Question

Use the following information to answer questions 2-4.

Assume there are only two producers of tennis rackets: Wilson and Prince. The market demand for tennis rackets is depicted by the algebraic formula P = 100 - Q, where P stands for price and Q stands for quantity of rackets. If the market were monopolized, the resulting formula for the monopolist's marginal revenue would be MR = 100 - 2Q, where MR stands for marginal revenue. Assume that both producers face a constant marginal cost of $20 and that there are no fixed costs.

2. If Wilson and Prince form a cartel and each agrees to produce one half of the monopolist's profit-maximizing output, how many rackets would each manufacturer produce?

3. When Wilson and Prince collude so as to maximize their combined profits, what is the price of tennis rackets? (For example if your answer is $400 then 400)

4. How much profit (in dollars) does each manufacturer earn when they agree to produce the monopoly outcome and divide the profit evenly? (For example: If your answer is $400 then enter 400).

Answer 1

2. Joint profit maximization occurs when MR = Total MC
So, 100 - 2Q = 20
So, 2Q = 100-20 = 80
So, Q = 80/2 = 40

Each produce one half of the profit maximizing output = 40/2 = 20
So, each manufacturer produce 20 rackets

3.  P = 100 - Q = 100 - 40 = 60
The price of tennis rackets is 60

4. Total profit = Total revenue - Total cost = (P*Q) - (MC*Q) = (P-MC)*Q = (60-20)*40 = 40*40 = 1,600
Profit is divided evenly between each manufacturer. So, each gets a profit of 1,600/2 = 800
Each manufacturer earn 800.