Capital & Wealth

1. Capital & Wealth Discussion of past-paper • 1987 C10

2. A student entering the University of Hong Kong will have no income for three years, but after graduation his income will rise at a fairly rapid rate for years thereafter. As an alternative, this student could go out to work immediately after matriculation, and his initial income will be considerably higher than if the enters the University, although his income through time will increase at a slower rate. Assume wealth maximization is the only objective of the student.

3. (a) If the total income in life of getting a university education is greater than that of not entering the university, will the student always choose the university education? Explain. (8 marks) (b) If the total income in life is higher without the university education, will the student ever choose to enter the university? Explain. (8 marks) (c) Will your answers in (a) and (b) be different if the university makes available low‑interest loans to students? Explain. (8 marks)

4. Suggested Approach: A general situation Income stream ($) A university graduate A matriculant U M Time Present 3-year later Retirement age

5. (a) If the total income in life of getting a university education is greater than that of not entering the university, will the student always choose the university education? Explain. (8 marks)

6. Suggested Approach: (a) Income stream ($) A university graduate U A matriculant M Time Present 3-year later Retirement age

7. (a) If the total income in life of getting a university education is greater than that of not entering the university, will the student always choose the university education? Explain. (8 marks) • Not always choose the university education • If the interest rate is high enough, the discounted present value (i.e. wealth) of not entering university will be higher because the initial income is higher during the early years.

8. (b) If the total income in life is higher without the university education, will the student ever choose to enter the university? Explain. (8 marks)

9. Suggested Approach: (b) Income stream ($) A university graduate U A matriculant M Time Present 3-year later Retirement age

10. (b) If the total income in life is higher without the university education, will the student ever choose to enter the university? Explain. (8 marks) • No • If the interest rate is positive, the wealth of not entering the university in this case is always higher.

11. (c) Will your answers in (a) and (b) be different if the university makes available low‑interest loans to students? Explain. (8 marks)

12. Suggested Approach: (c) Income stream ($) A university graduate A matriculant U M Time Present 3-year later Retirement age Interest income

13. Suggested Approach: (c) Income stream ($) A university graduate U A matriculant M Time Present 3-year later Retirement age

14. (c) Will your answers in (a) and (b) be different if the university makes available low‑interest loans to students? Explain. (8 marks) • In (a), a young person who otherwise would choose not to enter the university may now be encouraged by the low-interest loan to attend the university. • Answer in (b) is not changed, unless the student can borrow the low-interest loan and lend it out at a big gain.