The Efficiency of Metering Tie-Ins

Thom Lambert —  20 July 2011

Have you ever had to get on your hands and knees at Office Depot to find precisely the right printer cartridge?  It’s maddening, no?  Why can’t the printer manufacturers just settle on a single design configuration, the way lamp manufacturers use common light bulbs?

You might think the printer manufacturer is trying to enhance its profits simply by forcing you to buy two of its products (the printer + the manufacturer’s own ink cartridge) rather than one (just the printer).  But that story is wrong (or, at best, incomplete).  Printers tend to be sufficiently brand-differentiated to enable manufacturers to charge a price above their marginal cost.  Ink, by contrast, is more like a commodity, so competition among ink manufacturers should drive price down near the level of marginal cost.  A printer manufacturer could fully exercise its market power over its printer — i.e., its ability to profitably charge a printer price that exceeds the printer’s cost — by raising the price of its printer alone.  It could not enhance its profits by charging that price and then requiring purchasers to buy its ink cartridge at some above-cost price.  Consumers would view the requirement to purchase the manufacturer’s “supracompetitively priced” ink cartridge as tantamount to an increase in the price of the printer itself, so the manufacturer’s tie-in would effectively raise the printer price above profit-maximizing levels (i.e., profits would fall, despite the higher effective price, because too many “marginal” consumers — those who value the manufacturer’s printer the least — would curtail their purchases).

If printer buyers consume multiple ink cartridges, though, a printer manufacturer may enhance its profits by tying its printer and its ink cartridges in an attempt to price discriminate among consumers.  The manufacturer would lower its printer price from the profit-maximizing level to some level closer to (but still at or above) its cost, raise the price of its ink cartridge above the competitive level (which should approximate its marginal cost), and require purchasers of its printer to use the manufacturer’s (supracompetitively priced) ink cartridges.  This tack enables the manufacturer to charge higher effective prices to high-intensity users, who are likely to value the printer the most, and lower (but still above-cost) prices to low-intensity users, who likely value the printer the least.  Economists call this sort of tying arrangement a “metering tie-in” because it aims to meter demand for the seller’s tying product (the printer) and charge an effective price that corresponds to a buyer’s likely willingness to pay.

When a seller imposes a metering tie-in, higher-intensity consumers get less “surplus” from their purchases (the difference between their outlays and the amount by which they value what they’re buying), but total market output tends to increase, as the manufacturer sells printers to some buyers who value the printer below the amount the manufacturer would charge for the printer alone (i.e., the profit-maximizing, single-product price).

In his recent high-profile article, Tying, Bundled Discounts, and the Death of the Single Monopoly Profit Theory, Professor Einer Elhauge contends that metering tie-ins like the one described above tend to reduce total and consumer welfare.  He maintains that tie-ins of the type described are a form of welfare-reducing “third-degree” price discrimination.  He illustrates his point using a stylized example involving a printer manufacturer who sells consumers up to three ink cartridges. 

In a response to Professor Elhauge’s interesting article, I attempted to show that his welfare analysis turns on his assumption that printer buyers use only 1, 2, or 3 ink cartridges.  I demonstrated that Professor Elhauge’s hypo generates a different outcome — even assuming that this sort of metering tie-in is “third-degree” price discrimination — if ink cartridges are smaller, so that high-intensity consumers purchase 4 or more ink cartridges.

In some very helpful comments on my forthcoming response article, Professor Herbert Hovenkamp observed that there is a bigger problem with Elhauge’s analysis:  It assumes that the price discrimination here is third-degree price discrimination, when in fact it is second-degree price discrimination.

Below the fold, I discuss Elhauge’s analysis, my initial response (which remains valid), and the more fundamental problem Hovenkamp observed.  (And for those interested, please download my revised response article, which now contains both my original and Hovenkamp’s arguments.)

