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Problem 1. Let market demand in the cement industry be given by Q(P) = 200- P. There are only two firms in the industry and the total cost function for each firm is C(qi) = 20qi + 400, where i = 1, 2. 1. What is the marginal cost for both firms? 2. Represent the market price as a function of each firm's output, qi and q2. 3. What is the marginal revenue for firm one? Write as a function of each firms quantity, qi and q2. 4. Find the best-response function of each firm. 5. Suppose firm 2 produces nothing, that is, 92 = 0. What is firm 1's output level? Compare the quantity with the monopoly output level (if there was only one firm with the same cost curve). 6. Using the Cournot model, find each firm's output, profit, and price in equilib rium. 7. Now suppose technical innovation makes each firm's fixed cost is zero, that is, C(qi) = 20qi, where i = 1, 2. Find each firm's output, profit, and price. Compare with them before the innovation. 8. What is consumer surplus in equilibrium? How does it compare with consumer surplus under monopoly? (Hint: Recall from geometry class that the area of a triangle is ? (base x height)) 9. Is the equilibrium outcome efficient? Why or why not? If it is not efficient, what would the efficient quantity to produce be? What is the consumer surplus10. and producer surplus under the efcient level? Are both consumers and the two rms better off ? Suppose a technology company develops yet another innovation. They have developed a production process that allows rms to produce concrete with the cost function 0(q1) = 84;. They offer to license this technology to rm one (and not rm two) for $1,000 dollars. Should rm one take the deal? (Hint: The new cost function is really C(qz) = 1000 + 8%)