Consider 2 firms facing the demand curve P905Q where Q Q1Q2

Consider 2 firms facing the demand curve: P=90-5Q, where Q =Q1+Q2

The firms\' cost functions are C1(Q1)=15+Q1 and C2(Q2)=15+30Q2

How much should Firm 1 be willing to pay Firm 2 if collusion is illegal but a takeover is not? Firm 1 should be willing to pay __.

Solution

If the firms collude, they face the market demand curve, thus their marginal revenue curve is: MR = 90 10Q.

Set marginal revenue equal to marginal cost (the marginal cost of Firm 1, because it is lesser than that of Firm 2) to determine the profit-maximizing quantity,

90 10Q = 18; Q =7.2; Substituting Q = 7 into the demand function to determine price: P = 54