# Monopoly and Four Firm Concentration Ratio

1). Suppose the demand curve for a monopolist is Qd = 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit.

a). Find the monopolist's profit-maximizing output and price.

b). Calculate the monopolist's profit.

c). What is the Lerner index for this industry?

2). The top four firms in Industry A have market shares of 30, 25, 10, and 5 percent, respectively. The top four firms in Industry B have market share of 15, 12, 8, and 4 percent, respectively. Calculate the four-firm concentration ratios for the two industries. Which industry is more concentrated?

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#### Solution Preview

Solution:

1) Suppose the demand curve for a monopolist is Qd = 500 - P, and the marginal revenue function is MR = 500 - 2Q. The monopolist has a constant marginal and average total cost of $50 per unit.

a). Find the monopolist's profit-maximizing output and price.

To maximize profits, a monopolist sets his output in such a way that

Marginal Revenue = ...

#### Solution Summary

There are two problems. Solution to first problem describes the steps for finding profit maximizing output, price and maximum profit. It also calculates Lerner Index for the industry. Solution to second problem calculates four firm concentration ratios for two industries.