1. In a duopolistic market (2 firms in oligopoly) firms choose the price at whic

Question

1. In a duopolistic market (2 firms in oligopoly) firms choose the price at which their produce will sell. The market demand is given by P=1000-2Q. Total cost for firm i is given by 50qi where qi is the quantity produced by firm i (i = 1,2).

(a) Given a Bertrand situation, what price will be charged in equilibrium? What quantity will be sold? What is the deadweight loss to society?

(b) How would you expect the market outcome to change if:

i) These two firms operate continually in the market for many years

ii) One firm has a binding capacity constraint (i.e. his production facilities are not of a high enough standard that he can supply half the market demand at a price =50).

*Note: this is one question divided to sections.

Explanation / Answer

P = 1000 - 2Q = 1000 - 2(q1 + q2) = 1000 - 2q1 - 2q2

C = 50qi

C1 = 50q1 and C2 = 50q2

Under Bertrand model, price is equated with marginal cost (at equilibrium)

Thus, P1 = 1000 - 2q1 - 2q2 = 50

similarly, P2 = 1000 - 2q1 - 2q2 = 50

Thus q1 = q2

Therefore

1000 - 4q1 = 50

q1 = 950/4 = 237.5

Hence q1 = q2 = 237.5 and P1 = P2 = 50

Since output is produced where AR = MC thus there will be no deadweight loss under bertrand model.

b)

i. when these two firms operate continually in the market for many years the market outcome will not change since they are drawing only normal profits and there is no deadweight loss.

ii. If one firm is not able to produce half of the market demand at a given price of 50 then it produces the quantity less than its quota then it will have to increase the price but as it increases the price it will loose its market to the other firm thus the market outcome will reduce.

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