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 IfWilson 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? 5.1. 15 Please enter a whole number, with no decimal point

Answer 1

15 units

Step-by-step explanation:

Given:

The demand formula, P = 100 – Q - equation (I)

The marginal revenue formula, MR = 100 – 2Q - equation (II)

Marginal cost, MC = 40 (constant)

There exists a cartel equilibrium; which means MR = MC

Substituting MC = 40 into equation (II), we have

100 – 2Q = 40

2Q = 100 - 40 = 60

Q = 60/2

= 30

Hence, each firm produces 30/2 = 15 units