Problem Set 4: Human Capital 1. Ella is about to choose a career path. She has narrowed her options to two alternatives. She can either become a marine biologist or a concert pianist. Ella lives two periods. In the rst, she gets an education. In the second, she works in the labour market. If Ella becomes a marine biologist, she will spend 15,000 on education in the rst period and earn 439,000 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 Ella can lend and borrow money at a 5 percent rate of interest between the two periods. Which career will she pursue? What if she can lend and borrow money at a 15 percent rate of interest? Will she choose a different option? Why? (b) Suppose musical conservatories raise their tuition so that it now costs Ella 60,000 to become a concert pianist. What career will Ella pursue if the interest rate is 5 percent? 2. Peter lives for three periods. He is currently considering three alternative education-work options. He can start working immediately, earning 100,000 in period 1, 110,000 in period 2 {as his work experience leads to higher productivity). and 690,000 in period 3 {as his skills become obsolete and physical abilities deteriorate). Alternatively, he can spend 50,000 to attend college in period 1 and then earn 180,000 in periods 2 and 3. Finally, he can receive a doctorate degree in period 2 after completing his college education in period 1. This last option will cost him nothing when he is attending graduate school in the second period as his expenses on tuition and books will be covered by a research assistantship. After receiving his doctorate, he will become a professor in a business school and earn 400,000 in period 3. Peter's discount rate is 20 percent per period. What education path maximizes Peter's net present value of his lifetime earnings? Jane has three years of college, Pam has two, and Mary has one. Jane earns 21 per hour, Pam earns 19, and Mary earns 16. The difference in educational attainment is due completely to different discount rates. How much can the available information reveal about each woman's discount rate? 4. Suppose Carl's wage-schooling locus is given by Years of Earnings Schooling 9 13,500 10 20,350 1 1 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 9 percent? 5. 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. Finns wish to use education as a screening device where they intend to pay 25,000 to workers without a diploma and K to those with a diploma. In what range must K be to make this an effective screening device? 6. Jill is planning the timing of her on-the-job training investments over the life cycle. What happens to Jill's OJT investments at every age if (a) The market-detennined rental rate to an efciency unit falls? (b) Jill's discount rate increases? (c) The government passes legislation delaying the retirement age until age 70. (d) Technological progress is such that much of the OJT acquired at any given age becomes obsolete within the next 10 years. 7. An economist nds the following results: ln(l')=9.90+0.07S+0.O3E+0.04A0.0053=1=E+0.008A*E where {My} is the log wage, S are the years of schooling, E are the years of experience, A is ability and So? and Add? are the interactive terms of education and ability with experience respectively. Are the above results compatible with the human capital theory or with the signalling theory