Table of Contents
Perloff 11.8, 12; WB 21.
In models of perfect competition, there is a "law of one price" — any firm or consumer offering to trade at a different price would either be worse off or find no takers. However, non-uniform pricing is typical in monopolies and oligopolies.
We discuss why non-uniform pricing is used, look at a few very special cases, and note that it can lead to efficient outcomes.
Pricing behavior has been classified in many different ways.I have tried to stay away from the terminology as much as possible, as we will only study a couple of pricing problems in depth.1
A wide range of pricing practices have been observed and studied; only a small fraction are mentioned below, appearing in boxes.
How can setting different prices help the firm? The potential answers are…
- Costs. It saves money.
- Strategy. It improves the firm's profits by changing the behavior of other firms.
- Direct discrimination. The seller makes customized offers using what she knows about each buyer's WTP.
- Indirect discrimination. The seller makes a menu of offers, and the buyer's WTP is revealed through his choice.
Often more than one of these will be at work. The last two cases describe price discrimination — setting non-uniform prices to take advantage of consumers.2
It is worthwhile to remember that non-uniform pricing may simply reflect costs.
Non-uniform (and uniform) pricing for strategic reasons has long been an area of active research.
Collusion or price-fixing. How can pricing policies can be used to maintain collusion between sellers? In particular, can firms that violate the price-fixing agreement be effectively punished by a price war? From game theory, we know that if there is only weak punishment for breaking the agreement, it is more tempting.
“Predatory” pricing. How can pricing policies help current firms keep out potential competitors?
Direct price discrimination
When the firm uses what it knows about each buyer to make customized price offers, it is directly discriminating. This requires
- …consumers with different WTPs — either one buyer vs another; or the first unit vs the second,
- …market power — the ability to price above MC, and
- …some way of preventing or controlling resale.
Why are these conditions necessary? (1.) If all buyers have the same WTP, there is no benefit from charging multiple prices. (2.) If the firm cannot price above marginal cost, it certainly cannot charge multiple prices. (3.) If consumers can trade the good among themselves, those charged the lowest price can resell to those with a higher price, cutting out the firm's hoped-for profits.
Note that the firm has to have market power, but it does not have to be a monopolist. Oligopolists also practice price discrimination.
Perfect price discrimination
When the firm knows everything about every buyer, it can charge the full WTP for each unit sold. This is also called first-degree price discrimination (1DPD).
This is a special case of perfect price discrimination because the firm is using the best imaginable policy, extracting all the buyers' surplus. By capturing all the surplus, this non-uniform pricing policy eliminates the dead weight loss we measured earlier. In other words, it is efficient. However, this result rests on the strong assumptions (i) that the firm knows everything about the Demand of every buyer and (ii) that it can prevent resale.
Indirect pricing policies, like two-part tariffs, can also achieve efficient outcomes.
- Is perfect price discrimination efficient?
- Given a Demand curve and a cost function for a monopolist, calculate the CS, PS and DWL of perfect price discrimination.
Imperfect price discrimination
When the firm does not know everything, but still uses some information about each buyer to set prices — for example, it knows that students have lower incomes — it is directly, but imperfectly price discriminating. This is also called third-degree price discrimination (3DPD). The classic case is that of a monopolist producing for two types of consumers, as seen in WB 21.
- Given a cost function and Demand for two types of consumers, find the monopolist's optimal sales and prices for each type of consumer P1M,P1M,q1Mq2M.
Discrimination can be based on the characteristics of the buyer, or on some of the buyer's actions that do not change in response to the seller's pricing policies.
Where they live. The Economist's Big Mac index documents McDonald's non-uniform burger pricing.
Age. The old and the young get discounts at movie theaters.
Homeownership and marriage. Homeowners and married couples might (I don't know) get better deals on car loans, but they won't decide whether or not to marry or buy a house based on this price difference.
Credit-card ownership and travel. McAfee mentions that "special offers" are made to frequent fliers and credit card-holders.
In each of these cases, the seller could argue that her pricing is based on costs. The Big Mac Index, for example, is designed to illustrate exchange rates, not price discrimination.
