1. The following question refers to a model of imperfect monopsonistic wage discrimination against females like the one presented in class. a) Indicate how imperfect monopsonistic wage discrimination between males and females can explain the persistence of male-female wage differentials for equally productive workers while at the same time explain the existence of a mixed work force within the firm.All problems are due in class next week. Be complete and succinct. Feel free to work together, but submit your own answers. 1. Recall that the Law of Demand states that demand curves are always downward-sloping. That is, people want to buy more of some good when its price is lower. a. Why is a firm's short-run demand for labor downward-sloping? b. Is the firm's long-run demand for labor necessarily downward-sloping? Explain, using the substitution and scale effects. 2. Most industrial farms hire migrant workers, so the market for such workers is reasonably taken to be perfectly competitive. Suppose that all farms individually have a short-run elasticity of labor demand of -0.5. In other words, if the wages of migrant workers in a local labor market rose by 10% (say, because many of those workers decided to work at a recently-opened nearby factory), the farms in the area would want to hire 5% fewer workers. Nevertheless, it is true that if the wages of migrant workers rose by 10% everywhere, employment of migrant workers would fall by less than 5 percent in the short run. a. Explain why the reduction in employment would be less than 5 percent in the latter case. (Hint: Read pp. 141-143 of your textbook carefully (pp. 140-142 if you have the old edition).) b. In light of the short-run elasticity of demand for migrant workers, how easy do you think it would be for the industrial farms to replace the workers' efforts by using the existing stock of farm machinery more intensely? c. If the nationwide 10% wage increase were permanent, would the employment of migrant workers fall more in the short run or in the long run? Why? 3. The HRB Corporation is the world's only manufacturer of air filters for Zamboni engines. Last year, HRB charged $20 per filter and sold 1 million of them, and it paid all of its production workers $10 per hour. This year, something happened at HRB headquarters (not announced to the public) that caused HRB to lower its price to $18 per filter. (HRB is still a profit-maximizing company.) This enabled HRB to sell 1.2 million filters. Its workers all continue to earn $10 per hour. a. What is the elasticity of demand for Zamboni air filters? b. How much additional revenue does HRB earn if it sells one more air filter this year? How much additional revenue would HRB have earned if it sold one more air filter last year? c. How much are HRB's employees paid relative to the value they create? (That is, what is the ratio of the wage to the value of the worker's marginal product (price x MP_)?) d. What was the workers' marginal product last year? What is it this year? e. Suppose you are considering only two explanations for the increase in HRB's output: (1) HRB invested in better equipment and kept the same number of workers, or (2) HRB hired more workers to use its existing equipment. Given your observations above, which makes more sense? Why? Problem Set 5: Personnel Economics Economics 415 All problems are due at the next class meeting. Be complete and succinct. Feel free to work together, but submit your own answers. 1. In class we discussed several compensation schemes that employers may use to motivate workers. a. "Pay for performance" schemes may take several forms. One is a piece rate scheme, in which there is an explicit mathematical formula that translates workers' output into pay. (For example, a worker might be paid $5 per unit of out put he or she produces.) A second scheme awards workers a year-end bonus that depends on their annual performance review. Question: All else equal, would Caucasian or African-American workers have a stronger preference for the piece rate relative to the bonus system? Why? b. Women are more likely than men to hold jobs that pay workers a piece rate, but less likely to hold jobs that promise workers raises if they perform well. Why might that be? (Hint: This is not about discrimination.)All problems are due in class next week. Be complete and succinct. Feel free to work together, but submit your own answers. 1. Recall that the Law of Demand states that demand curves are always downward-sloping. That is, people want to buy more of some good when its price is lower. a. Why is a firm's short-run demand for labor downward-sloping? b. Is the firm's long-run demand for labor necessarily downward-sloping? Explain, using the substitution and scale effects. 