First Degree Price Discrimination

Under first-degree price discrimination, or perfect price discrimination, each unit of the good is sold to the individual who values it most highly, at the maximum price that this individual is willing to pay for it.

Consider Figure 25.1, which illustrates two consumers' demand curves for a good. Think of a reservation price model for demand where the individuals choose integer amounts of the goods and each step in the demand curve represents a change in the willingness to pay for additional units of the good. We have also illustrated (constant) marginal cost curves for the good.

A producer who is able to perfectly price discriminate will sell each unit of the good at the highest price it will command, that is, at each consumer's reservation price. Since each unit is sold to each consumer at his or her reservation price for that unit, there is no consumers' surplus generated in

WILLINGNESS TO PAY

WILLINGNESS TO PAY

MC

WILLINGNESS TO PAY

QUANTITY

QUANTITY

First-degree price discrimination. Here are two consumers' demand curves for a good along with the constant marginal cost curve. The producer sells each unit of the good at the maximum price it will command, which yields it the maximum possible profit.

this market; all the surplus goes to the producer. In Figure 25.1 the colored areas indicate the producer's surplus accruing to the monopolist. In an ordinary competitive market setting these areas would represent consumers' surplus, but in the case of perfect price discrimination, the monopolist is able to appropriate this surplus for itself.

Since the producer gets all the surplus in the market, it wants to make sure that the surplus is as large as possible. Put another way, the producer's goal is to maximize its profits (producer's surplus) subject to the constraint that the consumers are just willing to purchase the good. This means that the outcome will be Pareto efficient, since there will be no way to make both the consumers and the producer better off: the producer's profit can't be increased, since it is already the maximal possible profit, and the consumers' surplus can't be increased without reducing the profit of the producer.

If we move to the smooth demand curve approximation, as in Figure 25.2, we see that a perfectly price-discriminating monopolist must produce at an output level where price equals marginal cost: if price were greater than marginal cost, that would mean that there is someone who is willing to pay more than it costs to produce an extra unit of output. So why not produce that extra unit and sell it to that person at his or her reservation price, and thus increase profits?

Just as in the case of a competitive market, the sum of producer's and consumers' surpluses is maximized. However, in the case of perfect price discrimination the producer ends up getting all the surplus generated in the market!

We have interpreted first-degree price discrimination as selling each unit at the maximum price it will command. But we could also think of it as selling a fixed amount of the good at a "take it or leave it" price. In the

First-degree price discrimination with smooth demand Figure curves. Here are two consumers' smoothed demand curves 25.2

for a good along with the constant marginal cost curve. Here the producer maximizes profits by producing where price equals marginal cost, just as in the case of a competitive market.

case illustrated in Figure 25.2, the monopolist would offer to sell units of the good to person 1 at a price equal to the area under person l's demand curve and offer to sell x\ units of the good to person 2 at a price equal to the area under person 2's demand curve £?. As before, each person would end up with zero consumer's surplus, and the entire surplus of A -f B would end up in the hands of the monopolist.

Perfect price discrimination is an idealized concept—as the word "perfect" might suggest—but it is interesting theoretically since it gives us an example of a resource allocation mechanism other than a competitive market that achieves Pareto efficiency. There are very few real-life examples of perfect price discrimination. The closest example would be something like a small-town doctor who charges his patients different prices, based on their ability to pay.

EXAMPLE: First-degree Price Discrimination in Practice

As mentioned earlier, first-degree price discrimination is primarily a theoretical concept. It's hard to find real-world examples in which every individual is charged a different price. One possible example would be cases where prices are set by bargaining, as in automobile sales or in antique markets. However, these are not ideal examples.

Southwest Airlines recently introduced a system called Ding that attempts something rather close to first-degree price discrimination.1 The

1 See Christopher Elliott, "Your Very Own Personal Air Fare," New York Times, August 9, 2005.

system uses the Internet in a clever way. The user installs a program on her computer and the airline sends special fare offers to the user periodically. The fares are announced with a "ding" sound, hence the system name. According to one analyst, the fares offered by Ding were about 30 percent lower than comparable fares.

But will these low fares persist? One might also use such a system to offer higher fares. However, that possibility seems unlikely given the intensely competitive nature of the airline industry. It's easy to switch back to standard ways of buying tickets if prices start creeping up.

25.3 Second-Degree Price Discrimination

Second-degree price discrimination is also known as the case of nonlinear pricing, since it means that the price per unit of output is not constant but depends on how much you buy. This form of price discrimination is commonly used by public utilities; for example, the price per unit of electricity often depends on how much is bought. In other industries bulk discounts for large purchases are sometimes available.

