(Assume firms compete over quantity) Two identical firms are serving a market in

Question

(Assume firms compete over quantity) Two identical firms are serving a market in which the inverse demand function is given by P = 400-2Q (P = 400-2(q1+q2)).

The marginal costs of each firm are $40 per unit.

(a) Now suppose both firms falsely believe they are the first mover when they are actually producing at the same time (This would be like Toyota and Ford secretly producing automobiles early with the intent to release their numbers before the other starts production. However, when they go to announce how many they have made before the other, each finds out that both firms produced at the same time).

Solve for (each firms quantity, total quantity, price, each firms profit, and total profit) for i= {1,2}

Explanation / Answer

Follower firm(firm2’s) BRF2 , q2 =[ a – c – bq1]/2b   (same as counot)

Since here , a = 400 , b = 2 and c = 40 ,

S0, BRF2 = [400 - 40 - 2q1]/2*2

q2 = 90 - q1/2

Step -2

Leader firm1 residual demand

P = 400 - 2(q1+q2) = 400 - 2(q1 + 90 - q1/2)

P = 220 - q1

Hence , the MR associated with residual demand is

MR = 220 - 2q1

Putting MR =MC

220 - 2q1 = 40

q1 = 180/2 = 90

Similarly by symmetry q2 = 90

and hence , Q = q1 + q2 = 90 + 90 = 180

P = 400 - 2Q = 400 - 2*180 = 40

Profit for firm 1 = P*q1 - MC*q1 = 40*90 - 40*90 = 0

Profit for firm 2 = P*q2 - MC*q2 = 40*90 - 40*90 = 0

So, Total profit = 0

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