Exercise 1. Production function model {30 points) Consider an economy with a representative household that consists of 500 workers and owns $100 million of capital (E = 500,}? = 100). There is a representative firm with a Cobb-Douglas production function that rents capital and hires labor to produce. Assume that the TFP parameter equals one (A=1), and we have that Y = KII'ZLl/z. Notice that the parameter a: = 1&2 is different than usual. Markets are competitive. 1. (10 points) Solve for the equilibrium. You should get numbers for (Y,K,L,r,w). 2. (10 points) Plot the rental price of capital (Y-axis) against capital per capita (X-axis). And show with an "x\" the point that characterizes the equilibrium. - In this plot rental price (7") and capital p.c. (k) are your variables. 3. (5 points) Calculate the labor share (share of labor income in total income} for this economy. 4. (5 points) Why is that economists use the parameter a = 1/3 as the standard value in their models