Let us consider the case depicted earlier in Figure 25.2. We saw that the monopolist would like to sell an amount x\ to person 1 at price A+ cost and an amount xi> to person 2 at price B+ cost. To set the right prices, the monopolist has to know the demand curves of the consumers; that is, the monopolist has to know the exact willingness to pay of each person. Even if the monopolist knows something about the statistical distribution of willingness to pay—for example, that college students are willing to pay less than yuppies for movie tickets—it might be hard to tell a yuppie from a college student when they are standing in line at the ticket booth.

Similarly, an airline ticket agent may know that business travelers are willing to pay more than tourists for their airplane tickets, but it is often difficult to tell whether a particular person is a business traveler or a tourist. If switching from a grey flannel suit to Bermuda shorts would save $500 on travel expenses, corporate dress codes could change quickly!

The problem with the first-degree price discrimination example depicted in Figure 25.2 is that person 1—■the high-willingess-to-pay person—can pretend to be person 2, the low-willingess-to-pay person. The seller may have no effective way to tell them apart.

One way to get around this problem is to offer two different price-quantity packages in the market. One package will be targeted toward the high-demand person, the other package toward the low-demand person. It can often happen that the monopolist can construct price-quantity packages that will induce the consumers to choose the package meant for them; in economics jargon, the monopolist constructs price-quantity packages that give the consumers an incentive to self select.

In order to see how this works, Figure 25.3 illustrates the same kind of demand curves used in Figure 25.2, but now laid on top of each other. We've also set marginal cost equal to zero in this diagram to keep the argument simple.

QUANTITY QUANTITY QUANTITY

Second-degree price discrimination. These are the demand curves of two consumers; the producer has zero marginal cost by assumption. Panel A illustrates the self-selection problem. Panel B shows what happens if the monpolist reduces the output targeted for consumer 1, and panel C illustrates the profit-maximizing solution.

As before, the monopolist would like to offer x® at price A and to offer x2 at price A -b B -f C. This would capture all the surplus for the monopolist and generate the most possible profit. Unfortunately for the monopolist, these price-quantity combinations are not compatible with self-selection. The high-demand consumer would find it optimal to choose the quantity x® and pay price A; this would leave him with a surplus equal to area B, which is better than the zero surplus he would get if he chose x2.

One thing the monopolist can do is to offer x2 at a price of A + C. In this case the high-demand consumer finds it optimal to choose x2 and receive a gross surplus of A -f B + C. He pays the monopolist A + C, which yields a net surplus of B for consumer 2—just what he would get if he chose x\. This generally yields more profit to the monopolist than it would get by offering only one price-quantity combination.

But the story doesn't end here. There's yet a further thing the monopolist can do to increase profits. Suppose that instead of offering x\ at price A to the low-demand consumer, the monopolist offers a bit less than that at a price slightly less than A. This reduces the monopolist's profits on person 1 by the small colored triangle illustrated in Figure 25.3B. But note that since person l's package is now less attractive to person 2, the monopolist can now charge more to person 2 for By reducing x?, the monopolist makes area A a little smaller (by the dark triangle) but makes area C bigger (by the triangle plus the light trapezoid area). The net result is that the monopolist's profits increase.

Continuing in this way, the monopolist will want to reduce the amount offered to person 1 up to the point where the profit lost on person 1 due to a further reduction in output just equals the profit gained on person 2. At this point, illustrated in Figure 25.3C, the marginal benefits and costs of quantity reduction just balance. Person 1 chooses x™ and is charged A; person 2 chooses x\ and is charged A + C + D. Person 1 ends up with a zero surplus and person 2 ends up with a surplus of B—just what he would get if he chose to consume x™.

In practice, the monopolist often encourages this self-selection not by adjusting the quantity of the good, as in this example, but rather by adjusting the quality of the good. The quantities in the model just examined can be re-interpreted as qualities, and everything works as before. In general, the monopolist will want to reduce the quality offered to the low end of its market so as not to cannibalize sales at the high end. Without the high-end consumers, the low-end consumers would be offered higher quality, but they would still end up with zero surplus. Without the low-end consumers, the high-end consumers would have zero surplus, so it is beneficial to the high-end consumers to have the low-end consumers present. This is because the monopolist has to cut the price to the high-end consumers to discourage them from choosing the product targeted to the low-end consumers.

EXAMPLE: Price Discrimination in Airfares

The airline industry has been very successful at price discrimination (although industry representatives prefer to use the term "yield management.") The model described above applies reasonably well to the problem faced by airlines: there are essentially two types of consumers, business travelers and individual travelers, who generally have quite different willingnesses to pay. Although there are several competing airlines in the U.S. market, it is quite common to see only one or two airlines serving specific city pairs. This gives the airlines considerable freedom in setting prices.

