What level of output should you produce in the short run? b. What is your profit in the short run? c. What will happen in the long run?
You are a manager in a perfectly competitive market. The market equilibrium price for the good you produce is $35. Your total cost is 𝑇𝐶 = 80 + 5𝑄 + 30𝑄 2 and marginal cost is 𝑀𝐶 = 5 + 60𝑄. a. What level of output should you produce in the short run? b. What is your profit in the short run? c. What will happen in the long run? 3. A local tomato farm, firm i, operates in a perfectly competitive market and has total costs of production given by 𝑇𝐶𝑖 = 500 + 10𝑄𝑖 + 5𝑄𝑖 2 and marginal cost given by 𝑀𝐶𝑖 = 10 + 10𝑄𝑖 . The market demand for tomatoes is given by 𝑄𝑀𝐾𝑇 𝑑 = 105 – 0.5𝑃. The market demand represents quantity demanded across all buyers. Notice the use of subscript i to distinguish the output of firm i (𝑄𝑖) from 𝑄𝑀𝐾𝑇 𝑑 and the output of other tomato farms operating in this perfectly competitive market. At market equilibrium, 𝑄𝑀𝐾𝑇 𝑑 = 𝑄𝑀𝐾𝑇 𝑠 = ∑ 𝑄𝑖 𝑁 𝑖 a. Write the equations showing the farm’s average total cost, average variable cost, and average fixed cost, each as a function of quantity (𝑄𝑖 ). b. What is the break-even price and break-even quantity for this firm in the short run? c. What is the shut-down price and shut-down quantity for this firm in the short run? d. If the market price of the product is $50, how many units will this firm produce? e. Given a market price of $50, how many firms are in this market? 4. A monopoly firm faces the following market demand 𝑃 = 100 − 𝑄. The firm’s total cost curve is 𝑇𝐶 = 10 + 5𝑄 and marginal cost is 𝑀𝐶 = 5. a. What is the profit maximizing price and quantity for this firm? Calculate profit. b. How does your answer change if the firm has to pay a lump-sum tax of $500? NOTE: A lumpsum tax is like an additional fixed cost. We can express total cost as 𝑇𝐶 = 10 + 𝑡𝑎𝑥 + 5𝑄. c. For what lump-sum tax value does the monopolist shut down in the long run?