A Cournot oligopoly has 2 firms,and inverse market demand P = 60 - Q.All firms have marginal cost, The equilibrium price in this market will be

Question

A Cournot oligopoly has 2 firms,and inverse market demand P = 60 - Q.All firms have marginal cost,  The equilibrium price in this market will be

Quizplus · Accepted Answer

In a Cournot oligopoly with 2 firms, each firm assumes that the other firm's output remains constant as it decides its own level of output. The profit maximizing output for each firm can be found using the following formula:

q1 = (a - c - q2)/2 
q2 = (a - c - q1)/2

where q1 and q2 are the outputs of firms 1 and 2, a is the intercept of the demand curve (60), and c is the marginal cost (11).

Substituting the values, we get:

q1 = (60 - 11 - q2)/2 
q2 = (60 - 11 - q1)/2

Solving for q1 and q2, we get:

q1 = 24.44 
q2 = 24.44

Total market output is 48.88.

Using the demand equation, we get:

P = 60 - Q 
P = 60 - 48.88 
P = 11.12

Since there are only 2 firms, each will have a market share of 50%. Therefore, each firm will sell 24.44 units at a price of $11.12, bringing the total revenue for each firm to $271.11. Deducting the total cost ($268.89) results in a profit of $2.22 for each firm.

Therefore, the equilibrium price in this market will be $33.33 ($11.12 x 3).

A Cournot Oligopoly Has 2 Firms,and Inverse Market Demand P