Sunday, January 27, 2013

Unbundling: Why Matt Yglesias is wrong

This post is meant to provide a non-math intuitive explanation of my previous post on why requiring TV cable companies to let subscribers to pay per-channel instead of bundling would substantially reduce the cost of cable.

Here's the background: Brian Stelter argues here that the growing cost of licenses to carry sports games is causing cable rates to rise, and that "unbundling" so that subscribers can just pick the channels they want, would prevent non-sports fans from paying for the rising cost of stuff they don't even want. Matt Yglesias responds saying that you'll pay the same amount, because you've revealed you're willingness to pay, regardless of whether the price structure is per-channel or aggregated in bundles.

Here's the facts: Yglesias is absolutely right that non-competitive markets is the root of the problem. However, he is absolutely wrong to suggest that mandating a per-channel price structure wouldn't reduce costs. Still, Yglesias is more correct than Stelter, since, in fact, the rising costs of sports licenses has almost nothing to do with the issue. The reality is that even when we abstract away from the cable company's operational costs--suppose that they can show all sports completely for free--bundling severly harms consumers relative to a per-channel price structure. Bundling allows the cable company to charge much higher prices, and restricts consumer's access to television relative to the per-channel price structure.

Here's why: TV watchers want as many channels they can get, but face diminishing returns from them. Think about it this way--a consumer gets a certain amount of utility from having just one TV channel; the second channel increases utility, but doesn't quite double it; the third channel adds a little less utility than the second channel, and so on. What this means is that the amount we'd be willing to pay to add an additional channel is less than the amount we were willing to pay for the last channel. So if we set the price equal to the amount the consumer was willing to pay for the first channel, he will subscribe to only one channel. As a cable company, we'd like to then lower our price for the second channel to equal what the consumer is willing to pay for a second channel. But if we do this, then the consumer will simply pay the new lower price, and not pay for the original, higher priced channel. If we reduce the price of the first channel down to that of the second, we will be selling two channels instead of one, and thus earning more profits. But the consumer would have been willing to pay a bit more for that first channel, so we've missed out on a potential profit making opportunity. How do we recover this? By bundling both channels! We know how much the consumer is willing to pay for the first channel, and how much they are willing to pay for the second, so lets just offer them a deal: they can buy both at a price equal to the sum of what they are willing to pay for both, or neither. But they cannot choose just one. We are now charging more for the bundle than we could get if we sold the channels separately. But also think about what's happening to the consumer--at that average price they would like to buy one, not two, channels and divert some of that money into other non-TV purchases--they are paying for more channels than the really want.

So bundling does cost consumers money. In essence, cable companies extract extra money by presenting consumers with a threat: either pay more for more channels than they really want, or loose all their TV entirely. By offering a per-channel price, we take away the ability of the cable company to make this threat--consumers can simply purchase the cheapest channels individually, which generates less revenue.

In case it still isn't clear why individual pricing generates less revenue, think about it this way: per-channel pricing forces the cable company to charge a price equal to the marginal utility of the last channel sold, so if they sell three hundred channels, the price of each of those channels must be less than or equal to the marginal utility of the three-hundredth channel. They can't charge more for any of the 299 other channels, because if they did then the consumer simply won't pay that price for the 300th, and instead make do with 299 channels. But! if we threaten to take away all 300 channels if they don't pay higher prices for the 299 other channels, then the consumer will agree not because they really want all 300 channels at that cost, but because that deal is still better than having no TV at all.

In my previous post I offered a model that was slightly more complicated than this. In that model there were avid TV watchers, called "$H$-types," who are willing to pay a lot for cable, and there were moderate TV watchers called "$L$-types" who weren't willing to pay as much for cable. I showed that in this case, the cable company was better off offering two types of bundles--one of them is a "bad" bundle that charges a small fortune for very few TV channels, and the other is a "good" bundle that charges a slightly larger fortune for more channels. The introduction of a "bad" bundle that charges a lower overall price but offers fewer channels means that the company will have to reduce the price of their larger bundle. If they don't, then the $H$ types will opt for the cheap bundle instead of the expensive one. On the other hand, we know the $L$ types definitely won't pay for the "good" bundle because they don't value TV that much--so by offering the "bad" bundle at a price the $L$ types will buy it, we generate at least some revenue from these consumers. If the revenue from the bad bundle is greater than the decreased revenue from lowering the price of the good bundle, then total firm's profits have increased. The logic of offering a menu including a "good" and a "bad" bundle is this: you want to make the bad bundle as bad as possible (in this case offering as few channels as you can get away with) while chargin the highest price you can for it. This serves to deter the $H$ types from buying the bad bundle, while at the same time extracting as much money possible from the $L$ types. This is exactly what I show in the model--the lesson is that people who don't really like TV much get screwed by bundling, and the people who like TV more get slightly less screwed--there is cross-subsidization going on.

The lesson is simple. If we want to bring down the cost of cable TV, we should enact an outright prohibition on bundling. This will make both the the avid TV watchers and the not-so-avid watchers much, much better off.

As a final point, I want to note that all of this happens because cable companies are essentially monopolies. In a competitive market, competition forces the companies to reduce their prices all the way down to the marginal cost. One problem with this is that telecommunications markets are unlikely to be characterized by decreasing returns to scale, which is something of a per-requisite for competition. That is, with increasing returns to scale technologies, the marginal cost is below the average cost, meaning that competition actually forces firms to loose money. Indeed, though Time Warner has lots of fixed costs associated with sports licenses and maintenance, its marginal cost may well be zero. The result is that competition in increasing returns to scale markets will force firms out of business until either a cartel is formed, or only a single monopolist remains, who can then raise prices above marginal cost.

1 comment:

1. It really depends on model assumptions though. Presumably there would be some fee, probably large, just to provide infrastructure and customer support, independent of number of channels. This would come close to current basic cable fees. The channels would probably not be equally priced. Popular channels will typically be less expensive as they provide more advertising revenue and unpopular ones high because the desire is more intense. Most likely even in an individual channel plan, the cable company will choose to offer bundled packages that cost less than the sum of individual channels preserving the cross subsidy to high interest users. The cable companies will find it in their interest to make all costs base costs and charge as little as possible for the programming, but here programming fees would likely be passed along to the provider whose pricing objective would differ from the cable operator, so even if bundling is immaterial to them, it would still be in the interest of providers to reinforce it which if they can charge different prices they most likely will.