Firm 1 and firm 2 produce a same product which they sell to a market inverse dem

Question

Firm 1 and firm 2 produce a same product which they sell to a market inverse demand function

p(Q)= 120- Q. Firm 1 has a contant marginal cost of c1=15 and firm 2 has a constant marginal cost of c2=30

a) suppose the firms choose prices to compete. Suppose further that prices must be in dollars and cents, so that for example $12.31 or $12.00 is a permissible price, but $12.315 is not. Find Bertrand equilibrium prices for the firms. How much profit does each make in Bertrand equilibrium.

b) Now suppose that firm 1's marginal cost changes to c1=30, firm 2's marginal cost changes to c2=76, but market demand remains as before. Suppose further that the two firms interact in the market indefinetly. Will each firm have any incentive to form a cartel with the other? Support your answer.

Explanation / Answer

a) demand p = 120- q

firm 1 mc =mr

15 = 120 - 2q implies q = 105/2 =52.5 p = 120-52.5 = 67.5 profit =52.5 *( 67.5 -15) = 2756.25

firm 2 mc =mr

30 =12 -2q implies q =45 p =75 profit = 45 *(75-30) =45*45 = 2025

b) c1 =30 implies p=45 profit =2025 for firm 1   

c2 =76 implies q=22 p =98 profit = 22 *(98-76) =22 *22 = 484

yes they have incentive t o maximize profits because combined profit in case a> profit in case b

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