2. Most industrial farms hire migrant workers, so the market for such workers is reasonably taken to be perfectly competitive. Suppose that all farms individually have a short-run elasticity of labor demand of -0.5. In other words, if the wages of migrant workers in a local labor market rose by 10% (say, because many of those workers decided to work at a recently-opened nearby factory), the farms in the area would want to hire 5% fewer workers. Nevertheless, it is true that if the wages of migrant workers rose by 10% everywhere, employment of migrant workers would fall by less than 5 percent in the short run. a. Explain why the reduction in employment would be less than 5 percent in the latter case. (Hint: Read pp. 141-143 of your textbook carefully (pp. 140-142 if you have the old edition).) b. In light of the short-run elasticity of demand for migrant workers, how easy do you think it would be for the industrial farms to replace the workers' efforts by using the existing stock of farm machinery more intensely? c. If the nationwide 10% wage increase were permanent, would the employment of migrant workers fall more in the short run or in the long run? Why? 3. The HRB Corporation is the world's only manufacturer of air filters for Zamboni engines. Last year, HRB charged $20 per filter and sold 1 million of them, and it paid all of its production workers $10 per hour. This year, something happened at HRB headquarters (not announced to the public) that caused HRB to lower its price to $18 per filter. (HRB is still a profit-maximizing company.) This enabled HRB to sell 1.2 million filters. Its workers all continue to earn $10 per hour. a. What is the elasticity of demand for Zamboni air filters? b. How much additional revenue does HRB earn if it sells one more air filter this year? How much additional revenue would HRB have earned if it sold one more air filter last year? c. How much are HRB's employees paid relative to the value they create? (That is, what is the ratio of the wage to the value of the worker's marginal product (price x MP_)?) d. What was the workers' marginal product last year? What is it this year? e. Suppose you are considering only two explanations for the increase in HRB's output: (1) HRB invested in better equipment and kept the same number of workers, or (2) HRB hired more workers to use its existing equipment. Given your observations above, which makes more sense? Why? Problem Set 5: Personnel Economics Economics 415 All problems are due at the next class meeting. Be complete and succinct. Feel free to work together, but submit your own answers. 1. In class we discussed several compensation schemes that employers may use to motivate workers. a. "Pay for performance" schemes may take several forms. One is a piece rate scheme, in which there is an explicit mathematical formula that translates workers' output into pay. (For example, a worker might be paid $5 per unit of out put he or she produces.) A second scheme awards workers a year-end bonus that depends on their annual performance review. Question: All else equal, would Caucasian or African-American workers have a stronger preference for the piece rate relative to the bonus system? Why? b. Women are more likely than men to hold jobs that pay workers a piece rate, but less likely to hold jobs that promise workers raises if they perform well. Why might that be? (Hint: This is not about discrimination.)c) One of the conditions necessary for monopsonistic wage discrimination against women as a group is that their labour supply to the firm must be more inelastic than that of males, at their respective wages and employment. Would you expect this to be the case -- why or why not?3. A researcher estimates the following wage equation for underwater construction workers: W = 10 + 5D Where W=the wage in dollars per hour and D=the depth underwater at which workers work, in meters. a) Based on this information, draw the offer curve and possible indifference curves for two workers, A and B: A works at a depth of 3 meters and B works at 5 meters. wage UB UA (5, 12.50) $10 (3,11.50) offer curve depthProblem 1 (40p) (Well-behaved preferences) Lila spends her income on two goods: food, I1, and clothing. I2. a) The price food is pi= 2 and one piece of clothing costs p2= 4 . Show geometrically Lila's budget set. if her income is m = 30. Find the relative price food in terms of clothing (one number)? Where can the relative price be seen in the graph of a budget set? (one sentence) b) Lila's preferences are represented by utility function U(s,1) = (n) (1). We know that her preferences can be alternatively represented by function Explain the idea behind "monotonic transformation" (one sentence) and derive function V from U. ) Assuming utility function V(I,,) = 2 Inc1+ Inc2 -Find marginal rate of substitution (MRS) for all bundles (derive formula). For bundle (8, 8) find the value of MRS (one number). Give economic interpretation of MRS (one sentence). Which of the goods is more valuable given consumption (8,8)? -Write down two secrets of happiness that determine optimal choice given parameters pi, p, and m. Explain economic intuition behind the two conditions (two sentences for each). -Using secrets of happiness derive optimal consumption 21 ,12 , given values of pi= 2, py= 4 and m = 30. Is the solution corner or interior (chose one) d) (Harder) Using magic formulas for Cobb-Douglass preferences argue that the two commodities are 1) ordinary; 2) normal; and 3) neither gross complements nor gross substitutes (one sentence for each property). Problem 2 (15p) (Perfect substitutes) You are planing a budget for the state of Wisconsin. The two major budget positions include education, In and health care, 12. Your preferences over the two are represented by function a) Find marginal rate of substitution (give number). bj Find optimal consumption of ri and 12. given prices pi= 2 and p2= 1 and available funds m = 50 (two numbers). ") Is solution interior? (yes-no answer). Is marginal utility of a dollar equalized? (give two numbers and yes-no answer) Problem 3 (20p) (Intertemporal choice) Zoe is a professional Olympic skier. Her income when "young" is high (m,= 30) but her future (period two) is not so bright (my= 20) a) Depict Zoe's budget set, assuming that she can borrow and save at the interest rate r = 100%. Partition her budget