# Price Discrimination Enables New Products and Services to Exist

A common sentiment that I encounter in the tech policy world is a visceral opposition to price discrimination. This is odd to me, because as an economist, I know that price discrimination often leads to more efficient outcomes. One particular element of this added efficiency is that when fixed costs are present, price discrimination allows products and services to be profitable that would not be profitable under standard pricing. This means that if we were to ban price discrimination, we would not get these products at all.

The tech world is filled with lots of smart people who understand math, so for this post, I am going to try to make the case with algebra and a wee bit of calculus. If you can follow along, great; if not, I’ll get you in some other post.

Let’s start with a basic, normalized linear demand function:

$Q = 1 - P$

$Q$ is quantity and $P$ is price. The results of this exercise will translate easily to any linear demand function, and they will apply broadly to all demand functions, so why not make it easy on ourselves?

Let’s assume that firms have a fixed cost $F$ and a marginal cost $C$. Firms’ total costs are:

$F + QC$

Total revenue for the firm is just price times quantity, so it is equal to $QP$. If we are concerned that not even one firm might serve this market, then it is useful to look at the monopoly case, where market $P$ and $Q$ are equal to firm $P$ and $Q$. In this context, we can substitute $1 - Q$ for $P$, and therefore, total revenue is equal to $Q(1-Q)$.

Total profit is simply total revenue minus total costs. Therefore:

$\pi = Q(1-Q) - F - QC$

What prices and quantities maximize profit? To calculate this, we can take a partial derivative of profit with respect to $Q$ and set it to zero. This condition will hold where profit is maximized.

$\dfrac{\partial\pi}{\partial Q} = 0 = (1 - Q) - Q - C = 1 - 2Q - C$

Solving for $Q$,

$Q = \dfrac{(1-C)}{2}$

Plugging this expression for $Q$ into the demand function lets us solve for $P$:

$P = 1 - \dfrac{(1-C)}{2}$

$P = \dfrac{(1+C)}{2}$

This is the profit-maximizing $P$ and $Q$ for a monopolist in this market in terms of $C$. Note that $F$ drops out. The profit-maximizing values don’t depend on $F$.

What does depend on $F$, however, is whether the firm is earning enough at these values of $P$ and $Q$ to stay in business. In particular, profit needs to be zero or positive for the firm not to shut down.

$\pi = Q(1-Q) - F - QC \geq 0$

Substituting $\frac{(1-C)}{2}$ for $Q$:

$\frac{(1-C)}{2}(1-\frac{(1-C)}{2}) - F - \frac{(1-C)}{2}C \geq 0$

Gathering terms:

$\frac{(1-C)}{2}(1 - \frac{(1-C)}{2} - C) \geq F$

Simplifying:

$\dfrac{(1-C)}{2}\dfrac{(1-C)}{2} \geq F$

$\dfrac{(1-C)^2}{4} \geq F$

So without price discrimination, this market will be served if and only if $F \leq \frac{(1-C)^2}{4}$. If we want to plug in some numbers, assume that $C = 0$; in this case the market will be served only if $F \leq 0.25$.

Want to try it with price discrimination now?

With marginal cost equal to $C$, a monopolist would produce $1 - C$ units. Assuming that the monopolist is able to charge each consumer the maximum they are willing to pay, then profit can be expressed like this:

$\pi = \int^{1-C}_0 (1 - Q - C) dQ - F$

Computing the integral:

$\pi = [Q - \dfrac{Q^2}{2} - CQ]_0^{1-C} - F$

This is equal to:

$\pi = (1 - C) - \dfrac{(1 - C)^2}{2} - C(1 - C) - F$

$\pi = \dfrac{(1 - C)^2}{2} - F$

Since profits must be non-negative for the firm to stay in business:

$\dfrac{(1 - C)^2}{2} - F \geq 0$

or

$\dfrac{(1 - C)^2}{2} \geq F$

So this market, with perfect price discrimination, will be served if $F \leq \frac{(1 - C)^2}{2}$. This means that the fixed cost can be twice as high (with linear demand) and the product or service will still be provided. If we want to plug in $C = 0$, then the market will be served as long as $F \leq 0.5$.

