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