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 = AK1/5 14/5 Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet- itive firms are price-takers and choose how much capital and labor to demand by maximizing profits. Let w and r denote the wage and rental rate of one unit of labor and capital respec- tively. (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model? (5 points)