Why does this matter in the tech world? Because a lot of tech products and services have very high fixed costs. Building out wired and wireless broadband networks, for instance, is extremely costly. Marginal costs are often relatively low.

If we want to reap the benefits of new and innovative tech products, we must be prepared to accept price discrimination at least some of the time. There are products that are viable with price discrimination that are not viable without it—and if we ban price discrimination like some people thoughtlessly advocate, we won’t get them.

# Common Mistakes Made By Economics Journalists

Ezra Klein, a journalist who writes about economic policy, offers a list of common mistakes made by economists. Ezra’s list is not bad, but I can’t help but feel that turnabout is fair play. If economic journalists can tell economists that they’re doing it wrong, it seems only fitting that economists should be allowed to return the favor. So without further ado, common mistakes made by economics journalists:

1. Referring to oneself as an expert in economics. Economists want to attract people to our discipline, so we refer to the “economic way of thinking” as something that anyone can do. Sadly, that is not true. Anyone can get a lot smarter by learning their first bit of economics, but non-economists interpret personal diminishing returns in this regard as knowing all there is to know. Real expertise takes a big commitment plus the right personal characteristics (including personality).

2. Failing to distinguish between settled theory and open theoretical disputes. Price theory is settled. If price theory strongly implies something, that something does not need empirical support, though it may of course need to be interpreted properly. Macroeconomic issues such as the effectiveness of fiscal policy are not settled; these claims are in need of empirical support, which, it should be stressed, is not easy to come by. If it were, we would have settled the theoretical issues long ago.

3. Gleefully citing behavioral economics as overturning the basic economic model. There’s a lot to like about behavioral economics, but mostly it informs us about small deviations from rational choice predictions, e.g., preference reversals when agents are almost indifferent in the first place.

4. A preoccupation with public policy. Much of what is fascinating in economics has little relevance to the everyday political wrangling that goes on in the press. Even when something has policy implications, often the non-political elements of the theory are the most interesting. Why not spend some time on the good stuff?

5. Coverage should correlate more strongly with importance of the topic, at least partially determined by the size of the economic distortion. No matter what side you take, union policy is relatively unimportant. The size of the distortion generated by immigration restrictions, however, is enormous. Your readers need to understand this.

6. Too verbose. Would it be too much to ask to replace a few paragraphs now and again with a single equation?

This list would presumably be longer if I consumed more mainstream media. Got any more items? I’ll add, though I shouldn’t have to, that this list is not directed specifically at Ezra.

# App Store Economics

If you follow me on Twitter, you may have noticed last week that I have an app in the new Mac App Store. It’s called Gmail Dock, you can find more info about it here and here, and you can buy it here.

I am an economist, not a programmer, so what am I doing with an app in the App Store? This question got me thinking about the economics of the App Store, and I think I have a satisfactory answer.

As with most things, it begins with Ronald Coase (who turned 100 last month, huzzah!). What are stores? They are mechanisms for reducing transaction costs. Notice that I said “reducing.” Store owners are middlemen, and they take a cut of the proceeds for their trouble. Apple takes 30% of gross sales. Nevertheless, the value of their brokering services exceeds their cut of gross sales, so on net they reduce transaction costs.

When transaction costs are lower, we know from The Nature of the Firm that firms get smaller. They outsource more. More people start firms to which other firms outsource, so there are more entrepreneurs. Most importantly, patterns of specialization change. Instead of doing something for myself, I will be more likely to pay someone else to do it for me.

I wonder what The Nature of the Firm would have said if it had been written today, when so many businesses deal in products, such as software, that are characterized by high fixed costs and low marginal costs. The specialization story changes a little. My own adventures with the App Store are instructive.

