# Dealing with Competition Models

Given the following: P = 20,000 - 15.6Q and TC= 400,000 +4640Q + 10Q2

where P is the product price, Q is the output level, and Q2 is Q squared

A. Given we have a monopoly due to a patent, determine the profit maximizing output level, the monopoly price, and economic profits(High price/high output model).

B. Assuming we have lost our patent but that the cost curves are the same AND we are in the long run, now find the price, output for the firm and output for the industry and firm profits for

1) a monopolistic competition model, and

2) perfect competition model

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#### Solution Preview

Monopoly:

Revenue = price X quantity = P X Q = (20000 - 15.6Q)Q = 20000Q - 15.6Q^2

MR = 20000 - 31.2Q

TC = 400000 +4640Q + 10Q^2

MC = 4640 + 20Q

Equating MR = MC gives 20000 - 31.2Q = 4640 + 20Q. This gives the monopoly output is Q = 300.

Monopoly price is P = 20000 - 15.6(300) = 15320

Profit = 15320 X 300 - 400000 - 4640(300) - 10(300)^2 = 1,904,000.

Now, we look at what happens with the perfect competition model:

In perfect competition, we know that 1) nobody earns economic profit and 2) price = marginal cost. Let's suppose that there are n sellers, each seller produces q units and the total ...

#### Solution Summary

The expert examines dealing with competition models.