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Firms 1 and 2 are Bertrand Duopolists. Firm 1 has MC1 = 1 and Firm 2...

Firms 1 and 2 are Bertrand Duopolists. Firm 1 has MC1 = 1 and Firm 2 has MC2 = 2.01. The demand for their product is p = 7 − Q, where Q is the total quantity demanded. What are the profits of each firm in equilibrium. Assume that prices can only be set to the nearest cent (e.g. $5.68 is allowed, but $5.6873723 is not.

PLEASE EXPLAIN THOUROUGHLY

ANSWER IS π1 = 5 and π2 = 0

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Answer #1

In case of Bertrand competition we know equilibrium is at a point where Price is equal to higher marginal cost

Since higher marginal cost=2.1 then price should be the less than 2.1 which gives maximum price.

Thus price=2 and all quantity will be sold by firm 1 only

If price is 2.1 then market is share by both firm which leads to lower profit for firm 1.

Thus Q1=5 and Q2=0

profit 1=(2-1)*5=5

ans profit 2=0

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