The automobile market has been used as an example of a Stackelberg oligopoly whe

Question

The automobile market has been used as an example of a Stackelberg oligopoly where one firm is the industry leader and the other firms will follow that lead. Assume the following equations were estimated for the automobile industry:

P=1000-(Q1+ Q2)

Ci=4Qi

Where Q2 represents the total output of all the followers in the industry.

Calculate the profit maximizing output for the industry leader, Q1.

Calculate the profit maximizing output tor the industry followers, Q2.

Calculate the profits for the leader.

Calculate the profits for the followers.

Explanation / Answer

P=1000-(Q1+ Q2)

Ci=4Qi

Step 1,

Profit of firm 2 = P*Q1 - C2 = [1000-(Q1+ Q2)]*Q2 - 4Q2

dProfit/dQ2 = 1000 - 2Q2 - Q1 - 4

Putting dProfit/dQ2 = 0

Q2 = 498 - Q1/2

Follower firm(firm2’s) BRF2 = 498 - Q1/2 (same as counot)

Step -2

Leader firm1 residual demand

P =100 - (Q1 + Q2) = 1000 - Q1 - 498 + Q1/2

P = 502 - Q1/2

Hence , the MR associated with residual demand is

MR = dTR/dQ1 = 502 - Q1

Putting MR =MC

502 - Q1 = 4

Q1 = 498

So, Q2 =  498 - Q1/2 =  498 - 498/2 = 249

P = 1000 - (498+249) = 253

Profit of Leader = (253 - 4)498 = 124,002

Profit of Follower = (253 - 4)249 = 62,001

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