(Scenario: Two Identical Firms)Use Scenario: Two Identical Firms.When the firms collude and produce the profit-maximizing output,what is the profit earned by each firm if they split production equally? Scenario: Two Identical Firms
Two identical firms make up an industry in which the market demand curve is represented by Q = 5,000 - 4P,where Q is the quantity demanded and P is price per unit.The marginal cost of producing the good in this industry is constant and equal to $650.Fixed cost is zero.

Question

Quizplus · Accepted Answer

When the firms collude and produce the profit-maximizing output, they produce where marginal cost (MC) equals marginal revenue (MR) and split production equally. 
The market demand function can be rewritten as P = 1,250 - 0.25Q. 
To find the quantity demanded at the profit-maximizing price, we set MR equal to MC: 
1,250 - 0.5Q = 650 
Solving for Q, we get Q = 1,200. 
Each firm produces 600 units of the good. 
To find the price, we substitute Q back into the demand function: 
P = 1,250 - 0.25(1,200) = $900 per unit. 
Each firm earns a profit of (900 - 650) x 600 = $150,000. 
Therefore, the total profit earned by both firms is $150,000 x 2 = $300,000. 
Since they split production equally, each firm earns $300,000/2 = $180,000.