There are two firms in a market for commercial dry suits. The market demand curv
ID: 1205260 • Letter: T
Question
There are two firms in a market for commercial dry suits. The market demand curve is P = 4,000 – 2.5Q, and each of the two firms has a total cost curve of C = 1,000 q with zero fixed costs. They have decided to collude with each other in order to obtain together the monopoly profits in the market. a. Calculate monopoly quantity and price of commercial dry suits. Show work. Calculate monopoly profits. Show work. We will refer to the profits as “gross profits” because the firms will have a cost in order to secure some of the profits. b. The firms find themselves in a game situation in order to split the total gross monopoly profits available from part a. They need to decide how many dry suits each of the firms will produce, which will determine the share of the profits each firm receives. This decision will be made at a secret (illegal) meeting between negotiators representing each of the firms. Each firm has a total of 2 negotiators and may send 0, 1, or 2 negotiators to the meeting. Sending a negotiator to the meeting costs $30,000. If the firms send equal numbers of negotiators to the meeting, they will end up with equal gross monopoly profits minus ($30,000 x number of negotiators). If 1 firm sends zero negotiators, while the other firm sends one or two, the firm that sends zero gets 1/9 of the gross profit, while the other firm gets 8/9 less ($30,000 x number of negotiators). If 1 firm sends in 1, while the other sends in 2, the firm that sends in 1 gets 1/3 of the gross profit less $30,000, while the firm that sends in 2 gets 2/3 of gross profit less $60,000. Fill out the payoff matrix below. Values should be expressed in thousands of dollars. The payoff before the comma should be Firm 1’s net profit (gross profit minus the cost of the negotiation), while the number after the comma should be Firm 2’s net profit: Firm 1 Strategy Firm 2 Strategy 0 negotiator 1 negotiator 2 negotiators 0 negotiator ( , ) ( , ) ( , ) 1 negotiator ( , ) ( , ) ( , ) 2 negotiators ( , ) ( , ) ( , ) c. What is the Nash equilibrium for the game? Explain. What is the maximin equilibrium for the game? Explain.
Explanation / Answer
Inerse dwmand curve : P = 4000 - 2.5Q
total cost curve C = 1,000 q
or MC = 1000q
total revenue = P*Q = (4000-2.5q)q = 4000q-2.5q2
marginal revenue = dtr/dq = 4000 - 5q
equating mr with mc
4000-5q = 1000q
1005q = 4000
monopol quantit = q = 4 approx
monopol price = p = 4000 - 2.5(4) = $3990
monopol profit = total revenue - total cost = P*Q - 1000Q = 3990*4 - 4000 = $11960.
Now lets have paoff matrix representing share of profit for the firms as follows:
thus the firms profit a each alternative are as follows:
Firm 2
0 N 1 N 2 N
Firm 1 0 N 5980, 5980 1328.88,7631.11 1328.88,4631.11
1 N 1328.88,7631.11 5980, 5980 986.66 , 1973.33
2 N 1328.88,4631.11 4973.33, -2013.33 5980, 5980
Sending 2 negotiators from firms each will be the equilibrium strateg as this is the dominant strateg.
Firm 2 0 N 1 N 2 N Firm 1 0 N 1/2,1/2 1/9,8/9 1/9,8/9 1 N 8/9,1/9 1/2,1/2 1/3,2/3 2 N 8/9,1/9 2/3,1/3 1/2,1/2