Chapter 18

Pricing Policies

McGraw-Hill/Irwin Copyright © 2008 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Main Topics

Price discrimination: pricing to extract surplus

Perfect price discriminationPrice discrimination based on observable

customer characteristicsPrice discrimination base on self-

selection

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Price Discrimination: Pricing to Extract Surplus

Monopolist’s profit would be larger if he could solve two problems

Consumers who buy some of the product receive some consumer surplus Monopolist could increase profit if he could charge them a

higher price Consumers aren’t buying some units that they value

less than the monopoly price but more than marginal cost Monopolist could increase profit if he could charge these

buyers less for those units of the good Monopolist might be able to do better by price

discriminating: charging different prices for different units of the same good

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Price Discrimination: Pricing to Extract Surplus

To be able to price discriminate: A firm must have some market power

If not, a price above marginal cost will result in zero sales The good or service must be difficult to resell

Otherwise few sales will occur at the higher price Firm must also be able to distinguish sales for which the

purchasers have a high willingness to pay from those they have a low willingness to pay

A monopolist can perfectly price discriminate if he knows perfectly the customer’s willingness to pay for each unit he sells and can charge a different price for each unit

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Price Discrimination: Pricing to Extract Surplus

Usually, a firm does not perfectly know a customer’s willingness to pay

Two different ways to distinguish purchases for which the customer has a high vs. a low willingness to pay

Price discrimination is based on observable customer characteristics when a firm can distinguish consumers with a high vs. low willingness to pay

Price discrimination is based on self-selection when the firm offers a menu of alternatives Designed so that customers will make choices based on their

willingness to pay In quantity-dependent pricing, the price a consumer

pays for an additional unit depends on how many units she has bought

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Perfect Price Discrimination

Under perfect price discrimination, the firm knows perfectly its customers’ willingness to pay

Can set the price for each individual consumer equal to her willingness to pay

Marginal revenue curve coincides with the market demand curve

Profit-maximizing sales quantity occurs where the market demand curve crosses the marginal cost curve

Monopolist produces the same quantity as would occur in a competitive industry Each consumer consumes the same quantity as they would

under perfect competition No deadweight loss

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Figure 18.2: Perfect Price Discrimination Sales Quantity

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Two-Part Tariffs

Two-part tariffs are another quantity-dependent pricing plan that allows a perfectly discriminating monopolist to maximize profit

With a two-part tariff, consumers pay a fixed fee plus a separate per-unit price for each unit they buy Examples: amusement parks, rental car companies

Commonly used by monopolists and firms whose market power falls short of monopoly

Advantage is simplicity: name just two prices To maximize profit, set per-unit charge equal to

marginal cost

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Figure 18.4: Profit with aTwo-Part Tariff

Per-unit charge equals marginal cost

Fixed fee is the consumer’s surplus at that per-unit price

Maximizes aggregate surplus

Leaves the consumer no surplus

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Sample Problem 1 (18.2):

If the ice cream company from figure 18.2 (page 669) sells to Juan (whose demand curve is shown on page 524) using a two-part tariff with a per-cone price on $1.50, what is the largest fixed fee it can charge Juan and still persuade Juan to make a purchase? How does its total revenue from Juan under this two-part tariff compare to its total revenue from Juan when it sells Juan four cones, each priced at Juan’s willingness to pay for it? What is its total profit from Juan?

Price Discrimination Based on Observable Characteristics

Most often a firm’s ability to price discriminate is imperfect

May be able to sort consumers into rough groups based on observable characteristics But know no more about their willingness to pay Cannot engage in quantity-dependent pricing because cannot

track purchases Example: small town movie theater with four consumer groups

(adults, seniors, students, kids) To maximize profit consider each group’s demand

curve separately Set price to maximize profit earned from that group

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Price Discrimination Based on Observable Characteristics

Set different prices whenever the groups have different elasticities of demand

Charge a higher price to groups with less elastic demand

Generally the group that will face the higher price is the one with the less elastic demand at the profit-maximizing no-discrimination price

Starting at that price, monopolist will: Raise the price of the less elastic group Lower the price of the more elastic group

Can find optimal prices and quantities for each group using algebra

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Figure 18.5:Profit-Maximizing Price to Two Groups

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Sample Problem 2 (18.4)

Suppose moviegoer’s demand functions are QS = 800 – 100P and QA = 1600 – 100P for students and other adults respectively. Marginal cost is $3 per ticket. What prices will the monopolist set when she can discriminate and when she cannot? How will discrimination affect her profit?

Welfare Effects of ImperfectPrice Discrimination

Profit is at least as large with discrimination as without Can always charge every group the same price, won’t charge different

prices unless it benefits the firm Price discrimination affects different groups of consumers

differently Worse off it my price rises as a result of discrimination, better off if it

falls Two main effects on consumer and aggregate surplus:

Different consumers pay different prices, inefficient because a consumer who faces a low price and decides to buy may have a lower willingness to pay than a consumer who faces a high price and decides not to buy

May encourage the monopolist to sell more, increase both consumer and aggregate surplus

Opposing effects can combine to either raise or lower consumer and aggregate surplus

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Welfare Effects of ImperfectPrice Discrimination

In Figure 18.7, total consumer surplus is smaller with discriminationThe gain to college students is smaller than the loss

to other adultsAggregate surplus is also smaller with

discriminationGain in profit ($800) is smaller than the loss in

consumer surplus ($1,200)The number of tickets sold is the same

But inefficiently distributed with discrimination

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Figure 18.7: Welfare Effects of Price Discrimination

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Sample Problem 3 (18.8)

What is the effect of discrimination on consumer and aggregate surplus in exercise 18.4?

