Question

Suppose a monopolist faces consumer demand given by

P=300?11Q

with a constant marginal cost of ?$100 per unit? (where marginal cost equals average total cost. assume the firm has no fixed? costs).

If the monopoly can only charge a single? price, then it will earn profits of ?$__. ?(Enter your response rounded as a whole? number.) ?

Correspondingly, consumer surplus is ?$__. ?

However, if the firm were to practice price discrimination such that consumer surplus becomes? profit, then, holding output constant at 100, the monopoly would have profits of ?$__.

Answer 1

The inverse demand function is given as . The MC is given as constant, and is . The total revenue will be , and hence, the marginal revenue will be hence or . If the firm charges a single price, then the profit maximization will be at where marginal revenue is equal to the marginal cost, ie or or . The price will hence be setted as or .

The cost faced by the firm is , which produces marginal cost and average cost of $100, with no fixed cost. Hence, total cost is or . The total revenue at profit maximizing quantity is , ie or . The profit is hence, .

If the monopoly can only charge a single? price, then it will earn profits of ?$909.

The consumer surplus will be the area of triangle ABE, ie or or .

Correspondingly, consumer surplus is ?$455.

In case of price discrimination, the firm charges the price at MC, but takes the profit of the whole consuemer surplus as profit, charging it to the consumers as an entry fee. The consumer surplus in that case would be the area of triangle below the demand curve and above marginal cost curve. At P=MC, quantity demanded is or . Hence, the area of triangle will be or , which will be the monopoly producer's profit.

However, if the firm were to practice price discrimination such that consumer surplus becomes? profit, then, holding output constant at 100, the monopoly would have profits of ?$1818.