating differential that compensates Mexican farmworkers for the greater difficulty and danger they face. KrugWellsECPS3e_Micro_CH19.indd S-267

8 S-268 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME c. Assuming that the quantity of labor demanded for any given wage is the same for the two groups means that one demand curve can be drawn to represent employers demand responses in both markets. The compensating differential that Mexican farmworkers demand relative to their peers in California is illustd by their supply curve of labor in the accompanying diagram, which lies above and to the left of the supply curve of their Californian peers. $11 9 Labor supply of Mexican farmworkers in Mexico Labor supply of immigrant Mexican farmworkers in California Compensating differential Demand 0 9. Kendra is the owner of Wholesome Farms, a commercial dairy. Kendra employs labor, land, and capital. In her operations, Kendra can substitute between the amount of labor she employs and the amount of capital she employs. That is, to produce the same quantity of output she can use more labor and less land; similarly, to produce the same quantity of output she can use less labor and more land. However, if she uses more land, she must use more of both labor and capital; if she uses less land, she can use less of both labor and capital. Let w* represent the annual cost of labor in the market, let r L * represent the annual cost of a unit of land in the market, and let r K * represent the annual cost of a unit of capital in the market. a. Suppose that Kendra can maximize her profits by employing less labor and more capital than she is currently using but the same amount of land. What three conditions must now hold for Kendra s operations (involving her value of the marginal product of labor, land, and capital) for this to be true? b. Kendra believes that she can increase her profits by renting and using more land. What three conditions must hold (involving her value of the marginal product of labor, land, and capital) for this to be true? 9. a. The three conditions are: (1) Kendra s current value of the marginal product of land = r*. L Only if this is satisfied should Kendra leave the amount of land she employs unchanged. (2) Kendra s current value of the marginal product of labor < w*. Only if this is satisfied should Kendra reduce the amount of labor she employs. (3) Kendra s current value of the marginal product of capital > r*. K Only if this is satisfied should Kendra increase the amount of capital she uses. b. The three conditions are: (1) Kendra s current value of the marginal product of land > r L *. Only if this is satisfied should Kendra increase the amount of land she employs. (2) Kendra s current value of the marginal product of labor > w*. Kendra must hire more labor if she employs more land. Thus, only if this condition is satisfied should Kendra increase the amount of labor she employs along with the amount of land. (3) Kendra s current value of the marginal product of capital > r K *. Kendra must use more capital if she employs more land. Thus, only if this condition is satisfied should Kendra increase the amount of capital she uses along with the amount of land. KrugWellsECPS3e_Micro_CH19.indd S-268

9 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME S For each of the following situations in which similar workers are paid different wages, give the most likely explanation for these wage differences. a. Test pilots for new jet aircraft earn higher wages than airline pilots. b. College graduates usually have higher earnings in their first year on the job than workers without college degrees have in their first year on the job. c. Full professors command higher salaries than assistant professors for teaching the same class. d. Unionized workers are generally better paid than non-unionized workers. 10. a. This is most likely because being a test pilot for a new aircraft design is more dangerous than flying a commercial airliner. So the most likely explanation is that of compensating differentials. b. This is probably due to differences in human capital. More education gives a worker greater amounts of human capital. So more education usually translates into greater earnings. c. This is also probably due to differences in human capital. Because full professors have been teaching longer than assistant professors, their greater on-the-job experience has given them greater human capital. And greater human capital translates into higher salaries. d. Unions exercise considerable bargaining power in negotiating wages for their members. This results in higher wages and therefore wage differences that are not explained by marginal productivity theory. 11. Research consistently finds that despite nondiscrimination policies, African-American workers on average receive lower wages than White workers do. What are the possible reasons for this? Are these reasons consistent with marginal productivity theory? 11. One possible reason is that this is the result of discrimination in the workplace. And, as you know, discrimination is not consistent with marginal productivity theory. But another possible reason for this income disparity is that it may be a result of past discrimination, which is consistent with marginal productivity theory. In the past, because of overt discrimination, the educational opportunities for African-American children were severely limited. These children are today s workers, and if their educational attainment is lower, they embody less human capital and are therefore paid a lower wage. So the current income disparity may imply past discrimination but be consistent with marginal productivity theory. But even if this is true, keep in mind that marginal productivity theory does not give moral justification to the current distribution of income. 12. Greta is an enthusiastic amateur gardener and spends a lot of her free time working in her yard. She also has a demanding and well-paid job as a freelance advertising consultant. Because the advertising business is going through a difficult time, the hourly consulting fee Greta can charge falls. Greta decides to spend more time gardening and less time consulting. Explain her decision in terms of income and substitution effects. 12. As Greta s hourly consulting fee falls, the opportunity cost of leisure time spent working in her yard also falls. So the substitution effect will push Greta toward spending more time gardening and less time consulting. However, the income effect of a fall in the consulting fee makes Greta poorer and since leisure is a normal good less inclined to consume leisure. That is, the income effect will push Greta toward working more. If, overall, Greta decides to work less, the substitution effect must have dominated the income effect. KrugWellsECPS3e_Micro_CH19.indd S-269

