2nd Midterm Study Questions
1) Suppose that Dent Carr’s long-run total cost of repairing s cars per week is c(s) = 3s2 + 12. If the price he receives for repairing a car is $24, then in the long run, how many cars will he fix per week if he maximizes profits? (Answer: 4)
2) A firm has the long-run cost function C(q) = 6q2 + 486.In the long run, it will supply a positive amount of output, so long as the price is greater than? (Answer: 108)
3) On a small island, papayas can only be sold in the market in the center of the island. Although papayas only cost $1 to raise, they can be sold in the market for $3. But it costs $.10 per kilometer to transport each papaya to market. If an acre of land grows 200 papayas, how much rent does an acre of land 4 kilometers from the market command? (Answer: 320)
4) Brand X is one of many firms in a competitive industry where each firm has a constant marginal cost of 2 dollars per unit of output. If marginal cost for Brand X rises to 4 dollars per unit and marginal costs of all other firms in the industry stay constant, by how much does the price in the industry increase? (Answer: 0)
5) In a certain industry, the supply curve of any firm is Si(p) = . If a firm produces 5 units of output, what are its total variable costs? (Answer: 25)
6) A monopolist faces the inverse demand function described by p = 50 – 4q, where q is output. The monopolist has no fixed cost and his marginal cost is $5 at all levels of output. What is the monopolist’s profits as a function of his output? (Answer: 45q – 4q2)
7) A monopolist faces the inverse demand curve p = 64 – 2q. At what level of output is his total revenue maximized? (Answer: 16)
8) A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of –4. The firm finds it optimal to charge a price of $24 for its output. What is its marginal cost at this level of output? (Answer:18 )
9) A profit-maximizing monopolist faces a downward-sloping demand curve that has a constant elasticity of –3. The firm finds it optimal to charge a price of $12 for its output. What is its marginal cost at this level of output? (answer: 8)
10) In a market with the inverse demand curve P = 10 – Q, Brand X is a monopolist with no fixed costs and with a marginal cost of $2. If marginal cost rises to $4, by how much will the price of Brand X rise? (answer:1)
11) Charlie can work as many hours as he wishes at a local fast-food restaurant for a wage of $4 per hour. Charlie also does standup comedy. Since Charlie lives in a quiet, rather solemn Midwestern town, he is the town’s only comedian and has a local monopoly for standup comedy. The demand for comedy is Q = 40 – P, where Q is the number of hours of comedy performed per week and P is the price charged per hour of comedy. When Charlie maximizes his utility, he spends at least 1 hour per week working at the restaurant and he gets at least 1 hour of leisure time. His utility depends only on income and leisure. How many hours per week does he perform standup comedy?(answer: 18)
12) An industry has two firms, a leader and a follower. The demand curve for the industry’s output is given by p = 456 – 6q, where q is total industry output. Each firm has zero marginal cost. The leader chooses his quantity first, knowing that the follower will observe the leader’s choice and choose his quantity to maximize profits, given the quantity produced by the leader. What output level will the leader choose? (answer: 38)
13) Peter Morgan sells pigeon pies from his pushcart in Central Park. Due to the abundant supplies of raw materials, his costs are zero. The demand schedule for his pigeon pies is p(y) = . What level of output will maximize Peter’s profits? (answer: 225)