Consider an industry consisting of two firms producing an identical product. The inverse market demand equation is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1 = 4Q1 and TC2 = 4Q2, respectively. Firm 1 is the Stackelberg leader and firm 2 is the Stackelberg follower. The profit of the Stackelberg follower is:
$864.
$576.
$432.
$288.
$1,152.
In Stackelberg model where firm 1 is a first mover, it must take the reaction function of firm 2 in its computation of marginal revenue.
Derivation of firm 2’s reaction function
Total revenue of firm 2 = P*(q2) = (100 – 2(q1 + q2))q2 = 100q2 – 2q2^{2} – 2q1q2
Marginal revenue = 100 – 4q2 – 2q1
Marginal cost = 4
Solve for the reaction function
100 – 4q2 – 2q1 = 4
This gives q2 = 24 - 0.5q1
Incorporate this in the reaction function o2f firm 1
Total revenue for firm 1 = P*(q1) = (100 – 2(q1 + q2))q1
TR = 100q1 - 2q1^2 - 2q1q2
= 100q1 - 2q1^2 - 2q1*(24 - 0.5q1)
= 100q1 - 2q1^2 - 48q1 + q1^2
= 52q1 - q1^2
MR = MC
52 - 2q1 = 4
q1 = 24 and so q2 = 12 units.
Price = (100 - 2*36) = $28
Profit for follower = (28 - 4)*12 = $288
Select $288
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