In the endogenous growth model, suppose that there are three possible uses of time. Let u denote the fraction of time spent working, s the fraction of time spent neither working nor accumulating human capital (call this unemployment), and 1 – u – s the fraction of time spent accumulating human capital. Assume that z = 1 and b = 4.2. Also assume that the economy begins period 1 with 100 units of human capital.
(a) Suppose that for periods 1, 2, 3, . . . , 10, u = .7 and s = 0.05. Calculate aggregate consumption, output, and the quantity of human capital in each of these periods.
(b) Suppose that, in period 11, u = 0.6 and s = 0.15. Then, in periods 12, 13, 14, . . . , u = 0.7 and s = 0.05. Calculate aggregate consumption, output, and the quantity of human capital in periods 11, 12, 13, . . . , 20.
(c) Suppose alternatively that in period 11, u = 0.6 and s = 0.05. Again, calculate aggregate consumption, output, and the quantity of human capital in periods 11, 12, 13, . . . , 20.
(d) Now suppose that in period 11, u = 0.6 and s = 0.10. Calculate aggregate consumption, output, and the quantity of human capital in periods 11, 12, 13, . . . , 20.
(e) What do you conclude from your results in parts (a)–(d)? Discuss.