4. (9 points) Consider a closed economy without government where the resource constraint is given by Y = C. and production is given by Y = ZVKVN = zK1/2 N1/2 with K = 400. The preferences of the representative consumer are U (C, 1) = In (C) + In (1) . (a) Suppose that z = 10. Show that if the consumer's time endowment is given by h = 6000 hours, the equilibrium quantity of leisure is 2h = 4000 hours. What is the real wage? (b) Suppose that z = 20. Show that the equilibrium quantity of leisure is still sh = 4000 hours. What is the real wage? (c) Comparing parts (a) and (b), what can you infer about the income and substitut tion effects of a productivity increase