Question

SCENARIO 3: Consider an industry consisting of two firms producing an identical product. The inverse market...

SCENARIO 3: 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.

Refer to SCENARIO 3. Firm 1 is the Stackelberg leader and firm 2 is the Stackelberg

follower. The profit of the Stackelberg leader is:

a. \$288.

b. \$432.

c. \$486.

d. \$576.

e. None of the above.

Ans. Option e

Inverse market demand function, P = 100 - 2q1 - 2q2

Total revenue of firm 2, TR2 = 100q2 - 2q2^2 - 2q2*q1

=> Marginal revenue of firm 2, MR2 = dTR2/dq2 = 100 - 4q2 - 2q1

Marginal Cost of firm 2, MC2 = dTC2/dq2 = 4

At equilibrium,

MR2 = MC2

=> 100 - 4q2 -2q1 = 4

=> q2 = 25 - 0.5q1 ---> Eq1

Substituting Eq1 in inverse market demand function, we get,

P = 100 - 2(25 - 0.5q1) - 2q1

=> P = 50 - q1

=> Total revenue of firm 1, TR1 = P*q1 = 50q1 - q1^2

=> Marginal revenue, MR1 = dTR1/dq1 = 50 - 2q1

and marginal cost, MC1 = dTC1/dq1 = 4

At equilibrium,

MR1 = MC1

=> 50 - 2q1= 4

=> q1 = 23 units

Profit = P*q1 - TC1

=> Profit = (50 - 23) * 23 - 4*23

=> Profit = \$529