Price Discrimination Handout PDF

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This is a very helpful handout from U of T to understand price discrimination....

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

ECO100: Introductory Economics Price Discrimination We start with the monopolist “constrained to charging the same price for all units,” depicted in Figure 1. It faces the demand curve MW T P , and to make matters simple, we assume this monopolist has a constant marginal cost of production equal to C . Because the monopolist has to charge the same price for all units, the marginal revenue must be strictly less than the demand curve. This reflects the fact that every time the monopolist decides to sell an additional unit, it has to lower its price, thus giving a discount to all those consumers who would have purchased at the higher price. The single-price monopolist chooses the quantity where the marginal cost of selling one more unit (M C = C ) equals the marginal benefit of doing so (MR), and charges the price (P M ) resulting in exactly ∗ units sold. QM

Figure 1: The single-price monopolist. From the perspective of efficiency (i.e., maximizing total surplus), the problem with monopoly is that the monopolist sells too few units. Efficiency requires transacting all units where the societal benefit is at least as large as the societal cost. Under the assumption that all costs are borne by the firm and all benefits accrue to the person getting the item, the efficient outcome Qeffic occurs at the intersection of the firm’s marginal cost curve and ∗ market demand. The monopolist, however, stops at QM , resulting in deadweight loss: the ∗ surplus that would have been generated had units from QM to Qeffic been transacted. One way of looking at the market failure under monopoly is that the monopolist cannot appropriate the surplus it would create by producing more. To illustrate, consider Ms. Qm+1. As shown in Figure 1, her willingness to pay is less than P m , so she does not get an item. Selling to Ms. Qm +1 is enticing: her willingness to pay is larger than the monopolist’s costs of providing an item. However, we assumed that the monopolist must sell all units at the

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

same price. The fact that the marginal revenue1 of selling unit Qm +1 is less than M C = C tells us that it would not be profitable to lower the price in order to sell to Ms. Qm + 1. Of course, if there was only a way to sell to Ms. Qm +1 without having to reduce the price on the first Qm units . . . Price discrimination is the business practice of not selling all units at the same price. In what I call “classic” price discrimination, different consumers pay different prices (i.e., it is between-consumer price discrimination). A broader interpretation of price discrimination also includes those cases where a particular consumer effectively pays a different amount for each unit purchased (i.e., within-consumer price discrimination). In what follows, we first consider classic price discrimination, and then look at the case where a consumer does not face a fixed per-unit price. Before getting into details, a brief note. My use of “monopolist” is somewhat misleading. In order for a firm to price discrimination, it is not necessary that it is a monopoly (i.e., it is the sole firm in the market). Rather what is necessary is market power. That is, if the firm faces a downward sloping demand curve, whether or not it is truly a monopolist, any of these price discrimination strategies may be available to it. 1 Classic Price Discrimination In this section, I implicitly, and sometimes explicitly, assume that each consumer in the market demands one and only one unit. The downward sloping market demand would in this case stem from the fact consumers vary in their willingness to pay for the one item: some are willing to pay a lot, others not so much. I do this solely because I think it helps with the intuition. The ideas in this section work just fine when each consumer has a downward sloping demand, but consumers differ in their elasticity of demand: some consumers demand the good rather inelastically while other consumers are rather responsive to price. The essence of classic price discrimination is straightforward: the monopolist charges a high price to those consumers with a high willingness to pay, and charges a low price to those consumers with a low willingness to pay. (In the more general case where a consumer may demand multiple items, the monopolist charges a high price to consumers with relatively inelastic demand, and charges a lower price to those consumers with more elastic demand.) It’s great work if you can get it, but in order to do so, the monopolist has two hurdles. One practice that can severely limit a monopolist’s ability to price discriminate is arbitrage: the practice of buying a good in a market where the price is low and reselling it in a market where the price is high. It is easy to see why this can be a problem. You have a great plan to charge a high price to the “Highs” and a low price to the “Lows.” Mr. LowA then has a brilliant idea: buy from you at the low price, and resell it to the Highs at a medium price. Every time he does so, you are missing out on the extra money you could have made by selling directly to the Highs. We will not say too much more about arbitrage except: 1. The bigger the arbitrage problem, the less desirable price discrimination. 2. It may be in a firm’s best interest to take steps to limit arbitrage by making it less 1

Remember that the M R curve was derived under the assumption that all units are sold at the same price.

