Problem #1: Estimating the Marginal Return to Schooling Suppose Carl's wage-schooling locus is given by the following schedule: Years of Schooling Real annual earnings 8 $10,000 9 $12,800 10 $16,000 11 $18,500 12 $20,350 13 $22,000 14 $23,100 15 $23,900 16 $24,000 Suppose that the only cost of schooling is the opportunity cost of not working and earning money. Also, assume that Carl's life is infinitely long (this is a good approximation when the time horizon is long).

1. Derive the marginal rate of return schedule. (This is, calculate Carl's internal rate of return to each additional year of schooling).

2. When will Carl quit school if his discount rate is 4 percent? Why?

3. What will Carl's optimal schooling choice be if his discount rate is 12 percent? Why?

4. Suppose the government imposes an income tax of 20 percent. What is the effect of this income tax on Carl's educational attainment? Why?

Problem #2: Schooling Nancy is deciding on an optimal schooling strategy. She currently has zero years of schooling and knows she will live for 60 more years. In any given year she can either choose to add to her current level of schooling or she can work. If she decides to work, she will have an annual salary of S, where S is her current level of schooling (measured in years of schooling). If she decides to go to school, she will not have any income during that year, but her schooling 1 level will increase by 1 year. Schooling is otherwise free. Nancy's discount rate is r = 0. Nancy's objective is to maximize lifetime income.

1. What is Nancy's lifetime income as a function of her level of schooling, S?

2. What is Nancy's lifetime income if she gets no schooling? What is it if she goes to school for all 60 remaining years of her life? In words, describe the âcostâ to Nancy of choosing to attend school for 1 additional year.

3. Determine Nancy's optimal schooling level (hint: you can do this with calculus or by graphing her lifetime income and finding the level of schooling that maximizes that income).

4. During which part of Nancy's remaining life will she get her schooling?

Problem #1: Estimating the Marginal Return to Schooling Suppose Carl's wage-schooling locus is given by the following schedule: Years of Schooling Real annual earnings 8 $10,000 9 $12,800 10 $16,000 11 $18,500 12 $20,350 13 $22,000 14 $23,100 15 $23,900 16 $24,000 Suppose that the only cost of schooling is the opportunity cost of not working and earning money. Also, assume that Carl's life is infinitely long (this is a good approximation when the time horizon is long).

1. Derive the marginal rate of return schedule. (This is, calculate Carl's internal rate of return to each additional year of schooling).

2. When will Carl quit school if his discount rate is 4 percent? Why?

3. What will Carl's optimal schooling choice be if his discount rate is 12 percent? Why?

4. Suppose the government imposes an income tax of 20 percent. What is the effect of this income tax on Carl's educational attainment? Why?

Problem #2: Schooling Nancy is deciding on an optimal schooling strategy. She currently has zero years of schooling and knows she will live for 60 more years. In any given year she can either choose to add to her current level of schooling or she can work. If she decides to work, she will have an annual salary of S, where S is her current level of schooling (measured in years of schooling). If she decides to go to school, she will not have any income during that year, but her schooling 1 level will increase by 1 year. Schooling is otherwise free. Nancy's discount rate is r = 0. Nancy's objective is to maximize lifetime income.

1. What is Nancy's lifetime income as a function of her level of schooling, S?

2. What is Nancy's lifetime income if she gets no schooling? What is it if she goes to school for all 60 remaining years of her life? In words, describe the âcostâ to Nancy of choosing to attend school for 1 additional year.

3. Determine Nancy's optimal schooling level (hint: you can do this with calculus or by graphing her lifetime income and finding the level of schooling that maximizes that income).

4. During which part of Nancy's remaining life will she get her schooling?