## Quantitative Problems

 1. What factors are responsible for the huge swings in college enrollment rates over the past 40 years or so? 2. What factors explain the dearth of elderly students who attend college? 3. A basic tenet of the human capital model is that schooling increases future earnings. What explains the human capital earnings nexus? 4. What is the effect of an increase in the rate of interest on the level of schooling? Why? 5. Douglas is contemplating undertaking a degree in (advanced) flower pressing. The facts are as follows: tuition is s = 60,000; he can earn as a part-time waiter in college; the interest rate is r = 10%; and he anticipates earning w = \$144K after he graduates. If, instead, he does not enroll in college, then he will earn per annum during each period. Is it optimal for him to enroll in the program? What if w increases to \$155K? 6. With considerable protest from students, the British government has recently begun reforming its system of higher education. In particular, it has moved away from providing "free" education toward a system in which students must pay for their tuition and financially support themselves. To accomplish this goal, it has instituted a student loan system, which allows students to borrow at the market rate of interest. Is this a wise policy? Does it necessarily disadvantage students from low-income families? 7. Consider a perfectly competitive economy in which r = i (s*)—the rate of interest equals the net return to human capital investments. What would happen if the government offers subsidized student loans at the rate of interest ? Outline the conditions that must hold in order for government subsidized education to be efficiency enhancing. 8. Suppose that the wage-schooling schedule is and that the rate of interest rate is r. It can be shown that the marginal return to schooling investments is . What condition governs the optimal choice of education, s*? If r = 5% and if , what is the optimal schooling level? 9. Suppose that everything is the same in Question 8, except that the wage depends on innate ability according to . (In which case, the marginal return to schooling is .) If for high-ability workers and for low-ability workers, determine their optimal levels of schooling. What are their earnings? 10. Again suppose that everything is the same as in Question 8 except that there is unemployment. More specifically, Betsy lives in a boom town where she is guaranteed to find work, and Douglas lives in a depressed city where there is a 20% chance he will be unemployed after he finishes his studies. If and r = 5%, how much education will they each undertake? 11. During a recession, there is usually an uptick in college applications. Why might this be the case? How does this square with the unemployment human capital model presented in the text?