Question

# Consider an industry consisting of two firms producing an identical product. The inverse market demand equation...

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 – 2q22 – 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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