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?
3. How much profit (in dollars) does each manufacturer earn when they agree to produce the monopoly outcome and divide the profit evenly?