Intermediate Microeconomics

Professor Yongmin Chen

Topic 8. Price and Output under Monopoly

Monopoly

A monopoly is a situation where there is only one seller in the market. Contrary to a firm under perfect competition, which has no effect on the market demand and thus is a price taker, a monopolist's demand coincides with the market demand, and the monopolist is a price setter..

There are several possible reasons for the existence of monopolies, and they may differ in their implications for economic welfare.

First, a firm may control the entire supply of a basic input that is needed to produce a certain product.

Second, the industry may be a natural monopoly. An industry is called a natural monopoly if production exhibits decreasing average cost (economies of scale) in the output range that would meet the entire market demand at a profitable price. In such an industry, it is desirable to have only one firm to minimize the production cost. Public utilities are often examples of natural monopolies.

Third, monopolies may be created through laws and government regulations. One case is the legal protection for patents. The purpose of this is to provide incentives for innovation. It typically involves the trade-offs between dynamic efficiency and static efficiency. Another situation is that the government may issue a license only to a particular firm in a market.

Monopoly Pricing

How does a monopolist set price to maximize profit? It will set price such that MR = MC. To a monopolist, its MR curve is below its demand curve.

Since MR = p(1+1/h), the profit-maximization condition for the monopolist can be written as:

p(1+1/h) = MC

The profit-maximizing price for the monopolist is (if 1+1/h is not zero):

p = MC / (1+1/h)

Example 8-1. Suppose MC = 1, and h = -2, what is the monopoly price?

Example 8-2. The shape of the total and marginal revenue curves of a monopoly firm.

Example 8-3. Marginal revenue formula for the linear demand function.

Example 8-4. Suppose Firm A is the sole producer of a product that has market demand given by

Q = 1000 - 2p

The firm's marginal cost is

MC = 300 + 9Q

(a) What is the firm's marginal revenue function?

(b) How much quantity should the firm produce?

(c) What is the firm's maximum profit?

Example 8-5. Is it true that a monopolist will always have positive profit?

Example 8-6. Authors usually receive a royalty that is a fixed percentage of the price of the book. Show that an author has an interest in a book's price being lower than the price which maximizes the publisher's profits.

Example. Can cost-plus pricing be profit maximizing?

A common pricing practice by firms is to set price as cost plus a markup, or p = cost(1 + markup). Often average cost is used in this calculation. We know a profit-maximizing firm will set p = MC / (1-1/h). Suppose the firm sets p = MC(1 + markup). In order for this to be consistent with profit-maximization, let 1/(1-1/h) = 1 + markup, then markup = [h/(h-1)] - 1. Therefore cost-plus pricing can be consistent with profit-maximizing pricing if MC is used as the cost and if markup is equal to [h/(h-1)] - 1. When demand is more elastic, the profit-maximizing markup will be lower.

Monopoly price is higher than marginal cost. This creates a dead-weight loss. (Recall that under perfect competition, price equals marginal cost). See a graphic illustration. The area that is between the supply curve and the price line measures producer surplus. The area between the price line and the demand curve measures consumer surplus. Compared with perfect competition, monopoly price is higher and output is lower. Social welfare, which is often measured by the sum of consumer and producer surpluses, is lower under monopoly. There are different estimates of how large is the dead weight loss due to monopoly.

Under perfect competition, no firm can earn positive profit in the long-run. A monopolist, however, can earn positive profit even in the long run. Because of this, a monopolist may try to prevent entry by new firms. Or a firm may try to drive its rivals out of the market to obtain a monopoly position (such actions are illegal in the U.S.).

So far, we have assumed that the monopolist operates in a single plant. What happens if it operates in two plants? The outputs in both plants would be such that the marginal costs in both plants are equal to marginal revenue. Thus, in the optimal, both plants would have the same marginal cost.

Example 8-7. A monopolist has two plants, with the following marginal cost functions:

MC₁ = 50 + 2Q₁

MC₂ = 80 + Q₂

If the monopolist wants to produce 100 units of total output, how much should it produce in plant 1?

The Social Cost of Monopoly

A monopolist decides its optimal output by equating marginal revenue with marginal cost. But since marginal revenue is lower than price for a monopolist, at the optimal output of a monopolist, social surplus is not maximized. This loss in social surplus, which occurs because monopoly output is too low compared to the social optimal, is called a dead-weight loss.

Capturing Surplus through Price Discrimination

Price discrimination is the act of charging different prices for an identical product to different consumers or to the same consumer but for different quantities. Price discrimination is a common way for firms to capture consumer surplus and increase profits.

There are three types of price discrimination:

(a) First-degree price discrimination ( perfect price discrimination): each unit is sold at its marginal value to the consumer. Thus all consumer surplus is transferred to the producer. Ironically, if a monopoly firm is able to practice perfect price discrimination, the usual deadweight loss associated with monopoly disappears. See a graphic illustration.

What is the marginal revenue curve under first-degree price discrimination?

Examples of perfect price discrimination: Undergraduate financial aid at colleges; …

(b) Second-degree price discrimination (block pricing): The same customer pays a different price for different quantities of an identical good. See a graphic illustration. This type of price discrimination is quite common: Buy one and get the second one at the half price; access charge for phone services, two-part tariffs.

(c) Third-degree price discrimination (group price discrimination): Charging different prices to different consumers with different price elasticities. Suppose there are two separate markets (two different groups of consumers), then the condition for profit-maximization is to charge prices in the two markets such that

MR₁ = MR₂ = MC

Example 8-8. Suppose the demand on market 1 is

Q₁ = 100 - 5p

and the demand on market 2 is

Q₂ = 150 - 10p.

MC = 2. How can the firm set prices on each market to maximize profit?

Group price discrimination implies that the firm will charge a lower price for the group (class) with more elastic demand. This type of price practice is also quite common: First-class and coach fares for airline tickets; Advance purchase discounts; student discounts; etc.

To practice third-degree (group) price discrimination, it is necessary that consumers have different price elasticities, can be identified and segregated at moderate cost, and that it is not easy for resale of the good.

Example 8-9. The economics of dumping.

The Regulation of Monopoly

Example 8-10. Rate of return regulation.

Example 8-11. Price-cap regulation.