Except for age, one could argue that these consumer-level factors are influenced by the firm's pricing policies. For example, a consumer might be less likely to move to China if McDonald's raises the price of Big Macs there; or might marry just to get better loan offers. If that is so, it is indirect price discrimination.
Indirect price discrimination
If the seller cannot see which buyers are high-value and which are low-value, it might create a menu of choices available to all consumers. The hope is that the high-value buyers will select the high-price items off the menu, and low-value buyers will opt for the cheap items. In other words, the seller hopes that buyers will reveal their WTPs through their purchasing decisions. This is also called second-degree price discrimination (2DPD) or self-selection.
Indirect discrimination requires
- …consumers with different WTPs, and
- …market power.
The firm does not need to prevent resales because each consumer chooses what they get. In contrast, with direct discrimination the seller chooses what each consumer gets, and disgruntled consumers may want to buy on the resale market.
We talk about high-value and low-value consumers below, but there could be a range of consumers with different WTPs.
Choice of how much
Membership discounts. The seller can charge a different price to consumers who pay a fixed membership fee PA. As seen earlier, this leads to a kinked budget line.
Two-part tariffs. Two part tariffs are a special, extreme case of membership discount. The consumer cannot buy any of the good until first paying an access fee PA. After paying the access fee, the consumer can purchase the good at the usage price PU. The seller's optimal pricing policy PA* and PU* will set the usage fee efficiently PU*=MC and extract all of the consumer surplus PA*.
Quantity discounts. The seller can offer lower per-unit prices to consumers that buy more units. Quantity premiums — where the seller charges more to big buyers — are also possible.
- Given a Demand curve and a cost function for a monopolist, find the monopolist's optimal two-part tariff, and calculate the CS, PS and DWL.
Choice of when
Yield management with a fixed supply of perishable goods. Hotels, live-entertainment theaters and airlines may price cheaply if there is excess supply of tickets or rooms close to when these goods perish. If this works out well, high-value consumers will buy at the early, high prices.
Early adopters. Apple and Nintendo charge a premium to consumers who are willing to pay extra to buy early.
Choice of which version
When separating high- and low-value buyers through their purchasing decisions, it is often useful to create different versions of a product, some of which are of deliberately poor quality and yet no cheaper to produce; and others, which are very high quality but cost little extra. This product-line pricing or versioning may help the firm exploit its more loyal, high-value consumers while still reaching many low-value customers.
Damaged goods. A ticket seller can attract low-value consumers by offering cheaper seats. However, it has make these seats very unappealing to prevent high-value buyers from switching. Jules Dupuit first observed this for riding on the train: riding coach is so unpleasant that those who can afford it ride first-class. It is also seen in computer chips, computer software (think Windows Starter Edition).
Augmented goods.3 Similarly, the seller can create especially appealing products to draw the high-value buyers. Examples include adding bonus content to special edition DVDs, books and video games; and adding amenities like free drinks on first-class flights.
Choice of combination
Bundling. The seller may set a price on a "bundle" of two or more goods. Pure bundling is forcing the consumer to buy two goods together by refusing to sell one or both of them separately. Mixed bundling is offering the consumer a deal for buying two goods together, so that the price of the bundle is not equal to the sum of the goods' individual prices.
Tying complementary goods. The purchase of two goods may be tied by legal contract. For example, Perloff says renters of IBM's punch card machines had to agree not to buy punch cards made by other companies. Or two goods may be tied by intentional incompatibilities. For example, razors might be incompatible with razorblades made by other companies; and similarly for printers and ink.
- Perloff, Chapter 12 ``Pricing''
- Preston McAfee's "Price Discrimination", 2008 written for the American Bar Association
- Arbitrage by bootlegging cigarettes (WSJ, July 2009)
- Coupons. This American Life, October 2009 "Someone Else's Money" (listen for free online) Act One. "One Pill Two Pill, Red Pill Blue Pill." Planet Money's Chana Joffe-Walt explains why prescription drug coupons could actually be increasing how much we pay, and prevent us from even telling how much drugs cost.