Suppose that there are two firms in a duopoly market producing identical product

Question

Suppose that there are two firms in a duopoly market producing identical
products. These firms are trying to decide how much to produce given other firm’s
decision (Cournot Model).
Suppose that the demand curve facing this market is P = 50 – Q, such that
Q =q1+q2, where q1 is quantity produced by firm 1 and q2 is quantity produced by
firm two. Also assume that marginal cost facing these firms are equal to zero. So,
MC1 = MC2 =0.
a) Find reaction curve for each firm
b) Find equilibrium quantity produced by each firm. What is the total quantity
produced in the market in equilibrium?

Explanation / Answer

a) P = 50 – Q

  Q =q1+q2

So,  P = 50 – q1 - q2

TR1 = P x q1 = 50q1 - q12 - q2q1

MR1 = 50 - 2q1 - q2

For equilibrium, the condition is MR1 = MC1

  50 - 2q1 - q2 = 0

2q1 = 50 - q2

q1 = 25 - 0.5q2 (firm 1's reaction curve)

Similarly,

P = 50 – q1 - q2

TR2 = P x q2 = 50q2 - q1q2 - q22

MR1 = 50 - q1 - 2q2

For equilibrium, the condition is MR2 = MC2

  50 - q1 - 2q2 = 0

2q2 = 50 - q1

q2 = 25 - 0.5q1 (firm 2's reaction curve)

b) Substituing firm 2's reaction function in firm 1's reaction function, we get

q1 = 25 - 05q2 =  q1 = 25 - 0.5(25 - 0.5q1)

q1 = 25 - 12.5 + 0.25q1

so, 0.75q1 = 12.5

q1 = 12.5/0.75 = 16.67 units

Similarly,

q2 = 25 - 0.5q1 =  q2 = 25 - 0.5 x 16.67 = 16.67 units

Therefore, equilibrium quantity produced by each firm is 16.67 units. And the total quantity
produced in the market in equilibrium is 33.34 units (16.67 + 16.67)

Related Questions

Navigate

• Browse (All)
• Browse S
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.