10 S-270 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME 13. Wendy works at a fast-food restaurant. When her wage was $5 per hour, she worked 30 hours per week. When her wage rose to $6 per hour, she decided to work 40 hours. But when her wage rose further to $7, she decided to work only 35 hours. a. Draw Wendy s individual labor supply curve. b. Is Wendy s behavior irrational, or can you find a rational explanation? Explain your answer. 13. a. Wendy s individual labor supply curve has the backward-bending shape shown in the accompanying diagram. $7 Individual labor supply curve (hours) b. Wendy s behavior has a perfectly rational explanation. As the wage increases, the opportunity cost of leisure increases. So the substitution effect says to consume less leisure and work more. At the same time, an increase in the wage makes Wendy richer in a real sense. And since leisure is a normal good, the income effect says to consume more leisure and work less. Income and substitution effects work in opposite directions. As Wendy s wage rises from $5 to $6, the substitution effect dominates the income effect. As her wage rises further to $7, the income effect dominates the substitution effect. 14. You are the governor s economic policy adviser. The governor wants to put in place policies that encourage employed people to work more hours at their jobs and that encourage unemployed people to find and take jobs. Assess each of the following policies in terms of reaching that goal. Explain your reasoning in terms of income and substitution effects, and indicate when the impact of the policy may be ambiguous. a. The state income tax is lowered, which has the effect of increasing workers after-tax wage. b. The state income tax is increased, which has the effect of decreasing workers after-tax wage. c. The state property tax is increased, which reduces workers after-tax income. 14. a. The effect of this policy on the incentive to work is ambiguous. A lower income tax has the effect of raising workers wages in a real sense. The substitution effect will induce people to work more, but the income effect will induce them to work less. So this is an effective policy only if the substitution effect is stronger than the income effect. b. The effect of this policy on the incentive to work is also ambiguous. A higher income tax has the effect of reducing workers wages in a real sense. The substitution effect will induce people to work less, but the income effect will induce them to work more. So this is an effective policy only if the income effect is stronger than the substitution effect. KrugWellsECPS3e_Micro_CH19.indd S-270

11 CHAPTER 19 FACTOR MARKETS AND THE DISTRIBUTION OF INCOME S-271 c. This policy will unambiguously encourage people to work more. The increase in the property tax makes people feel poorer, and as a result, they will consume less of all normal goods. Since leisure is a normal good, people will consume less leisure and work more. This policy influences how much labor is supplied only through the income effect. There is no substitution effect on the quantity of labor supplied in this case since the opportunity cost of leisure has not changed. 15. A study by economists at the Federal Reserve Bank of Boston found that between 1965 and 2003 the average American s leisure time increased by between 4 and 8 hours a week. The study claims that this increase is primarily driven by a rise in wage s. a. Use the income and substitution effects to describe the labor supply for the average American. Which effect dominates? b. The study also finds an increase in female labor force participation more women are choosing to hold jobs rather than exclusively perform household tasks. For the average woman who has newly entered the labor force, which effect dominates? c. Draw typical individual labor supply curves that illust your answers to part a and part b above. 15. a. As wage s rise, the substitution effect says to consume less leisure, because leisure has just become relatively more expensive. However, the income effect says to consume more leisure, because a wage increase makes consumers richer and leisure is a normal good. Since the overall effect has been for leisure time to increase as a result of the wage increase, the income effect must have been stronger than the substitution effect. b. As wage s rise, income and substitution effects work in the same ways as in part a. However, since female labor force participation has increased, the substitution effect must have been stronger for new female workers. (Why is this? For individuals who are not participating in the labor market, an increase in the wage has only a substitution effect, leading them to consume less leisure since its opportunity cost has risen that is, leading them to work more. Since they are not earning income from work, an increase in the wage has no income effect.) c. The accompanying diagram shows a typical labor supply curve for all workers in panel (a) and for new female workers in panel (b). (a) All Workers (b) New Female Workers KrugWellsECPS3e_Micro_CH19.indd S-271

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Unit 7 Problem Set. b. Suppose that a huge wave of corporate downsizing leads many terminated employees to open their own businesses.

Unit 7 Problem Set. b. Suppose that a huge wave of corporate downsizing leads many terminated employees to open their own businesses. Goldwasser AP Microeconomics NAME Unit 7 Problem Set 1. In 2007, national income in the United States was $11,186.9 billion. In the same year, 137 million workers were employed, at an average wage of $57,526