Homework answers / question archive / University of Pittsburgh Fall 2014 Intermediate Microeconomics Third Exam 1)Which of the following instances will total revenue decline? A

University of Pittsburgh Fall 2014 Intermediate Microeconomics Third Exam 1)Which of the following instances will total revenue decline? A

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5. Ann runs a firm that sells multi-passes to intergalactic cruises in a competitive market. Her short-run cost function is given by C(q) = q² + 25q + 144.
   1. If the market price is $75/pass, how many units will Ann produce?
   2. At what price will Ann earn zero economic profits?
   3. If the price falls below the level you found in part (b), will Ann shut down? If so, explain. If not, below what price will she shut down?
   4. Now consider a long run scenario in which we assume the possibility of entry/exit. What will be the long run market price? Will Ann remain in the market? Explain.
6. A monopolist’s demand function is P = 500 - 5Q, and its total cost function is TC = 2500 + 100Q − 5Q² + 1/3Q³, where Q is output produced and sold.
   1. At what level of output (Q) and price (P) will total profits be maximized?
   2. At what level of output (Q) and price (P) will total revenue be maximized? Should the monopolist decrease its price and increase its output relative to the value you found in part (a)? Explain.
7. Consider an aircraft manufacturer that sells fighter jets to two countries at war with one another. Let us make the completely unreasonable assumption that jets can be produced at a constant marginal cost of $10 million per unit. For simplicity, assume MC = 10. The demand for jets in each of the countries is given by: P_A = 50 − 0.5Q_A & P_B = 20 − 0.25Q_B.
   1. If the manufacturer can charge different prices to each country, what price and quantity will it sell to each?
   2. If the manufacturer cannot price discriminate, what price and quantity of aircraft will it sell to each country?

8. Consider a market in which each identical consumers have the following demand for golf, q = 100 − p, where q is the number of rounds of golf played per year and p is the price per round. The only golf course in an isolated town incurs a marginal cost of $20 per round of golf.
   1. Suppose the golf course behaves like a standard monopolist. What is the optimal price and quantity in this market? What revenue does the firm earn per consumer?
   2. Now suppose the golf course wants to be clever. It wishes to charge an annual membership fee as well as a fee per round of golf. It decides to set the price of each round of golf equal to its marginal cost of production. What is the consumer surplus associated with this pricing strategy?
   3. Suppose the golf course charges consumers a flat fee equal to the value of consumer surplus you found in part (b) and a fee per round of golf equal to the price you used in part (b). What is the firm’s revenue per consumer under this scheme? Does the firm optimally employ this scheme or does it prefer to behave as a standard monopoly? Explain.
9. There are two ice cream vendors in Arlington, Nebraska. [Actually there are none.] Suppose the market inverse demand for their product is P = 12−Q and one vendor has constant marginal cost of 2, i.e. MC₁ = 2. Suppose the second vendor opened in town later and the Arlington labor market is thin (there are few workers) giving the original vendor a first mover advantage allowing it to employ a more efficient staff. Suppose, therefore, that the second vendor has MC₂ = 4. Suppose these two vendors compete as Cournot Duopolists.
   1. Derive and graph the reaction curves for each firm.
   2. Find the equilibrium price and quantity.

1. 3. Find the profits realized by each firm when they produce as Cournot Duopolists. Find the total producer surplus i.e. market profit.

 (d) Arlington is naturally prone to small town politics. Suppose the original ice cream vendor wishes to take advantage of this. What arrangement will make both vendors better off while incentivizing the second vendor to stay out of the market?

10. Consider a monopolist facing a general linear market demand: P = a − bq, with MC = c. Now marginal costs double. What does economic theory predict will happen to the monopolist’s price in general i.e. double, increase but less than double, etc? Show formally ( mathematically ).
11. Consider two Cournot competitors selling complementary goods with demand curves given by: p₁ = 100 − q₁ + 0.5q₂ & p₂ = 100 − q₂ + 0.5q₁. Suppose each firm has a marginal and average cost of $10.
    1. What about the demand equations indicate that these goods are complements? How do they differ from the standard Cournot Model?
    2. Find the equilibrium prices and quantities.
    3. Suppose the two firms merge. By doing so, the newly merged firm will act to maximize the joint profits π(q₁,q₂) = π₁(q₁,q₂) + π₂(q₁,q₂). Find the joint profit maximizing price and quantities.
    4. Are the combined profits greater or smaller from merging? That is, is merging profitable for firms? Explain.
    5. Are consumers better or worse off with the firms merging? What does this imply about anti-trust policy toward mergers of firms selling complementary goods ( such as airplanes and engines, computer and processors, cars and tire companies, etc.)