The Efficiency of Cable Bundling

Thom Lambert —  10 July 2011

As I noted in a post last month, the Ninth Circuit recently threw out an antitrust challenge to cable operators’ refusal to provide cable channels on an a la carte, rather than bundled, basis.  (Josh also had some insightful comments on the Ninth Circuit’s Brantley decision.)  In my post, I promised that I would later explain how channel bundling, which permits cable operators to price discriminate and extract greater consumer surplus, may nonetheless benefit consumers by expanding output.  Having just finished incorporating a number of helpful comments Herbert Hovenkamp gave me on a forthcoming tying/bundling article (more about that later!), now seems like a swell time to return to the topic of cable bundling.

 To begin, consider how the refusal to provide cable channels except in bundled “tiers” can expand an operator’s profits and reduce short-term consumer surplus.  As George Stigler famously observed in connection with the Supreme Court’s Loew’s decision (which addressed movie studios’ “block-booking” of feature films), a seller of multiple products for which demand is not positively correlated may find its ability to raise prices constrained by the willingness-to-pay (“reservation price”) of more price-sensitive (“higher elasticity”) consumers and may evade that constraint by selling its products on a bundled basis. 

 Suppose, for example, that a cable operator has two channels – ESPN and the Family Channel – and two customers – a bachelor and a married father of four.  The bachelor, who has more disposable income than the family guy, mainly watches sports but occasionally catches a flick on the Family Channel.  The father and his family, by contrast, watch more Family Channel programming than ESPN.  Bachelor values ESPN at $45/month and the Family Channel at $20/month.  Family Guy values the Family Channel at $35/month and ESPN at $25/month.  For simplicity’s sake, assume the cable operator’s marginal cost of providing each channel is zero.

 Under these assumptions, the cable operator would earn profits of $90/month by providing the channels a la carte.  It would charge $25/month for ESPN and $20/month for the Family Channel (in each case, the reservation price of the high-elasticity consumer), and would sell two subscriptions to each channel.  Total consumer surplus, then, would be $35:  Family Guy would enjoy surplus of $15 on the Family Channel and no surplus on ESPN; Bachelor would enjoy surplus of $20 on ESPN and none on the Family Channel.

 By selling the channels on a bundled basis exclusively, the cable operator could enhance its profits by 33%, to $120/month.  It could do so by charging $60 for the ESPN/Family Channel package (this reflects the high-elasticity consumer’s reservation price for the bundle) and selling two packages.  Total consumer surplus, though, would fall to $5:  Bachelor would pay $60 to get $65 of subjective value, and Family Guy, required to pay his full reservation price for the package, would enjoy no surplus.

 So how could this sort of surplus-extractive policy ever benefit consumers?  By expanding overall market output.  Allow me to explain.

 Whenever there is a lack of perfect competition for a seller’s good (so that above-cost pricing is possible) and consumers vary substantially in their reservation prices for the good, the seller will have a difficult time determining its profit-maximizing price.  Setting price too low will leave money on the table from high-value consumers.  Setting price too high will preclude sales to those consumers, possibly great in number, who would be willing to pay a lower, but still above-cost, price.  In such circumstances, the sort of “Stigler-type” bundling described above can be quite useful to multi-product sellers. 

 As economists Yannis Bakos & Erik Brynjolfsson have demonstrated, if consumers demand either one or zero units of each of a seller’s goods and consumers’ reservation prices for the goods are bounded and independent, the law of large numbers assures that the variance of consumers’ average valuations of the components in a bundle will shrink as the number of components in the bundle grows.  This then implies that, as the bundle grows, the variation of consumers’ valuations of the bundle as a whole will shrink in proportion to the bundle’s total value.  Eventually, the seller will confront a situation where demand is highly elastic around the median value for the bundle but inelastic away from that value.  Thus, when the marginal cost for each of the components in a bundle is negligible, as is the case with “information goods” (generally defined as things that can be digitized, such as cable programming), the seller can maximize its profits by tying many such goods together to “bunch” reservation prices and then setting its price for the bundle just below the point at which reservation prices tend to bunch.  If it does so, most potential consumers will purchase the bundle.

 Such a pricing strategy is likely to enhance total welfare by overcoming a problem plaguing sellers of non-rivalrous goods and other goods with significant fixed, but extremely low marginal, costs of production.  For such goods, the cost of supplying an additional user is negligible, so charging a non-negligible (or, in the case of goods with zero marginal cost, a positive) price for using the good is inefficient.  The excessive price will dissuade use by consumers who attach an above-cost, but below-price, value to the good and will thus squander potential surpluses.  At the same time, if the product at issue were priced at marginal cost, the seller would not be able to recoup its total costs of providing the good.  What is needed, then, is a pricing mechanism that permits use by all consumers attaching an above-cost value to the good but still provides the seller with enough revenue to cover the total cost of producing the good.

