# A profit-maximizing monopolist faces the demand curve q= 100 - 3p. It produces at a constant...

## Question:

A profit-maximizing monopolist faces the demand curve q= 100 - 3p. It produces at a constant marginal cost of $20 per unit. A quantity tax of $10 per unit is imposed on the monopolist's product. The price of the monopolist's product:

a. rises by $5.

b. rises by $10.

c. rises by $20.

d. rises by $12.

e. stays constant

## Monopoly Profit Maximization:

In a monopoly, the sole seller maximizes profit by producing at a level that equates marginal revenue and marginal cost. Marginal revenue is not the same as the marginal willingness to pay for the good by the consumer.

## Answer and Explanation: 1

The answer is a).

We first compute the price without the tax. The inverse demand function is:

- p = 100/3 - q/3

and the marginal revenue is:

- MR = 100/3 - 2q/3

Profit is maximized when marginal revenue is equal to marginal cost, i.e.,

- 100/3 - 2q / 3 = 20
- 40/3 = 2q/3
- q = 20

and the price is p = (100 - 20) / 3 = 80/3

With the tax, the marginal cost is 20 + 10 = 30. The profit-maximizing quantity is:

- 100/3 - 2q/3 = 30
- 10/3 = 2q/3
- q = 5

and the price is p = (100 - 5) / 3 = 95/3

Thus the difference in price = 95/3 - 80/3 = 15/3 = $5.

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Chapter 16 / Lesson 6Explore the concept of pure monopoly. Learn the definition of a pure monopoly and understand its characteristics. See pure monopoly examples and when they occur.

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