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ECON 4220- Fall 2013 Problem Set 3-Human Capital 1) Suppose the labor supply curve is upward sloping and the labor demand curve is downward sloping.

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ECON 4220- Fall 2013 Problem Set 3-Human Capital 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 reveal that the wage fell while employment rose. Which curve must have shifted and in which direction to produce this e/ect? 2) The market for semiskilled labor can be represented by the following supply and demand curves: E D = 32 ; 000 & 4 ; 000 w and E S = & 8 ; 000 + 6 ; 000 w where E = millions of person hours per year and w = the wage in dollars per hour. a) Calculate the equilibrium price and quantity that would exist under a free market. b) Calculate the total gains (surplus) in this economy 3) Debbie is about to decide which career path to pursue. She has narrowed her options to two alternatives. She can either a biologist or a concert pianist. Debbie lives for two periods. In the &rst, she gets an education. In the second, she works in the labor market. If Debbie becomes a biologist, she will spend $15,000 on education in the &rst period and earn $472,000 in the second period. If she becomes a concert pianist, she will spend $40,000 on education in the &rst period and then earn $500,000 in the second period. a) Suppose Debbie can lend and borrow money at a 5 percent annual rate. Which career will she pursue? What if she can lend and borrow money at a 15 percent rate of interest? Will she choose a di/erent option? Why? b) Suppose musical conservatories raise their tuition so that it now costs Debbie $60,000 to become a concert pianist. What career will Debbie pursue if the discount rate is 5 percent. 4) Suppose the skills acquired in school depreciate over time, perhaps because technological change makes the things learned in school obsolete. What happens to a worker±s optimal amount of schooling if the rate of depreciation increase? 5) Suppose workers di/er in their ability, but have the same discount rate. Is it possible for the more able workers to choose less schooling? 6) Suppose there are two types of persons, high ability and low ability. A particular diploma costs a high ability person $8,000 and costs a low ability person $20,000. Firms wish to use education as a screening device where they 1
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intend to pay $25,000 to workers without a diploma and $ K to those with diploma. In what range must K be to make this an e/ective screening device? 7) Suppose Carl&s wage-schooling locus is given by Years of Schooling Earnings 6 10,000 7 12,800 8 16,000 9 18,500 10 20,350 11 22,000 12 23,100 13 23,900 14 24,000 Derive the marginal rate of return schedule. When will Carl quit school if his discount rate is 4 percent? What if the discount rate is 12 percent? 8) Explain in details using graphs on how di/erences in discount rates between two people lead to di/erences in schooling and earnings (the persons have identical ability). 2
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