Managerial Application 123

Do Colleges Price Discriminate?

Most college students receive financial aid. At many colleges, the average financial aid recipient comes from a family with annual income in excess of $50,000—and many came from families with incomes exceeding $100,000. As a result, some economists suggest that college financial aid is not about "needy students" but is instead a means of price discrimination designed to extract the largest net amount from students, their families, and the government.

Some economists argue that colleges levy a list price (tuition) set far above what most people can pay and then offer varying discounts (financial aid) so that each customer is charged what the traffic will bear. Financial aid is available when the cost of college exceeds the "expected family contribution," a measure based on family income, assets, the number of children, and so on. Even a small college could lose millions of dollars in federal aid if it kept tuition affordable. According to critics, federal subsidies and virtual exemption from antitrust laws have produced skyrocketing college costs and price discrimination. Economist Milton Friedman estimates that colleges could operate at a profit by charging half of what the Ivy League schools charge.

In defense of current financial aid practices, school administrators point out that many would be unable to afford college without some cross-subsidization among students. Private schools also use endowment income to supplement student tuition and fees, whereas public colleges and universities enjoy substantial tax-revenue income. Even the premiums paid by out-of-state students at leading state universities fail to cover fully allocated costs per student. However, average costs may not be relevant for pricing purposes. The marginal cost per student is often nearly zero, and even very low net tuition-plus-fee income can often make a significant contribution to overhead. From an economic perspective, the pricing practices of colleges and universities may in fact be consistent with the theory of price discrimination.

See: Lynn Asinof, "Colleges Clamp Down on Financial Aid, Making Haggling a Difficult Approach," The Wall Street Journal Online, April 11, 2002 (

Consumers' Surplus = 1/z [(80 X ($100 - $20)] = $3,200

Thus, $3,200 is the maximum membership fee the golfer in question would pay to play 80 rounds of golf per year when modest additional "greens fees" of $20 per round are charged. It follows that the profit-maximizing two-part pricing scheme is to charge each player an annual membership fee of $3,200 per year plus "greens fees" of $20 per round played. Total golf course revenues of $4,800 represent the full value derived from playing 80 rounds of golf per year, cover marginal costs of $1,600 (= $20 X 80), and result in a $3,200 profit for the golf course.

Throughout this discussion it has implicitly been assumed that the seller must enjoy at least some market power in order to institute any two-part pricing scheme. Otherwise, competitors would undercut the amount of annual membership fees, and per-unit prices would converge on marginal costs. Therefore, it is unsurprising that high golf membership fees tend to be most common in urban areas where conveniently located golf courses are in short supply. In outlying or rural areas, where restrictions on the location of new golf courses are less stringent, large membership fees tend to be relatively rare.

bundle pricing

A lump sum amount equal to the total area under the demand curve when P = MC

Bundle Pricing

Another way firms with market power enhance profits is by a variant of two-part pricing called bundle pricing. If you've ever purchased a 12-pack of soft drinks, a year's supply of tax preparation services, or bought a "two-for-the-price-of-one" special, you have firsthand experience with the bundle pricing concept. When significant consumers' surplus exists, profits can be enhanced if products are purchased together as a single package or bundle of goods or services. Bundles can be of a single product, like soft drinks or legal services, or they can be comprised of closely related goods and services. For example, car manufacturers often bundle "luxury packages" comprised of new car options like power steering, power brakes, automatic transmissions, tinted glass, and so on. Similarly, car dealers often bundle services, like oil changes, transmission fluid changes, radiator flushes, and tune-ups at a "special package price."

In the case of a single product sold in multiple-unit bundles, the optimal bundle price is derived in a manner similar to the optimal two-part price calculation described in Figure 12.3. As in the case of two-part pricing, the optimal level of output is determined by setting price equal to marginal cost and solving for quantity. Then, the optimal bundle price is a single lump sum amount equal to the total area under the demand curve at that point. In Figure 12.3(b), for example, the optimal bundle price of $4,800 would include the total value of consumers' surplus generated with a single per-unit price (or $3,200), plus total cost (or $1,600).

Optimal pricing for bundles of related but not identical products is figured in an analogous manner. Again, the total amount charged equals the value of the total area under the demand curve at the optimal output level, where output is defined as a bundle of related goods or services. As in the case of two-part pricing, the optimal level of output is determined by setting price equal to marginal cost and solving for quantity. Then, the optimal bundle price is simply a lump sum amount equal to the total area under the demand curve at that activity level. In the case of related but not identical products, bundle pricing is sometimes used because firms are not able to precisely determine the amounts different consumers are willing to pay for different products. If managers had precise information about the value of each individual product for each individual consumer, the firm could earn even higher profits by precisely tying the price charged to the value derived by each customer.

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