Assume there are only two producers of tennis rackets: Wilson and Prince. The ma

Question

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 $40 and that there are no fixed costs.

1. 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?

2. 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)

3. 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).

Explanation / Answer

Given that P=100-Q

thus, the total revenue is TR=P × Q = 100Q-Q2

Given MR=100-2Q and MC=40

A monopolist maximizes profit by producing a quantity where Marginal Revenue = Marginal Cost.

Thus, MR = MC

100-2Q =40

60 =2Q

Q =30

P=100 – 30 = 70

Therefore,

TR = P × Q =70 × 30=2100

TC = 40 × Q = 40 × 30=1200

Now, Profit =TC – TR = 2100 – 1200 = 900

Part 1:

Therefore the total rackets produced = 30.

Each produces = 30 ÷ 2=15 rackets (Condition given: each agrees to produce one half of the monopolist's profit-maximizing output).

Part 2:

When Wilson and Prince collude so as to maximize their combined profits, the price of tennis rackets is 70.

Part 3:

The total profit =TC – TR = 2100 – 1200 = 900.

So, they each make a profit of $450.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects