Bundling

In our final video on price discrimination, we're going to be talking about bundling.

Bundling is selling two or more goods together as a package so Microsoft, for example, sells Word, Excel, PowerPoint, a few other programs, together in a package called Office. You can also buy these programs individually but the total price then would much exceed the Office price. So most people buy it as Office. Cable TV is a collection, typically of, let's say, a hundred channels, or you might buy twenty channels, the movie pack -- you might add on to your hundred with the movie pack, a bundle or package. LexisNexis is a collection of thousands of different news sources.

Newspapers themselves are bundles. They're bundles, let's say, of sections: the sports section, the business section. Not everyone who reads the business section reads the sports section, and vice versa. Spotify, which we'll talk a little bit more about later, is a bundle of songs -- 16 million songs now and growing. It's surprising how much bundling can increase profits.

Let's look at a simple example. Suppose there are two products, Word and Excel. And let's imagine selling them at first individually. So for Word it's pretty clear that there are only two sensible prices. Amanda values Word at $100 -- Yvonne only at $40. So either the firm should price at $100 and just sell one unit or price at $40 and sell two. Same thing for Excel. Either the firm should price at $20 and sell two units, both to Amanda and to Yvonne, or sell at $90 and sell just one unit to Yvonne.

So let's take a look at the profits from the high price strategy, selling at $190. So in this case Microsoft will sell one unit at $100, one unit at $90 for a total profit of $190. Notice here we're assuming that marginal costs are zero so revenues are the same as profits. Now let's look at the low price strategy. In this case, Microsoft will sell two units of Word at $40 each and two units of Excel at $20 each for a total of $120. Now you can check the combinations here, but take it for granted that the maximum profit with the individual sale is from selling at the high price, and thus the profits are $190.

Now let's consider an alternative strategy. Suppose we combine Word and Excel in a product or a bundle called Office. Amanda values Office at $120. That is, the combination of Word for $100 and Excel for $20, she values for a total of $120. Yvonne values Office at $130. Again it's pretty clear that there are only two sensible prices -- sell at $130 and just sell one unit or sell at $120 and sell two. Pretty obvious that what you want to do is to price the bundle at $120, sell two units, make $240 and then notice bundling has increased profits by $50 or by 26%. Pretty good deal just for combining the products in a package.

So what's really going on here? The problem with selling Word and Excel individually is that the demands for the individual products are highly variable. So, Amanda values Word at $100, but Yvonne only at $40. On the other case for Excel, Amanda values Excel at $20, Yvonne at $90, so there's a lot of variability in the demands for the two products. That means that the firm is forced to make a choice to sell high but sell only a few copies or to sell low and to sell more copies.

On the other hand, look at what happens when the firm bundles. So the variability between the bundle values is now much, much lower. Because the variability is lower, the firm is able to price it closer to the mean and grab up more of the consumer surplus. Now in this case, the bundling works particularly effectively because Amanda and Yvonne have negative correlations -- that is Amanda has a high value for Word and a low for Excel while Yvonne has a high value for Excel and a low for Word. Negative correlation helps here a lot, but it's actually not necessary.

More generally what matters is that the demand for the bundle is less variable than the demand for the individual products. Zero marginal cost is also a big help here. And the principle here is that it's never wise to sell someone something if they value it at less than the cost. So imagine that somebody values a product at $20, and it costs you $30 to produce it. While you could get them to buy it as part of the bundle, but that's never going to maximize profit, because by taking that product out of the bundle you can cut your costs, $30, by more than you can cut the willingness to pay, $20.

So you never want to sell someone something if they value it at less than the cost. When marginal costs are positive, there's always a fear that by bundling you're going to be selling something that the person values at less than the cost. If marginal cost is zero, we don't have that problem, so we can bundle to our heart's content. So bundling is really going to work well when we have zero marginal cost products, like information goods. When marginal costs are zero, it could make sense to bundle hundreds or even thousands of goods together, information goods.

A very excellent paper on this by Bakos and Brynjolfsson, and their basic story is this: Suppose that consumers have different valuations for different goods. So for one good, for one consumer, the consumer may put a high value on that good but on the next good they may have a low value. Equally likely to have a high or low value. Now imagine that on the first good, the consumer has a high value. On the second good they're likely to have a value which is less high. So when you combine those two goods, you're going to get a more intermediate result, a result closer to the mean.

So when you add up or average all the different goods, maybe one here, and one here and one here -- you add more and more goods to the bundle -- what you get is a demand for the bundle which is closer to the mean. In terms of a demand curve, this setup means that the demand curve is linear, like this for an individual good, but if you have a two-good bundle, it increases the quantity demanded to the mean.

Let's in fact take a look at 20-good bundle. So the demand for a 20-good bundle, even though each individual good in that bundle has this linear demand -- the demand for the bundle itself is much greater at the mean. It's concentrated around the mean. You get this big increase in the quantity demanded at the mean as the bundle values go to the mean. Because the demand -- the quantity demanded -- is concentrated at the mean, just a small reduction in price can increase the quantity demanded, and that's what the firm will do. It'll drop the bundle price a little bit, sell a lot more, and eat up much more of the total consumer surplus. So that's why it makes sense to bundle thousands of goods when the goods have zero marginal cost.

