The market demand in a Bertrand duopoly is P = 10 − 3Q,and the marginal costs are $1.Fixed costs are zero for both firms.Based on this information we can conclude that:
A) P = $7 and firm 1 will sell 7 units of output.
B) P = $1 and firms 1 and 2 will each sell 7 units of output.
C) P = $1 and firms 1 and 2 will each sell 1.5 units of output.
D) P = $1.5 and firms 1 and 2 will each sell 10 units of output.

Question

Quizplus · Accepted Answer

In a Bertrand duopoly, each firm assumes that its rival's price is fixed and chooses its own output level to maximize profit. In this case, with zero fixed costs and a marginal cost of $1, each firm's profit-maximizing output level is where marginal revenue equals marginal cost, or Q = (10-P)/6. If one firm chooses an output level higher than its rival, it will be forced to lower its price in order to sell all its output, and its profit will be zero. Therefore, both firms will choose the same output level.
Setting the two firms' profit-maximizing output levels equal to each other gives: (10-P)/6 = (10-P)/6, which implies P = $1.5.
Substituting P = $1.5 gives Q = 1.25 for each firm's output level. This is the only choice that satisfies the market demand of P = 10 - 3Q, so the correct answer is C.

The Market Demand in a Bertrand Duopoly Is P =