Since the time of A.C. Pigou, it has been conventional to categorize price discrimination schemes into “degrees.”  First-degree price discrimination occurs when a seller charges each buyer his or her “reservation price” — i.e., the amount  by which the buyer values the product at issue.  Such price discrimination is efficient, because each unit that is valued by at least as much as it costs to produce is produced and sold; there is no “deadweight loss” resulting from the failure to produce units that are valued by more than their incremental production cost.  Because sellers never have access to individuals’ actual reservation prices, first-degree price discrimination does not exist in the real world.

Third-degree price discrimination, by contrast, is quite common.  In a third-degree price discrimination scheme, the seller divides consumers into groups and charges a different price to the members of different groups.  For example, movie theatres usually charge lower prices to senior citizens and students, reasoning that members of those groups have lower reservation prices than do non-student (and thus presumably employed) adults.

Unlike first-degree price discrimination, third-degree price discrimination may reduce total welfare.  Such a welfare reduction may occur because third-degree price discrimination tends to reallocate output from higher-valuing to lower-valuing consumers (which reduces total welfare) and may not increase total market output enough to make up for that welfare loss.  Let me explain.

Unlike first-degree price discrimination, third-degree price discrimination is “imperfect,” because membership in a customer group (e.g., senior citizens) is merely a proxy for willingness-to-pay for the product at issue, and within any group of buyers, there will be a range of reservation prices.  Given that group members differ in their willingness-to-pay, each purchaser category in a third-degree price discrimination scheme will exhibit a downward sloping demand curve, indicative of the fact that more customers within the group will buy the product, and more units will be sold, as the price is reduced.  A monopolist engaged in third-degree price discrimination will therefore consider each group’s demand function and will seek to set each group’s price at the level that maximizes the monopolist’s profits on sales to that group.  At that group-specific price, some low-valuation members will be priced out of the market, even though their willingness-to-pay exceeds both the seller’s costs and the willingness-to-pay of members of favored groups.  For example, if a theatre owner charged $6 for a senior ticket and $9 for a regular adult ticket, a non-senior adult who valued admission at $8.50 would not secure a seat at the show, while a senior who valued admission at only $6.25 would.

Now, this reallocation of welfare from higher-valuing to lower-valuing consumers would not cause the price discrimination scheme to reduce total welfare if the discriminatory scheme sufficiently increased total market output.  For example, if there were lots of seniors who valued theatre admission by an amount just below the price the theatre owner would charge if it had to charge a single non-discriminatory price, but few non-senior adults who valued theatre admission between $6 and $9, the surplus created by bringing new seniors into the market could exceed the surplus lost by reallocating theatre admission from non-senior adults to seniors who valued it less.  But this sort of total output increase is not guaranteed.

In arguing that metering tie-ins tend to injure consumers, Elhauge first contends that such tie-ins constitute a form of third-degree price discrimination.  This is so, he says, because they involve “categorizing tying product buyers into different groups (based on their number of tied product purchases) and charging each group a different effective price for the same tying product (by inflating tied product prices).”  Elhauge then posits an example in which the purported “third-degree” price discrimination scheme reallocates output from higher- to lower-valuing consumers without increasing output.

Elhauge’s example involves a printer and ink producer who has market power over his printer but faces a competitive ink market.  Purchasers of the printer use either one, two, or three ink cartridges and vary linearly in the degree to which they value a cartridge’s worth of printing.  In a somewhat complicated analysis (which I will not summarize here — it’s on pages 432-34 of his article), Elhauge compares output, price, and surplus when the seller can charge only a single profit-maximizing printer price versus when he engages in a metering tie-in.  (In the tying situation, the seller lowers his printer price to the level of marginal cost, ties in ink cartridges, and sets the cartridge price at a level that achieves the effective profit-maximizing price for each group of consumers.)  Elhauge shows that, relative to the single  price scenario, the tie-in arrangement lowers market output, enhances the seller’s profits, and reduces both consumer and total surplus.  Notably, the tie-in Elhauge hypothesizes would not bring any additional consumers into the market.  It would, though, reallocate output from higher-valuing to lower-valuing consumers.