Okay, let's say a few words about profits, consumer welfare and total welfare efficiency. This is a little bit tricky because the results are not perfectly general but the basic idea is this. Bundling increases profits, otherwise the firm wouldn't do it, and we've seen why it increases profits. Now some of that increase comes from reductions in consumer surplus, a transfer from consumers. But some of it comes from reductions in deadweight loss, that is it comes from increased sales. The increased sales add to efficiency. Overall consumer welfare could go up or down, holding fixed the number and quality of goods. At least in one classic case, in the big bundle zero marginal cost case, total welfare increases. That is the profits and the reduction in deadweight loss more than make up for reductions in consumer surplus.

Now, goods with zero marginal cost often have very high fixed costs, like software. There's a lot of investment in producing the software in the first place, even though it's easy to distribute. Movies and TV, information in general is like this. And to the extent that increased profits, increased investment in the fixed cost of creation, bundling will also tend to increase consumer welfare, as well as efficiency. So on average, my belief is that the case for bundling is actually pretty good.

Now let's look at an application. Cable TV is typically sold as a package or a bundle of hundreds of channels. And this makes a lot of sense because cable TV satisfies all of our conditions for bundling to be profitable and also to be efficient. For example, people who are watching a lot of ESPN are probably not watching a lot of Bravo, a lot of "Top Chef." Not only do preferences differ, but there's only 24 hours in a day. So if you're watching a lot of ESPN, you can't be watching a lot of "Top Chef" and vice versa. But this negative correlation among channel values creates a bundle value, which goes closer to the mean, which becomes more homogeneous. And that's exactly what we require for bundling to be profitable.

In addition, marginal costs are zero. So we don't have to worry about selling someone a channel which they value at less than the cost. We can give someone a channel for free without increasing our costs. In addition, cable TV has got a lot of fixed costs. First, the costs which are extensive of laying the cable, and also the costs of producing the programming itself. So for all of these reasons, negative correlation, zero marginal cost and high fixed costs, cable TV is an excellent candidate for bundling, but this makes a lot of people very upset. Because of negative correlation, people who watch football are not watching "Top Chef" and people watching "Top Chef" are not watching football, so some people feel that they're being ripped off -- that they're being forced to pay for something that they don't use and there's kind of a naive theory that if I'm paying a hundred dollars for a hundred channels, then under á la carte pricing -- if only I wasn't forced to buy the package -- I'd be paying $1 per channel, and I'd buy only the channels that I really want. But, of course, that theory is wrong. The per channel price would increase and would likely increase rather dramatically.

Moreover, we know from the theory of bundling that the firm makes the most profit when just about everyone is getting the same value from the bundle. So people shouldn't fear that they're being ripped off. People who will watch "Top Chef" -- they're getting a lot of value from the bundle. People watching football -- they're getting a lot of value from the bundle. There's no reason to think that one party is ripping the other party off. Now maybe overall we'd be better with more competition, but that's sort of a different question.

There's also in the case of cable TV, complicated dynamics between consumers, distributors and content sellers. It's unclear if you switch to á la carte pricing who would really grab up that consumer surplus. It's probably not going to be the consumers. It might be the distributors who sometimes push for á la carte pricing. It might even be the content sellers, but there'd be a lot of gaming of the system going on, and it's not that all clear that consumers would win that game. There would also be some increased costs if the cable companies had to sell by channel and if people could have, you know, all the combinations and permutations of different channels which was possible, would likely increase transactions costs. Maybe in this example only by a little bit.

Finally, if this decreased profits for the distributors, which it would, that is going to have ultimate effects on the quality and the number of channels, the number of content providers, and how much they're willing to invest in new programming, so overall my belief is that bundling is actually good for consumers and certainly not bad for consumers or not very bad for consumers. We don't want to follow the naive theory.

Okay, let's make one more point. Here's an interesting prediction from bundling theory. Music is currently sold in two different ways. iTunes sells more or less by the song, while something like Spotify or similar services, they sell you a whole package or a whole bundle. Bundling theory says that Spotify is going to win this competition -- that the profits are much greater for the bundler. This is not only because of the price discrimination reasons which we've been talking so far, but in this case the transactions costs really do matter.

So when iTunes sells by the song, and it's 99 cents per song, the cost of the credit card transaction can be as much as a dollar, or a $1.20 or 50 cents. It can be a significant cost, significant percentage of the value of the song. iTunes tries to handle this by only charging you, you know, for every five songs, or every two or three days. They try and combine as many purchases as possible, but still the transactions costs of micropayments are quite large, and that's another reason which is pushing the music business, in my opinion, to Spotify. So that's a little bit of investment advice. Don't blame me if it doesn't work, but I think that the bundling is going to win out.

Here's some places for further reading. Adams and Yellen have a classic on commodity bundling. You can easily find that on the web. A favorite of mine, the Bakos and Brynjolfsson paper -- these authors actually wrote two papers on the subject -- either of them is certainly worth reading. For a modern look at combining bundling and bargaining theory, you can take a look at Crawford and Yurukoglu. It's quite a complicated paper, putting together the industrial organization of these two topics. You may also want to go to Marginal Revolution, my blog with Tyler, and search for cable TV bundling. Both Tyler and I have short interesting posts on this topic. Thanks.