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

lucrative.2 The more interesting hurdle is the fact that in order to price discriminate, the monopolist needs to figure out who is really a high-WTP customer (i.e., one with inelastic demand) and who is really a low-WTP customer (i.e., one with elastic demand).3 Clearly, asking the customer directly is not “incentive compatible.” The current price of 128GB iPad Air is $629. If Apple started selling them for $300 to any customer who “testifies” that she is unwilling to pay $629 but is willing to pay $300, I am guessing that it will not sell very many at $629.4 1.1

WTP stamped on forehead: First-degree price discrimination

The first type of price discrimination we consider assumes away the need to figure out a customer’s willingness to pay. In this “model,” a customer’s WTP is figuratively stamped on her forehead. In this case, the monopolist’s job is easy. Customer i pays Pi , with Pi = max {W T Pi , C } , where C is the monopolist’s marginal cost and W T Pi is customer i’s willingness to pay. For example, assume C = $10. Customer 1 comes in with her willingness to pay stamped on her forehead: $25. The monopolist says that the price is $25, and as the customer is willing to pay $25, she pays $25 and leaves with the item.5 Customer 2 comes in with his WTP of $8 stamped on his forehead. The monopolist tells him the price is $10. Customer 2 leaves without an item. This scheme where the customer pays her willingness to pay (as long as it is at least as large as the marginal cost) is called first-degree price discrimination. The outcome is “interesting.” Referring back to Figure 1, Q∗m units are transacted, with only those with the highest willingness to pay getting the item. The outcome is therefore efficient (total surplus is maximized). While nifty in theory, this scheme scores pretty low on the feasibility scale. It is hard to find situations where the monopolist can figure out a consumer’s willingness to pay with such precision. (See below for some exceptions.) It is worthwhile considering first-degree price discrimination because it starkly highlights a couple of general features of price discrimination. 1. Price discrimination may increase total surplus. In this case, price discrimination definitely increases total surplus: everyone who was getting the good from the “single-price monopolist” still gets the good, and consumers who were not getting the good with a single-price monopolist (but are willing to pay at least C) now get the good. Any time this happens, surplus must increase. 2

For example, Apple limits the number of computers a consumer can buy at the lower “education” price. Grammarians will note that the hyphen is necessary for high-WTP customer, as the high modifies WTP and not the customer. 4 This is again the issue of “incentive compatibility”. Asking consumers is to state their willingness to pay is not incentive compatible as consumers have an incentive to lie. As much as some people love Apple products, I do not think most would have a problem lying to a Apple. 5 Some people are troubled by the fact that the customer is indifferent between buying an not buying. In that case, let us say the monopolist charges this customer $24.99. In that case, the customer is strictly better off purchasing. 3

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

2. Firms love it! Price discrimination increases producer surplus. 3. At least some consumers are worse off. With the single-price monopolist, demands represented by 0 to Q∗m got surplus. Under perfect first-degree price discrimination, the monopolist appropriates all consumer surplus. While perfect first-degree price discrimination is definitely a theoretical curiosity, there are a few real-world examples of producers approximating the scheme. One close situation is financial aid at U.S. colleges, especially elite colleges and universities. A year at Harvard costs approximately $72,576 for all expenses. If you are not able to pay, you and your parents complete a financial aid form, and Harvard calculates how much you can pay and that is all you pay. It helps that in addition to filling out this form, you and your parents need to submit tax forms.6 A second example is psychotherapists. Many report using a sliding scale where the therapist reduces the fees paid by those patients less able to pay. In this case, I guess therapists are counting on the fact that lying to your therapist is a pretty bad strategy if you want therapy to be successful. 1.2

