ECP 4403 FINAL E
X
AM Fall 2020
PLEASE FRAME OR HIGHLIGHT YOUR ANSWERS FOR EACH QUESTION.
1) Assume that two firms compete in an industry, both with constant marginal cost and average cost MC = 10. Assume the market inverse demand curve is P = 40 – .5(q1 + q2). Suppose that the CEOs of firms 1 and 2 meet one year at the Swan Ball and have an opportunity to chat about the competitive conditions in their industry. They decide that they should not behave so aggressively toward one another; instead, they agree that each of them should produce one-half of the monopoly output. The next morning, each CEO gets up and contemplates whether he or she should fulfill the agreement. Assuming that the two firms compete in quantities and will interact indefinitely in the market, for what values of the interest rate r is the agreement sustainable (e.g., through the use of trigger strategies)? Show all of your intermediate work to get full credit.
(a) Show that the single round profit per firm if both violate the agreement is $200.
Show that the single round profit per firm if both stick to the agreement is $225.
Show that the single round profit for the firm that cheats is (approximately) $253.
(b) Calculate the present discounted value of cooperating over the indefinite future, using trigger strategies. (Hint: If r is the rate of interest, then 1/(1+r) + 1/(1+r)2 + 1/(1+r)3 + … = 1/r).
Calculate the present discounted value of cheating over the indefinite future, using trigger strategies.
(c) For what values of r is the agreement sustainable through the use of trigger strategies?
(d) Suppose that the interest rate, r, is 0.95. Firm 1 CEO discovers a new technology that will make firm 1 the Stackelberg leader and, hence, earn the Stackelberg profit indefinitely. To own this technology firm 1 has to pay a lumpsum amount of $F. The CEO of firm 1 contemplates whether he or she should buy the technology and earn the Stackelberg leader profit indefinitely or keep the market conditions as it is now forever. Should the CEO buy the new technology? If yes, what is the maximum he or she would pay for the new technology? If no, explain.
(Hint: Decide what the market conditions are when r = 0.95. Are firms able to keep the collusive agreement or are they Cournot duopolists indefinitely?)
X
Store 1
Store 3
Store 2
Store 4
Firm A
Firm B
2) Four banana stores are located at equal intervals around a circular
desert island, whose circumference is one mile. The beach is equally
nice at all points along the shore, so the population of 10,000 people
have distributed themselves evenly around the perimeter. The center of
the island is mountainous, so people have to travel along the shore.
The weather is always pleasant, so people do not mind the fact that they
have to walk to the banana store, except that it takes 1 hour per mile of
commute. Each hour spent walking to and from the banana store is an
hour taken from their jobs as pearl divers, at which they make $40 per
hour. If a consumer lives x miles away from a store, then it takes
2x hours to go to the store and return home. Finally, each consumer will
buy one pound of banana and the value of consuming one pound of banana
is $200 to each consumer. Suppose that bananas grow in groves behind each store and just fall to the ground in perfect bunches when ripe, so the marginal cost of a pound of banana is zero. Assume that stores 1 and 2 merge (into firm A); and stores 3 and 4 merge (into firm B). All stores continue to sell bananas. Let PA denotes firm A’s price and PB denotes firm B’s price.
(a) What is the distance between firm A’s nearest store and the home of its marginal consumer?
(b) What is the demand function faced by firm A?
What is the profit function of firm A?
(c) What is firm A’s best response to the price PB being charged by firm B?
Find a symmetric Bertrand-Nash equilibrium in prices.
(d) The governing authority is criticized by the opposing political party about allowing the mergers to take place and is suggested that the governing authority should force the firms to open more banana stores in order to increase the welfare by lowering the transportation cost paid by the public. Calculate the total cost of transportation paid by the public when there are n banana stores (remember that the cost of transportation for x miles is 2x).
(e) If the fixed cost of a banana store is $50000, then to total cost of banana stores when there are n stores is $50000n. What is the efficient (socially optimal) number of stores?
Is the opposing party right to claim that there should be more banana stores for the benefit of the public?
3) A sticky goo oozes mysteriously from the rare wazoo tree, which grows only on the farm of Wolf Molder, just outside of Pullman, Washington. This goo, when smeared on the face, results in a tightening of the skin and the elimination of fine lines. Wolf bottles the goo at a cost of $2 per bottle and sells it to Donna Scali at a wholesale price of $w per bottle. Donna sells the goo to the general public over the Internet under the name “Youth Goo” at a price of $P per bottle. The retail demand for Youth Goo is given by P = 60 – .01Q.
(a) Write Donna Scali’s profit as a function of the number of bottles of Youth Goo she sells over the Internet and the wholesale price, πD(Q;w).
Write an equation characterizing Donna’s profit-maximizing choice of output as a function of the wholesale price w.
(b) What is Wolf’s profit as a function of the number of bottles of Youth Goo he sells to Donna, πW(Q)?
What is Wolf’s profit-maximizing choice of output?
(c) What are the resulting values of the wholesale and retail prices?
What are profits to Donna and Wolf?
(d) Wolf offers Dana a contract in the form of two-part tariff, a wholesale price, w, and a fixed fee, F. Calculate the wholesale price that Wolf charges, the optimal quantity that Donna buys, and Donna’s optimal price. What should be the range of the fee so that Donna would accept the offer and Wolf prefers this system?
(e) After a long Internet courtship, Wolf and Donna decide to become partners in business and in life. After combining their separate businesses (Youth Goo production and retail distribution, respectively), they conclude that they could make larger combined profits by choosing a different level of output. What is their new profit-maximizing level of output Q** and retail price P**?
What are their new profits?
PLEASE SUBMIT YOUR ANSWER BEFORE THE DUE TIME.
Good luck.