Short Question 2: (20 points) Consider the production model studied in Chapter 4. Final output in the economy is pro- duced using capital K and labor L. The production function is: Y = AKl/4L3/4 Assume that the supply of all inputs are exogenous and equal to E and K. Perfectly compet itive rms are price-takers and choose how much capital and labor to demand by maximizing prots. Let H) and 7' denote the wage and rental rate of one unit of labor and capital respec tively. (a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. (5 points) 4 (b) Derive the optimal hiring conditions for labor and capital and show that the wage (rental rate) must equal the marginal product of labor (capital). Explain the intuition for this result. Are there diminishing returns to these inputs in this model? (5 points) (c) Show that the solution for output per capita can be written as y 2 AH\". Observed GDP per capita. is 1.5 in this economy. Capital per person is 4. If fl = 1, What does this model predict for GDP per person? Does this model overpredict or underpredict GDP? Show your working. (5 points) (d) If the model is to explain the observed value of y, What must TFP (A) be equal to? Briey explain Why TFP might vary across countries. (5 points)