Monopolist sorts customers: Third-Degree Price Discrimination

The next form of price discrimination, third-degree price discrimination, relies on the monopolist identifying some observable, and not easily modifiable, customer characteristic that is correlated with willingness to pay (or elasticity of demand). The monopolist then charges a low price to those who can prove membership in the low-willingness-to-pay (i.e., elastic demand) cohort, and a higher price to all others. This is best demonstrated with an example. There are some instances where the exact same drug is approved for use both for humans and for animals. Although somewhat dated, a U.S. congressional study in 2000 reported that for eight then popular drugs approved for use in both markets, manufacturers charge twice as much when the drug is intended for human use. Classic third-degree price discrimination. It is easily observable whether the patient is, in fact, a dog or cat.7 Furthermore, one’s species ranks pretty high to the “hard to modify” scale.8 The fact that drug manufacturers charge a higher price in the human market is evidence that the average U.S. consumer with a sick child has more inelastic demand for an antibiotic than the average U.S. consumer with a sick pet.9 Further examples abound: Student discounts Many places offer students a discount upon presentation of a student ID. In general, students are more price sensitive than their gainfully employed counterparts.10 6 Given the low possibility of being audited, economists have found that Americans are surprisingly honest about paying their taxes, perhaps even irrationally honest. 7 In practice, you would get the low pet-use price by buying directly from your veterinarian, who is not licensed to prescribe drugs for humans. 8 Trust me, you are not going to fool a veterinarian with that chipmunk costume. 9 Clearly my wife is not the average consumer. Before accusing her of child abuse, I will note that we do not have children, only very-well-treated dogs. 10 Arbitrage alert! Students get a 20% discount at L’Espresso Bar Mercurio. How about you buy a coffee from Mercurio, and I pay you the regular price minus 10%. I am guessing that this is not generally worth either of our efforts.

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

Senior citizen discounts Many businesses offer discounts to senior citizens. The elasticity of demand from senior citizens stems from two sources. Many live on a fixed income lower than they had during their working years. Second, and at least as important, the modal senior who is not employed has a lot of time on her hands (low opportunity cost of time), and many are willing to use this time to search for bargains. Mathematica Mathematica is the mother-of-all math software programs. Are you a corporate user? It will cost your firm $2,495 for standard Mathematica.11 If you are a government user, standard Mathematica costs “only” $1,995. As an education user, Prof. Gazzale can pick up his very own copy for $1,095. But wait, you, as a student, can have your very own copy of Mathematica for $139.95. Clearly the fine folks at Mathematica are not too concerned about arbitrage . . . In all cases, the firm has identified an attribute that is verifiable and hard to fake. Importantly, this attribute is correlated with willingness to pay (i.e., a customer’s elasticity of demand). By correlated, we mean that those with the attribute will have, on average more elastic demand than those without the attribute. The firm then charges a lower price to the group with the more elastic demand and a higher price to the group with more inelastic demand. Of course “correlated with WTP” is not the same as “perfectly indicative of WTP.” If L’Espresso Bar Mercurio did not offer a student discount, many students would still get their caffeine fix from them. This is money “left on the table” by price discrimination. Assuming Mercurio is wise in their price discrimination strategy, the extra sales made by charging a lower price to a group which, on average, has more elastic demand will make up for the fact that some students would have purchased absent the discount. 1.3

Must price discrimination increase total surplus?