Price Discrimination andMarket Power

In a competitive market, firms can’t price discriminatePrice discrimination is a sign of a market that is not

perfectly competitiveCan be difficult to determine whether price

discrimination exists in a marketDifferent prices may reflect cost differences

Market does not have to be very far from perfectly competitive to exhibit discrimination

Oligopolists may price discriminate more than monopolists

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Price Discrimination Based on Self-Selection

Often firms cannot distinguish between groups of consumers based on observable characteristics

Price discrimination may still be possibleOffer a menu of alternatives

If properly designed, customers with different willingness to pay will choose different alternatives

A common practiceExamples: supermarket discounts for shoppers who

clip coupons, wireless phone companies with multiple calling plans

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Quantity-Dependent Pricing and Self-Selection

Recall that a perfectly discriminating monopolist maximizes profit with a two-part tariff

This level of profit is not achievable when consumers’ characteristics are not directly observable

If given the choice between two plans with the same per-minute price, all consumers will opt for the low-demand (low fixed fee) plan Consumers will not self-select based on willingness to pay

The monopolist can often do better by raising the per-unit charge above its marginal cost

Can do even better by offering a menu of different two-part tariffs

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Figure 18.9: Two-Part Tariff with Two Types of Consumers

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Clearvoice Wireless Example

Clearvoice is a wireless telephone monopolist in a rural area

Two types of consumers, high-demand and low-demand Distinct monthly demand curves for wireless minutes for each

group Clearvoice’s marginal cost is 10 cents If could observe consumer characteristics, would offer

two-part tariff with 10-cent per-minute price Fixed fee for low-demand customers: $8 Fixed fee for high-demand customers: $40.50

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Profit-Maximizing Two-Part Tariff

Suppose Clearvoice wants to offer a single two-part tariff

Per-minute price of 10 cents and monthly fee of $40.50 High-demand customers accept Low-demand customers reject

Per-minute price of 10 cents and monthly fee of $8 All consumer accept

Which plan is better? If there are a large number of low-demand customers, $8

monthly fee is better May be even more profitable to raise per-minute fee

above marginal cost

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Profit-Maximizing Two-Part Tariff

If the monopolist plans on selling to both types of consumer it is always profitable to raise the per-unit price at least a little above marginal cost Regardless of the types’ relative proportions

Would like to extract some of high-demand consumers’ surplus without changing surplus of low-demand consumer (already zero) Raise per-unit price to get more surplus from high-demand

consumers Adjust fixed fee so low-demand consumers’ surplus is

unchanged The smaller the faction of low-demand consumer, the

more worthwhile it is to raise the per-unit price Deadweight loss from low-demand consumers increases

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Figure 18.10: Benefits of Raising the Per-Minute Charge

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Using Menus to Increase Profit

Can do even better by offering a menu of two-part tariffs, each designed to attract a specific type of consumerCan eliminate some deadweight loss by introducing

a second tariff planExtract more surplus from high-demand consumers

by making the low-demand plan less attractive to high-demand customers

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Eliminating Deadweight Loss of High-Demand Consumers

Suppose Clearvoice offers a pair of two-part tariffs One designed for low-demand consumers:

Per-minute price of 20 cents, fixed fee of $4.50 Second option intended to attract high-demand

customers: Per-minute price of 10 cents, equal to Clearvoice’s marginal

cost Fixed fee should be set as high as possible without causing

high-demand consumer to choose the other plan With menu of plans:

Firm profits are higher from high-demand consumers Profits from low-demand consumers are the same Deadweight loss from high-demand consumers is eliminated

and extracted as surplus

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Figure 18.11: Menu ofTwo-Part Tariffs

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Making the Low-Demand Plan Less Attractive

Can increase profit even more by making the low-demand plan less attractive to high-demand consumers That plan determines the fixed fee the firm can charge a high-

demand consumer It is the level that makes the high-demand consumer

indifferent between the two plans Limit the number of minutes a consumer can purchase

in the 20-cent-per-minute plan Set the limit equal to the number low-demand consumers want Will have no effect on value a low-demand consumer derives Make the plan less attractive to high-demand customers Will increase the fixed fee Clearvoice can charge high-demand

consumers for the 10-cent-per-minute plan

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Figure 18.12: Capping Minutes

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Menu of Two-Part Tariffs

A firm can often profit by offering a menu of choicesDesigned for different types of consumers

To maximize its profits, firm should try to make each plan attractive to one group onlyAnd unattractive to other consumer groups

Firm benefits from setting the per-unit price in the plan intended for consumers with the highest willingness to pay equal to the marginal costEliminates deadweight loss for those consumers

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Sample Problem 4 (18.12):

Air Shangrila sells to both tourist and business travelers on its single route. Tourists always stay over on Saturday nights, while business travelers never do. The weekly demand function of tourists is QT = 6,000 – 10P, and the weekly demand function of business travelers is QB = 1,000 – P. If the marginal cost of a ticket is $200, what prices should Air Shangrila set for its tourist and business tickets? If the government passes a law that says all tickets must cost the same, what price will Air Shangrila set?