Consider a rm that uses both capital [K] and labour [L] to produce a final product {0] that it sells at the market price $5. The firm buys Labour at a cost of $4 per unit and capital at a cost of $10 per unit. The firm is a pricetaker for all prices with the following production function: 0 = 4K'f2L'r'z This production function implies the following: L1}? MPH = 2 I J, K *2 K152 MPL = 2 L192 Suppose also that the firm currently has 16 units of capital {K = 15} in the Short-Run. For C11 - C16. assume that we are operating in the Short-Run: 1. Given the above production function. write down an expression for Labour employed as a function of the quantity.' produced [i.e. L =f[C1l]I. 2. Use the MPL and the wage rate to write down an expression for the Firm's Marginal Cost per unit of output {0} produced as a function of Q. 3. Show that the firm's profitmaximizing quantity {CF} is equal to 160 in the shortrun. 4. What are the rm's variable costs WC] and fixed costs {FCJ at (1*? 5. What are this firm's shortrun profits in this example? 6. What would be the firm's ShortRun profits if it chooses to shut down? Should the firm keep producing in the short-run? HowI do you know? Use the same production function, MPK, MPL, and prices from Problem 1 {0. 1 - 6) for the following 0? - 09. Suppose also that we are now in the LongnRun, and that the firm has decided to still produce the same [1* as in Problem 1. That is, the firm decides to set C1 = 150'; 7. if the firm wants to cost minimize, what must be the ratio of K to L that they employ given the prices in this market? 8. Suppose that the firm wants to produce "' = 160. What is its cost-minimizing choice of K 31 L? 9. What are the firm's profits with this choice of K St L? is this greater than or less than 1your answer to 05? Why is this the case