We saw that first-degree price discrimination increased total surplus. What we will show in this section is that other forms of price discrimination need not increase total surplus. Importantly, we will identify the two opposing forces at play. Consider the practice of charging different prices for a drug depending on whether it is prescribed for humans (Phuman ) or their pets (Ppet), with Phuman > Ppet . Now, let us assume that this practice is outlawed: the monopolist must charge the same price, Pcombined, for both markets. Intuitively, the price that the monopolist would charge if it could not price discriminate would fall somewhere between the high price for humans and the lower prices for their pets: Phuman > Pcombined > Ppet . Now let’s go in reverse: start from no price discrimination and contemplate the surplus effect of allowing price discrimination. The good effect: compared to no price discrimination, allowing price discrimination lowers the price in the veterinary market, and thus increases sales of the drug in the veterinary market. The bad effect: compared to no price discrimination, allowing price discrimination increases the price in the human market, and thus decreases sales of the drug in the human market. The overall effect is more nuanced. The new sales due to price discrimination come from 11

A juiced-up “Enterprise” version can be yours for only $6,995.

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

the relatively low-WTP veterinary customers.12 We are gaining those who were not willing to purchase at Pcombined , but are now willing to purchase now that the price has decreased to Ppet . On the other side, introducing price discrimination causes us to lose relatively highWTP consumers in the human market: those who would have bought at Pcombined but no longer purchase when the price rises to Phuman . Holding quantity constant, taking items from consumers who are willing to pay a lot and giving them to consumers who are willing to pay less will decrease total surplus. Thus, “it depends” is the answer to the question of whether price discrimination will increase total surplus. We can, however, state a general rule. In order for price discrimination to have a shot at increasing surplus, the practice must increase the total number of units sold. In third-degree price discrimination, this increase in quantity must also make up for the fact that this practice replaces high-WTP consumers with relatively low-WTP consumers. Finally, we can now reassess first-degree price discrimination. Yes, the consumers added are low-WTP consumers (i.e., those who were unwilling to pay Pm∗ ), but importantly, the high-WTP consumers still purchase. 1.4

Second-degree price discrimination: consumers sort themselves

The next form of price discrimination, second-degree price discrimination, is a little harder to wrap one’s mind around. Once you do, however, you will see second-degree price discrimination everywhere. In second-degree price discrimination, the monopolist sells multiple versions of its products, and consumers sort themselves. In the two version case, it sells a “sweet” version for Psweet , and a “degraded” version for Pdegraded , with Psweet > Pdegraded . Done correctly, those with more inelastic demand purchase the sweet product and the more price sensitive purchase the degraded product. Not following? Let’s consider the iPad. In my simple model of iPad demand, everyone likes gigabytes. When it comes to price sensitivity, however, we have one group of customers who are rather price sensitive and another group of customers who are rather price insensitive. Apple then prices a 32GB iPad at $499 ($15.59 per GB) and a 128GB iPad at $629 ($4.91 per GB). Loving their GBs and being, by definition, price insensitive, the inelastic demand group buys the 128GB iPad. While the price sensitive group loves the idea of a 128GB iPad, they opt for the 32GB iPad as money is “more important” than GBs. Thus, pretty much everywhere we see a quantity discount, we are seeing second-degree price discrimination in action. The more price sensitive pay a lower overall prices, but counterintuitively they pay a higher price per unit. Less quantity is only one area in which we see “degraded” products. A view of seconddegree price discrimination going beyond quantity discounts allows us to make sense of a variety of business practises. One great example is airline pricing, where people sitting next to each other might have paid markedly different prices. A seat in an airplane going from city A to city B is only one part of the “bundle” of attributes purchased with a ticket. Other attributes include: ability to purchase at the last minute; ability to change itineraries at the last minute; and ability to return home on Friday and not spend the weekend at your 12

For better or worse, in calculating surplus, we are considering the WTP of the pet owner and not the

pet.

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University of Toronto Department of Economics

ECO101 Robert Gazzale, PhD

destination. All of these attributes are valued, but they are more valued by the business traveller than by the vacation traveller. In general, business travellers have more inelastic demand: driving is time consuming and business travellers have a high opportunity cost of time; if they need to go to city B, a flight to city C is a really poor substitute; and perhaps most importantl...