Consider a firm that uses both capital (K) and labour (L) to produce a final product...

 

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Consider a firm that uses both capital (K) and labour (L) to produce a final product (Q) 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: L¹2 K¹/₂ MPK = 2- K¹/₂ L¹2 Suppose also that the firm currently has 16 units of capital (K = 16) in the Short-Run. For Q1-Q6, 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(Q)). [1 point] MPL = 2- 2. Use the MPL and the wage rate to write down an expression for the Firm's Marginal Cost per unit of output (Q) produced as a function of Q. [3 points] 3. Show that the firm's profit-maximizing quantity (Q*) is equal to 160 in the short-run. [1 point] 4. What are the firm's variable costs (VC) and fixed costs (FC) at Q*? [2 points] 5. What are this firm's short-run profits in this example? [1 point] 6. 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] Consider a firm that uses both capital (K) and labour (L) to produce a final product (Q) 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: L¹2 K¹/₂ MPK = 2- K¹/₂ L¹2 Suppose also that the firm currently has 16 units of capital (K = 16) in the Short-Run. For Q1-Q6, 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(Q)). [1 point] MPL = 2- 2. Use the MPL and the wage rate to write down an expression for the Firm's Marginal Cost per unit of output (Q) produced as a function of Q. [3 points] 3. Show that the firm's profit-maximizing quantity (Q*) is equal to 160 in the short-run. [1 point] 4. What are the firm's variable costs (VC) and fixed costs (FC) at Q*? [2 points] 5. What are this firm's short-run profits in this example? [1 point] 6. 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]