Let Kt denote the quantity of capital a country has at the beginning of period t. Also suppose that capital depreciates at a constant rate d, so that dKt of the capital stock wears out during period t. If investment during period t is denoted by It , and the country does not trade with the rest of the world (the current account surplus is always zero), then we can say that the quantity of capital at the beginning of period t + 1 is given by Kt+1 = (1 − d)Kt + It . Suppose at the beginning of year 0 that this country has 80 units of capital. Investment expenditures are 10 units in each of year 0, 1, 2, 3, 4, . . . , 10. The capital stock depreciates by 10% a year.
(a) Calculate the quantity of capital at the beginning of years 0, 1, 2, 3, 4, . . . , 10.
(b) Repeat the above, except assume now the country begins year 0 with 100 units of capital. Explain what happens now, and contrast with before.
(c) What do you think would happen if instead of going from 0 to 10, it went from 0 to a million?