I wrote Gmail Dock entirely for my own use almost a year ago. I was tired of desktop email clients like Mac OS X’s Mail that were slow, bloated, and not as useful as the web-based Gmail. So I wrote something that attempted to bridge the gap between desktop email and webmail. I found it useful. But I didn’t try to sell it online because of the difficulty of marketing, distributing, and collecting payment. Giving it away would have made me strictly worse off because of support requests.

The App Store came along, and all of a sudden it was cost-effective to sell my software. I went into business. But the thing that is different from the Coasian story is that my pattern of specialization hasn’t actually changed. I’m still producing the same things that I produced before the store came into the picture. Lower transaction costs plus low marginal costs mean that people’s hobbies, creative outlets, and tinkering will increasingly become profitable side businesses. Who knows, maybe some day I’ll get paid to blog.

Those of us who do not spend all day in front of a TV create real value in our spare time. Lower transaction costs enable us to capture some of that surplus. To me, that is one of the important stories of how the App Store, the Internet, and the world of low marginal cost is changing society.

# Net Neutrality: More Complicated Than You Think

On the technology sites I frequent, TechCrunch and Hacker News, there has been an uproar over Google’s joint proposal with Verizon, in which traditional Internet service providers would be subject to net neutrality regulation and wireless providers would not. I think the outrage over Google’s alleged betrayal of Internet users is ill founded. Most of the criticism I’ve seen is not informed by a serious attempt to grapple with economic reality. The real story is much more complicated. It’s so complicated, in fact, that I’m not sure I can make any rigorous statements about net neutrality, but I will try to outline some of the issues.

Let’s start with the most important question: why did Google decide to start being evil? People seem to actually be asking this childish question. The answer, of course, is that good and evil is not a useful framework for analyzing Google’s actions (though if they open concentration camps I will take this back). Google is motivated by profit. It faces incentives. I outlined Google’s strategy for profit-maximization in A Theory of Google. The basic conclusion of that post is that Google benefits from widespread, cheap, and high-quality access to the Internet.

If that’s true, then why doesn’t Google support net neutrality for wireless providers? <sarcasm>It’s almost as though they haven’t given this any thought.</sarcasm> Except that their chief economist is Hal Varian, who is one of the top scholars of the industrial organization of information-intensive markets and coauthor of one of the seminal books of the field, Information Rules. Varian and his fellow Googlers must have some reason to believe that net neutrality could hinder the development of the wireless Internet (though it appears not all of the rank-and-file are on board).

The first step to understanding the economics of net neutrality is to recognize the large fixed costs that accompany any network industry. The presence of large fixed costs means that the simple price-equals-marginal-cost condition for efficiency no longer applies. If all customers were charged MC, the firm would go out of business. It could not cover its large fixed costs. Even if the costs were sunk, the firm would “go out of business” at the margin, refraining from adding capacity on which it would only lose money. In general, large fixed costs imply that price and/or quality discrimination is a necessary feature of an efficient equilibrium (that is, if consumers do not all have identical demand). Read Michael Levine to see how this is the case even in competitive markets!

Another feature of industries with high fixed costs is that they tend to be monopolized or at least highly concentrated. Economists use the term “natural monopoly” to refer to those cases in which the monopolization is due purely to fixed costs and not to any coercive factor. In fact, traditional ISPs, in addition to being natural monopolies, are also coercively monopolized due to municipal franchises that grant them exclusivity. They therefore do not face even potential entry into their markets. A monopolist ISP might favor its own properties on the web, which is what worries net neutrality advocates. But if the monopolist ISP is free to charge whatever prices it wishes for its service, it can’t gain from pushing its own properties, or at least not at the consumer’s expense. Its incentive is to make the Internet as valuable as possible for its consumers so that it can maximize its profits on its monopoly. Remember the logic of double marginalization. If the municipal franchise results in regulated prices, then the monopolist ISP may have a strong reason to favor its own content. It leverages its monopoly position to reap profits through unregulated content rather than regulated Internet service.

A third factor intrinsic to Internet service is congestion. Transferring data on a network reduces the ability of others to do the same. This is a negative externality that can be remedied through a Pigovian tax, or better yet, through a Coasian solution. After all, property rights are well defined and transactions are already occurring. The externality can be resolved by a change in the terms of the contract.

