Problem 3. (50 points) Consider an economy I with a representative household that consists of 1000 workers and owns $100 million of capital (I. = 1000,17? = 100). There is a representative rm with a Cobb- Douglas production function that rents capital and hires labor to produce. Assume that the TFP parameter equals one (A = l), we have Y = K1/3L2/3. Markets are competitive. 1. Dene an equilibrium in this economy. Follow class notes. (3 points) 2. Solve for the equilibrium. You should get numbers for (Y, K, L, 7', w). (5 points) 3. Graph by hand the followings: - Graph 1: Plot output per capita (Y-axis) against capital per capita (X-axis). And show with a symbol X the point that characterizes the equilibrium. (6 points) In this plot output per-capita (y) and capital per capita (k) are your variables, while all other are constant and equal to their assumed values. 0 Graph 2: Plot wages (Yaxis) against capital per capita (Xaxis). And show with a symbol X the point that characterizes the equilibrium. (6 points) In this plot wages (w) and capital per capita (k) are your variables. Consider another economy II with labor equal L=500 and capital equal to K=20. Assume that this economy also has a TFP parameter that equals one (A21). First, assume each of these economies are in autarky, so capital cannot ow across countries. 4. Show in your previous graphswith a circlethe equilibrium of economy II (12 points) Assume now that these economies open boundaries. So, capital can freely move across them. 5. Describe the new equilibrium. What are the new wages and rental rate of capital in each country? (Assume that there are no transaction costs of capital, so rental rates of capital should be the same; otherwise there would be an arbitrage opportunity.) (12 points) 6. In your previous two graphs, show with a square the new equilibrium with open boundaries. (6 points)