Consider a firm that uses both capital [K1 and labour {L} to produce a final product [OJ that it sells at the market price $5. The firm buvs 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: Q = 4K1/2L1/2 This production function implies the following: Ll/z MPK = 2 Klfz Klfz MPL = 2 1.1/2 Suppose also that the firm currently has 16 units of capital [K = 16} in the ShortRun. For Q1 Q6, assume that we are operating in the ShortRun: 1. Given the above production function, write down an expression for Labour employed as a function of the quantityr produced {i.e. L = f{Q}). [1 point] 2. Use the MPL and the wage rate to write down an expression for the Firm's Marginal Cost per unit of output {(1} produced as a function of Q. [3 points] 3. Show that the firm's profitmaximizing quantity {03\"} is equal to 160 in the shortrun. [1 point] 4. What are the firm's variable costs {VC} and fixed costs [FCJ at 03*? [2 points] Use the same production function, MPK, MPL, and prices from Problem 1 (Q l 6) for the following C17 Q9. Suppose also that we are now in the LongRun, and that the firm has decided to still produce the same [1* as in Problem 1. That is, the firm decides to set Q = 160. 7. lfthe firm wants to cost minimize, what must be the ratio of K to Lthat they employ given the prices in this market? [3 points] 8. Suppose that the firm wants to produce (1* = 160. What is its costminimizing choice of K & L? [3 points] 9. What are the firm's profits with this choice of K & L? Is this greater than or less than your answer to C15? Why is this the case? [2 points]