set into three regions: the area that involves saving, borrowing and none of the two. b) Find PV and FV of Zoe's lifetime income (two numbers) and show the two values in the graph. Interpret economically PV . c) Zoe's utility function is U (C, . C,) =InC+1 In C2 where discount rate is o = 2. Using magic formulas, find optimal consumption plan (C.C,) (two numbers) and the corresponding level of sav- ings/borrowing. S d) Is Zoe tilting her consumption over time? (yes-no answer). Problem 4 (25p) (Short questions) a) Given utility function U (C, R) = min (20, R), daily endowment of time 24h, price and wage pe= w = 2, find optimal choice of C, relaxation time R and labor supply L. (three numbers, use secrets of happiness for perfect complements). b) Find optimal choice given quasilinear preferences U (21, 12) = 21+100 In12, prices pi = $8, p2= $1 and income m = $60. Is your solution corner or interior? c) Assume Interest rate 7 = 10%. Choose one of the two: a consol (a type of British government bond) that pays annually $1000 forever, starting next year or cash $12. 000 now (compare PV). I) Your annual income when working (age 21-60) is $60,000 and then you are are going to live for the next 30 years. Write down equation that determines constant (maximal) level of consumption during your lifetime. Assume annual interest rate 7 = 2. Bonus question (Just for fun) a] Derive magic formulas for perfect complements U (21, 2, )= min (ar, . br, ) that give optimal choices I1, Ig as a function of a. b. p , py, m. b) Provide economic intuition for the magic formula for perfect complements (economic interpretation for the numerator and denominator).Problem 1 (40p) (Well-behaved preferences) Lila spends her income on two goods: food, I1, and clothing. I2. a) The price food is pi= 2 and one piece of clothing costs p2= 4 . Show geometrically Lila's budget set. if her income is m = 30. Find the relative price food in terms of clothing (one number)? Where can the relative price be seen in the graph of a budget set? (one sentence) b) Lila's preferences are represented by utility function U(s,1) = (n) (1). We know that her preferences can be alternatively represented by function Explain the idea behind "monotonic transformation" (one sentence) and derive function V from U. ) Assuming utility function V(I,,) = 2 Inc1+ Inc2 -Find marginal rate of substitution (MRS) for all bundles (derive formula). For bundle (8, 8) find the value of MRS (one number). Give economic interpretation of MRS (one sentence). Which of the goods is more valuable given consumption (8,8)? -Write down two secrets of happiness that determine optimal choice given parameters pi, p, and m. Explain economic intuition behind the two conditions (two sentences for each). -Using secrets of happiness derive optimal consumption 21 ,12 , given values of pi= 2, py= 4 and m = 30. Is the solution corner or interior (chose one) d) (Harder) Using magic formulas for Cobb-Douglass preferences argue that the two commodities are 1) ordinary; 2) normal; and 3) neither gross complements nor gross substitutes (one sentence for each property). Problem 2 (15p) (Perfect substitutes) You are planing a budget for the state of Wisconsin. The two major budget positions include education, In and health care, 12. Your preferences over the two are represented by function a) Find marginal rate of substitution (give number). bj Find optimal consumption of ri and 12. given prices pi= 2 and p2= 1 and available funds m = 50 (two numbers). ") Is solution interior? (yes-no answer). Is marginal utility of a dollar equalized? (give two numbers and yes-no answer) Problem 3 (20p) (Intertemporal choice) Zoe is a professional Olympic skier. Her income when "young" is high (m,= 30) but her future (period two) is not so bright (my= 20) a) Depict Zoe's budget set, assuming that she can borrow and save at the interest rate r = 100%. Partition her budget set into three regions: the area that involves saving, borrowing and none of the two. b) Find PV and FV of Zoe's lifetime income (two numbers) and show the two values in the graph. Interpret economically PV . c) Zoe's utility function is U (C, . C,) =InC+1 In C2 where discount rate is o = 2. Using magic formulas, find optimal consumption plan (C.C,) (two numbers) and the corresponding level of sav- ings/borrowing. S d) Is Zoe tilting her consumption over time? (yes-no answer). Problem 4 (25p) (Short questions) a) Given utility function U (C, R) = min (20, R), daily endowment of time 24h, price and wage pe= w = 2, find optimal choice of C, relaxation time R and labor supply L. (three numbers, use secrets of happiness for perfect complements). b) Find optimal choice given quasilinear preferences U (21, 12) = 21+100 In12, prices pi = $8, p2= $1 and income m = $60. Is your solution corner or interior? c) Assume Interest rate 7 = 10%. Choose one of the two: a consol (a type of British government bond) that pays annually $1000 forever, starting next year or cash $12. 000 now (compare PV). I) Your annual income when working (age 21-60) is $60,000 and then you are are going to live for the next 30 years. Write down equation that determines constant (maximal) level of consumption during your lifetime. Assume annual interest rate 7 = 2. Bonus question (Just for fun) a] Derive magic formulas for perfect complements U (21, 2, )= min (ar, . br, ) that give optimal choices I1, Ig as a function of a. b. p , py, m. b) Provide economic intuition for the magic formula for perfect complements (economic interpretation for the numerator and denominator)