Problem 1: Short-Run Profit Maximization [10 points] Consider a firm that uses both capital (K) and labour (L) to produce a final product (C1) 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 price-taker for all prices with the following production function: Q = 4K1/2L1/2 This production function implies the following: MPK 2W2 _ xlfz MPL 21w2 _ L1/2 Suppose also that the firm currently has 16 units of capital (K = 16) in the Short-Run. For Q1 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 (Le. 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 (C1) produced as a function of C1. [3 points] Show that the firm's profit-maximizing quantity (03\") is equal to 150 in the short-run. [1 point] What are the firm's variable costs (VG) and fixed costs (FC) at (1*? [2 points] What are this firm's short-run profits in this example? [1 point] What would be the firm's Short-Run profits if it chooses to shut down? Should the firm keep producing in the short-run? How do you know? [2 points]