We have seen that the optimal pricing policy for a monopolist dealing with two groups of consumers is to sell to the high-willingness-to-pay market at a high price and offer a reduced-quality product to the market with the lower willingness to pay. The point of the reduced-quality product is to dissuade those with a high willingness to pay from purchasing the lower priced good.

The way the airlines implement this is to offer an "unrestricted fare" for business travel and a "restricted fare" for non-business travel. The restricted fare often requires advanced purchase, a Saturday-night stayover, or other such impositions. The point of these impositions, of course, is to be able to discriminate between the high-demand business travelers and the more price sensitive individual travelers. By offering a "degraded" product—the restricted fares—the airlines can charge the customers who require flexible travel arrangements considerably more,for their tickets.

Such arrangements may well be socially useful; without the ability to price discriminate, a firm may decide that it is optimal to sell only to the high-demand markets.

Another way that airlines price discriminate is with first-class and" coach-class travel. First-class travelers pay substantially more for their tickets, but they receive an enhanced level of service: more space, better food, and more attention. Coach-class travelers, on the other hand, receive a lower level of service on all these dimensions. This sort of quality discrimination has been a feature of transportation services for hundreds of years. Witness, for example, this commentary on railroad pricing by Emile Dupuit, a nineteenth century French economist:

It is not because of the few thousand francs which would have to be spent to put a roof over the third-class carriage or to upholster the third-class seats that some company or other has open carriages with wooden benches ... What the company is trying to do is prevent the passengers who can pay the second-class fare from traveling third class; it hits the poor, not because it wants to hurt them, but to frighten the rich ... And it is again for the same reason that the companies, having proved almost cruel to the third-class passengers and mean to the second-class ones, become lavish in dealing with first-class customers. Having refused the poor what is necessary, they give the rich what is superfluous.2

The next time you fly coach class, perhaps it will be of some solace to know that rail travel in nineteenth century France was even more uncomfortable!

EXAMPLE: Prescription Drug Prices

A month's supply of the antidepressant Zoloft sells for $29.74 in Austria, $32.91 in Luxembourg, $40.97 in Mexico, and $64.67 in the United States. Why the difference? Drug makers, like other firms, charge what the market

2 Translation by R. B. Ekelund in "Price Discrimination and Product Differentiation in Economic Theory: An Early Analysis," Quarterly Journal of Economics, 84 (1970), 268-78.

will bear. Poorer countries can't pay as much as richer ones, so drug prices tend to be lower.

But that's not the whole story. Bargaining power also differs dramatically from country to country. Canada, which has a national health plan, often has lower drug prices than the United States, where there is no centralized provider of health care.

It has been proposed that drug companies be forced to charge a single price worldwide. Leaving aside the thorny question of enforcement, we might well ask what the consequences of such a policy would be. Would the world overall end up with lower prices or higher prices?

The answer depends on the relative size of the market. A drug for malaria would find most of its demand in poor countries. If forced to charge a single price, drug companies would likely sell such a drug at a low price. But a drug for diseases that afflicted those in wealthy countries would likely sell for a high price, making it too expensive for those in poorer areas.

Typically, moving from price discrimination to a single-price regime will raise some prices and lower others, making some people better off and some people worse off. In some cases, a product may not be supplied at all to some markets if a seller is forced to apply uniform pricing.

25.4 Third-Degree Price Discrimination

Recall that this means that the monopolist sells to different people at different prices, but every unit of the good sold to a given group is sold at the same price. Third-degree price discrimination is the most common form of price discrimination. Examples of this might be student discounts at the movies, or senior citizens' discounts at the drugstore. How does the monopolist determine the optimal prices to charge in each market?

Let us suppose that the monopolist is able to identify two groups of people and can sell an item to each group at a different price. We suppose that the consumers in each market are not able to resell the good. Let us use p\{y\) and £2(2/2) to denote the inverse demand curves of groups 1 and 2, respectively, and let c(yi -f y2) be the cost of producing output. Then the profit-maximization problem facing the monopolist is max pi{yi)yi+p2{y2)y2~c{yi+y2).

yiiV2

The optimal solution must have

That is, the marginal cost of producing an extra unit of output must be equal to the marginal revenue in each market. If the marginal revenue in market 1 exceeded marginal cost, it would pay to expand output in market 1, and similarly for market 2. Since marginal cost is the same in each market, this means of course that marginal revenue in each market must also be the same. Thus a good should bring the same increase in revenue whether it is sold in market 1 or in market 2.

We can use the standard elasticity formula for marginal revenue and write the profit-maximization conditions as

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