Suppose that instead of competing as a Cournot firm, Firm 1 decides to announce
ID: 1146663 • Letter: S
Question
Suppose that instead of competing as a Cournot firm, Firm 1 decides to announce its production decision before Firm 2 chooses its output. Thus, Firm 1 acts as Stackelberg firm. Use the same market demand, P= 204-4Q, and marginal cost, $12, as before irm 1 will produce 24 units, Firm 2 will produce 12 units, and the market price will be $ 60 (Enter your responses rounded to one decimal place.) irm 1's profit will be $ 1152, and Firm 2's profit will be S 576 (Enter your responses as integers.,) After a few years of Cournot and Stackelberg competition, the firms decide to collude and maximize their joint profit. They want to determine the total amount of utput they should produce, and then each firm will produce half that amount. The firms should produce a total ofunits, and the market price will then be (Enter your responses as integers.)Explanation / Answer
Stackelberg:
Q = Q1 + Q2
Firm 2 takes the output of firm 1 as a given:
Firm 2's profit: P2 = (204 - 4(Q1 + Q2)) x Q2 - 12 x Q2
Profit is maximized when dP2/dQ2 = 0:
204 - 4Q1 - 8Q2 - 12 = 0
Q2 = (192 - 4Q1)/8 = 24 - 0.5Q1
Firm 1's profit: P1 = (204 - 4(Q1 + Q2)) x Q1 - 12 x Q1
Profit is maximized when dP1/dQ1 = 0: (use Q2 from the equation above)
204 -4Q1 -12 -96 = 0
Q1 = 24 , Q2 = 12
P = 204 - 4 x 36 = $60
Firm 1 profit = 60 x 24 - 12 x 24 = $1152
Firm 2 profit = 60 x 12 - 12 x 12 = $576
Collusion:
Firms combine as one firm to behave as a monopoly:
Total production = Q
Profit (Pr) = PQ - 12Q = 192Q - 4Q2
Profit is maximized when dPr/dQ = 0
192 - 8Q = 0
Q = 24 (total production)
P = 204 - 4 x 24 = $ 108
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.