Question

In the Bertrand duopoly, market demand is Q = ? ? Bp, and firms have no fixed costs and identical marginal cost. Find a Bertrand equilibrium pair of prices, (p1 , p2 ), and quantities, (q1, q2), when the following hold.

a. Firm1 has fixed costs F>0.

b. Both firms have fixed costs F > 0.

c. Fixed costs are zero, but firm 1 has lower marginal cost than firm 2, so c2 > c1 > 0. (For this one, assume the low-cost firm captures the entire market demand whenever the firms charge equal prices.)

Answer 1

Consider there are two firms producing identical goods and they have same “MC = c”. So, because they are producing exactly identical goods, => they will reduce their “P” as they want to capture the majority of the market share to maximize the profit. So, they both will decrease their price and finally both will stop at “P1=P2=c”, where both of them are getting zero economic profit, => they will earn normal profit and will supply half to the total demand.

a).

Now, assume that “firm1” has fixed cost of “F1 > 0”. So, here they will still charge the same price as above that is “P1=P2=c” and will supply half of the total output supplied to the market. Since as we know that there is a fixed cost only in the SR. So, if they incur lose in the SR by the amount of the fixed cost, => there is a possibility that in the LR the firm will earn normal profit. So, both will charge “P1=P2=c”.

b).

Now, if both firm have a fixed cost of “F > 0”, => both will charge “P1 = p2 =MC = c” and will supplied half of the total production into the market. So, here both will incur lose by the size of the “F” but in the LR they both will earn normal profit.

c).

Now, suppose there don’t have any fixed cost but they have different “MC”, => MC1=c1 < MC2 = c2 > 0. So, here the 1^st firm have less marginal cost compare to the 2^nd firm, => 1^st one will charge “P1 = c2-e < c2”, where “e” be the positive very small quantity, => “firm1” will capture the entire market. So, here “firm1” will earn positive profit and “firm2” will earn nothing. So, here “P1=c2-e and P2=c2 > P1” and only “firm 1” will supply to the market.