The challenge, then, if you are socially benevolent, is to find a way (1) to efficiently incentivize investment in Internet service infrastructure, (2) to minimize the ill effects of the tendency of the industry to be monopolized, and (3) to reduce congestion, thereby making existing bandwidth capacity maximally valuable. This is not easy. The efficient solution would be something like the following. Consumers would pay for Internet service in two parts. First, they would pay an access fee, which varies from consumer to consumer in proportion to how much they value the Internet. Second, they would pay for the data they consume on a metered basis, with peak rates being higher than off-peak rates to efficiently allocate traffic. There would be no restrictions on the price or quality of service, though violations of service agreements would be prosecuted as fraud. Because the value of Internet service to consumers vastly exceeds the fixed costs associated with running an ISP, my intuition is that all monopolistic municipal charters should be abrogated and all markets contestable.

If that’s the ideal world, it’s not clear whether net neutrality brings us closer to it or further from it. Because we do not observe the ideal pricing structure, net neutrality regulations hamper firms’ ability to ease congestion by de-prioritizing what they believe is the lower-value traffic (remember, if optimal pricing exists, congestion is self-regulating). On the other hand, because some firms are coercive monopolies and face regulated pricing, net neutrality can improve welfare by taking away an inefficient monopoly rent.

Perhaps the most subtle way that net neutrality could be harmful is by aiding collusion between ISPs. If the firms have a sunk investment in infrastructure, regulations that make it more difficult to recover the value of new investments will discourage entry and expansion. Existing firms can carve up the current market and keep prices artificially high.

Google’s position, that traditional ISPs should be regulated and wireless ones should not, is defensible. Competition is more vigorous in the wireless sector than in the wired, and pricing is less regulated. Furthermore, the wireless industry is further from optimal capacity, so we ought to be sensitive to the incentives to invest.

I don’t mean to endorse Google’s proposal; rather, I wish to suggest that critics take the time to learn something about what it is they are criticizing. It’s dismaying to me that so many non-economists think they understand the effects of net neutrality. Skim some of TechCrunch’s recent posts on the topic: they are, frankly, asinine. It reminds me of a quotation from Murray Rothbard:

It is no crime to be ignorant of economics, which is, after all, a specialized discipline and one that most people consider to be a ‘dismal science.’ But it is totally irresponsible to have a loud and vociferous opinion on economic subjects while remaining in this state of ignorance.

# Economics as Thermodynamics

When human and physical capital accumulate, output grows. Most people would agree with this statement, but what does it mean? This depends on the meaning of the words capital and output. I don’t offer a precise definition, but both ideas seem to have something to do with useful configurations of matter and information. That is, capital and output are orderly. And whenever I think of order, I think of thermodynamics.

The second law of thermodynamics says that the entropy of the universe tends to a maximum. We cannot be sanguine about the very long-term prospects for the universe. But even though entropy increases in closed macroscopic systems, in open microscopic systems it may decrease for a period. Fortunately, Earth is an open microscopic system that is constantly (well, for now) importing negentropy from the sun, which is blowing up (tending toward disorder). This means that order is possible on Earth.

We can draw (arbitrary?) distinctions between the kinds of order that we observe on Earth. One kind of order we call “life”—we call the discipline that studies the production and depletion of this kind of order “biology.” Another kind of order we call “consciousness.” Consciousness is related to biology—it is a kind of spontaneous order that occurs within brains, which are living—but it is also studied by psychologists and philosophers.

Another kind of order is social order. This is the order that arises by interactions between (discrete?) consciousnesses. It is the domain of the social sciences, particularly economics. These interactions might include violence, altruism, and exchange. The task of economics, then, is to give an account of how these interactions (note to Hayek: not just exchange!) create or destroy order.

It is striking to me that many people reject the idea of intelligent design for life or consciousness, but accept it for social order. Social order involves conscious beings who consciously design things, but it is not itself designed. It grows organically, for the same reason that the other kinds of order grow: the application of energy, which in the case of Earth originated in the sun.