 Stigler-type bundling can assist here.  When the value of the individual elements in a bundle are uncorrelated, the proportion of potential users that are willing to pay the bundled price charged by the seller will expand as the number of bundled elements grows.  As long as an individual’s willingness to pay for the desired elements within the bundle exceeds the bundle’s price, the individual will view additional, undesired elements as having a marginal price of zero.  Bundling may therefore offer an imperfect solution to the difficulty afflicting sellers of non-rivalrous and other low-marginal cost goods:  It may enable the seller to cover the cost of creating such goods while confronting buyers with a zero marginal cost for any particular element of the bundle.  (For a lucid explanation of these points, see this terrific article by Stan Liebowitz and Steven Margolis.)

 In the end, then, cable bundling will encourage the production of more cable programming and will likely benefit consumers in the long-run.  The Ninth Circuit was right to throw out the Brantley plaintiffs’ claims.    


I’m off for a sailing trip in the British Virgin Islands.  When I return all tanned (well, burned) and rested, I’ll discuss Hovenkamp’s excellent comments on my forthcoming tying/bundling article.

Thom Lambert


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.

4 responses to The Efficiency of Cable Bundling


    If you wanted to illustrate the efficiency benefits of bundling, I don’t understand why you chose the reservation prices you did in your example. In your example, the consumer surplus falls for both consumers and thus both are worse off because of bundling. However, suppose the bachelor valued ESPN at $51/month and Family Channel at $20/month, while the family man valued ESPN at $25/month and Family Channel at $41/month. Then, if the cable company provided the channels a la carte, it would charge $51 for ESPN and $41 for Family Channel. This would price out the bachelor for Family Channel and the family man for ESPN, but the cable company would earn higher profits that way. Now, if the cable company bundled the channels, it could charge $66 for the bundle and both consumers would purchase the bundle. And, now in this case, both the bachelor and family man are better off with the bundle. However, note that in my example, the cable company could still offer the a la carte prices in addition to the bundled prices and everything would still work. It’s just that ever consumer would choose the bundled price.

    Moreover, the assumption of independent reservation prices seems pretty strong, especially given that cable companies offer bundles that contain similar channels (i.e., a premium sports package). Also, isn’t the independence assumption violated if people have a budget constraint? Allowing the number of channels in the bundle to go to infinity and applying the law of large numbers ignores the fact that people must operate on a budget. But still, this is thought provoking and I’ll have to take a closer look at the cited research.

      Paolo Siciliani 11 July 2011 at 11:52 pm

      Also, what if people want to buy only one channel – i.e. regardless (or because) of their budget contraints. In this case pure bundling would reduce output.
      Also, this little models are based on monopoly pricing, hence the assumption that in the unbundled case the monopolist set the price equal to the highest reservation price.


    I made a roughly similar argument last year with the added twist of discussing the emergence of a la carte streaming markets as a disruptive innovation.

    Paolo Siciliani 11 July 2011 at 5:00 am

    “At the same time, if the product at issue were priced at marginal cost, the seller would not be able to recoup its total costs of providing the good. What is needed, then, is a pricing mechanism that permits use by all consumers attaching an above-cost value to the good but still provides the seller with enough revenue to cover the total cost of producing the good.”

    Now, this is true for any product with high fixed and low marginal costs, I mean, any product taken in isolation. As you correctly pointed out, this cost configuration is the norm for “information products”, so cable channels are no special case. That is to say, marginal cost pricing would not be the likely market outcome in the unbundled case. iTunes does not sell in bundles, ebooks are not sold in bundles ect. (By the way, channels are already bundles, so what you talking about is bundles of bundles.)

    That is to say, arguing that unless firms are allowed to bundle high quality content will be priced out by marginal cost pricing is tendentious, it is based on the theoretical argument that fixed/common costs are sunk and thus irrelevant to pricing. This is a conundrum economists have long been struggling with, but when you observe real market outcomes, you find that the norm is average cost pricing, hence cost would be recovered even with unbundled pricing.

    The only reason why bundles would be good for society is that otherwise consumers would consume too low variety of content, but this presupposes a paternalistic approach where you want people to consume so called merit goods. I guess you don’t buy that kind of argument, do you?