Question

In a Cournot model determine the output of firm 1 and firm 2, assuming the market demand is given by P=80-Q and MC₁=MC₂=0.

a. Q1=33.33; Q2=33.33

b. Q1=35; Q2=35

c. Q1=40; Q2=40

d. Q1=26.67; Q2=26.67

e. none of the above

Answer 1

Because marginal cost is zero revenue maximization is similar as profit maximization

Revenue for the two firms are

R1 = 80Q1 - Q1^2 - Q1Q2 and R2 = 80Q2 - Q2^2 - Q1Q2

This gives the marginal revenue function equal to marginal cost function

80 - 2Q1 = Q2 and 80 - 2Q2 = Q1

Solve them to get

80 - 2Q1 = 40 - 0.5Q1

40 = 1.5Q1

Q1 = Q2 = 26.67

This implies that the two quantities are 26.67

Select option D