But isn’t this hypothetical, where buyers of the tying product consume, at most, three units of the tied product, awfully unrealistic?  Real-life metering tie-ins typically involve far more refined metering devices that segregate consumers into a much larger number of “groups.”  In my initial response to Elhauge’s article, I demonstrated that use of a “finer” meter — a slightly smaller ink cartridge that would divide the customer base into one-, two-, three-, and four-cartridge groups — would actually enhance total welfare.  It would do so because it would increase total market output by expanding sales to lower-valuation consumers who would not purchase the product at the uniform monopoly price.  (Again, I won’t go through the details of my analysis, which mirrors Elhauge’s but “shrinks” the size of the printer cartridge so that the most intense users purchase four cartridges.  The full analysis is on pages 37-41 of my paper.)

In his comments on my paper, Prof. Hovenkamp observed a further problem with Elhauge’s welfare analysis of metering tie-ins:  He wrongly assumes that they reflect third-degree price discrimination.  In actuality, Hovenkamp says, they involve second-degree price discrimination.  (See detailed analysis (with Erik Hovenkamp) here.) 

Second-degree price discrimination occurs when a seller charges various buyers different per-unit prices for his product but offers all buyers a single price schedule and allows them to select their per-unit price by altering their consumption patterns.  For example, a price schedule incorporating quantity discounts allows any consumer to opt for lower per-unit prices by achieving certain purchase targets.  Similarly, a fare schedule offering different prices for first- and second-class travel enables different consumers to choose different prices.  (While different classes of travel involve different amenities, a class-based fare schedule is still discriminatory in that the different fares involve different ratios of price to marginal cost — i.e., the seller mark-up is greater on first-class.)  Because metering tie-ins offer all consumers the same price schedule, they are best classified as second-degree price discrimination.

Unlike instances of third-degree price discrimination, second-degree price discrimination schemes do not result in the situation where a unit of output is allocated to a member of a “favored” group but denied to a higher-valuing member of a “disfavored” group.  Recall that the movie theatre pricing scheme discussed above ($6/senior ticket, $9/adult ticket) would allocate a seat to a senior citizen valuing admission at $6.25 but not to a non-senior adult valuing it at $8.75.  Contrast that to a fairly typical metering tie-in, such as one where a printer manufacturer lowers its printer price from the profit-maximizing level of $400 to $200 but then requires purchasers to use its paper, which is priced at $.04/sheet rather than the competitive price of $.02/sheet.  The effect of such a tie-in is to convert buyers’ fixed costs (for the printer) to variable costs (for the paper), thereby enabling some low-intensity users — those who don’t make enough prints to justify the high fixed costs — to enter the market.  But the fact that the exact same pricing scheme applies to all consumers ensures that at the margin, all consumers receive the same valuation.  Here, for example, the last copy purchased by the consumers who most value photocopies will create value of $0.04 for the ultimate purchaser, and the last copy purchased by consumers who least value photocopies will create value of $0.04 for the ultimate purchaser.  Thus,  the price discrimination inherent in a metering tie-in, unlike the movie theatre scenario, involves no transfer of surplus from high-value to low-value buyers.

This means that the primary driver of Elhauge’s welfare analysis — the reallocation of output from high- to low-value consumers — doesn’t apply to a metering tie-in.  In my response paper (pages 29-32), I explain why second-degree price discrimination in the form of metering is probably welfare-enhancing in most instances.  But since I’ve just broken the 2,000 word mark on this super-dry post, I’ll let you read that on your own.

If you have comments on the paper, which will be published in the Ohio State Law Journal, please let me know.  I can still do a few edits.

 

Thom Lambert

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I am a law professor at the University of Missouri Law School. I teach antitrust law, business organizations, and contracts. My scholarship focuses on regulatory theory, with a particular emphasis on antitrust.