Everything I have written so far has been non-normative. What are the ethical implications if we are willing to take a leap and say that order is good and disorder is bad? We should view actions which increase entropy as bad. Indiscriminate killing (and even indiscriminate ransacking), for instance, would be bad. Eating smart animals (including, but not limited to, other humans) instead of plants or dumb animals would be bad. Interfering with order-producing social processes (such as trade) would be bad. All this seems fairly plausible to me.

That’s what I have so far. What do you think?

# More Double Marginalization: Apple and Open Standards

The very clever Josh Knox points me to Steve Jobs’s open letter about Flash. Following up on my last post on double marginalization, he wonders if Apple’s distaste for Flash can be explained in those terms. Josh is absolutely correct.

The money sentence in Jobs’s letter is this:

Though the operating system for the iPhone, iPod and iPad is proprietary, we strongly believe that all standards pertaining to the web should be open.

Replace “though” with “because” and you have a succinct explanation for why companies like Apple would want to support open standards. Apple makes its margin on the iPhone; no need to let Adobe make a margin on content or development. If Apple can replace Flash on the web with open standards, Apple will make more money, and consumers will be better off by not having to (indirectly) pay the Adobe tax. Pretty much the only loser in this is Adobe.

# I'm not Afraid of Facebook

A lot of pixels have been spilled in the last week about how Facebook has seized control of the Internet with their new API initiatives. This is supposedly troubling: unlike Google, Facebook might be evil, the hand-wringers say. But even if Facebook is able to monopolize a large segment of our time on the Internet, I’m not worried. I have one simple reason: social networking is a network industry (seems obvious, no?).

Let me preface my argument by reiterating that there is a lot about Facebook that I don’t like. I hate the “walled garden” approach, and would prefer that decentralized protocols like those used in Google Buzz take off. I’m not a cheerleader for Facebook or its strategy by any means. Nevertheless, I don’t think Internet users have much to fear.

The way to start thinking about network effects is to think about fax machines. A fax machine is absolutely useless if you are the only one who has one. It’s only when other people have fax machines that they become useful. A fall in the price of fax machines has two effects. First, it will induce people to buy more fax machines—this is the ordinary demand effect of moving along the demand curve. Second, because people are buying more fax machines, fax machines become more useful, which increases demand for fax machines—the demand curve shifts out, amplifying the effect of the price drop on quantity. Since the effect is amplified, the true demand curve, the one that takes this into account, is very “flat” or elastic.

Facebook accounts are like fax machines—they are only useful if other people have them. There is the same positive feedback effect of price on quantity. As a thought experiment, imagine that Facebook started charging $10/month for access. My intuition is that many people get more than$10/month of value out of Facebook, and therefore would be willing to pay the fee. However, a lot of marginal users would drop the service. The fact that a lot of users would drop the service would make Facebook less useful to those people who remained; they may no longer get \$10/month worth of value out of Facebook if half their friends weren’t on it any more.

I’m not suggesting that Facebook is going to start charging a fee for access. But nevertheless, elastic demand plays a role in how it relates to its users. For instance, one way of cashing in on the service’s popularity would be to plaster it with interstitial ads. This would be kind of like charging a “price” for the service. Why doesn’t Facebook do this? Elastic demand. And elastic demand places limits on the amount of “evil” that Facebook can do, or at least the amount of wealth it can transfer from its users to itself.

Finally, think about network effects and monopoly. Goods and services that exhibit network effects are going to tend toward monopoly (at least if the network effect applies to the good or service directly, and not the protocol, as with fax machines). We should not be surprised that Facebook is becoming huge; if it wasn’t huge, something else would be huge. That’s just how these industries work. But with very elastic demand, having lots of users doesn’t translate into a large monopoly rent. And meanwhile, Google has a strong incentive to ensure that the Facebook tax is not very high.

So my advice is stop worrying and enjoy your consumer surplus. Facebook is not good or evil—it is profit-oriented and faces a serious demand constraint due to the nature of its own product.