Samuelson pointed out a long time ago that, if people like more sugar with their tea than with their coffee and coffee and tea are strong substitutes, coffee and sugar might be substitutes as defined in the usual practically measurable ways (or, alternatively, in terms of the sign of the mixed partial derivative of the cost-of-utility function).  When we talk about "substitutes", we usually have something a bit different in mind, though; something causal, even; coffee and sugar are complements in some direct sense.  (So especially in terms of a smooth, convex cost-of-utility function c(u,p_c,p_s,p_t) where the envelope theorem gives q_i=∂ c/∂ p_i and you're looking at second partials with respect to prices, it seems likely to me that holding something other than p_t fixed might capture this; q_t is the obvious alternative, and I'm currently leaning to the idea that that's correct, though not because I think "holding other quantities constant" is the way I'd want to tell the story.)

What makes complements and substitutes a valuable tool in the economic toolbox is that 1) they're relatively intuitive ideas, and 2) they are useful for efficient reasoning in many situations of economic interest; even in the above situation, at least in the hard-to-define sense that coffee and sugar are complements, these both largely hold, as evidenced by the fact that I wrote the first sentence of this email without appeals to detailed algebra or even long-winded explanations --- you understand intuitively that coffee and sugar are complements, and you understand why a price increase in one might yet lead to an increase in demand for the other, with this latter understanding fully driven by a recognition of other complementarities and substitutions.

I think the same is true of supply and demand; if you look at the factors that affect price and quantity, often the important ones can be fairly cleanly categorized as "demand-side" or "supply-side" and you can increase your chances of understanding a market by making that separation.  When you get heavily asymmetric information or liquidity issues or the like, supply-and-demand models become less clean — though, perhaps all the more compelling, are still certainly useful in guiding thought, even as you have to be a bit more attentive to how the whole system is behaving.  Supply-and-demand reasoning is a useful thing to teach to freshmen, not necessarily because there's a deep theoretical reason they would have to work as well as they do, but for the twin reasons that, in our real world, (1) they often work quite well, and (2) many adults young and old have folk-economic ideas for which supply-and-demand reasoning is far more often to lead to fewer mistakes rather than more confusion.

second best

One of the curious things we do is to subsidize environmental harm in the name of environmental good. We also forbid people doing things that they might wish to do, again often allegedly for their own good; I'm not thinking just here of situations in which "we" disagree with their assessments, or believe they aren't well informed about the choices they're making. While non-economists frequently run into trouble by not thinking to second-round effects, I'm referring here to situations in which the second-round effect is the real target of policy.

Taking the subway requires the production of electricity, among other environmental harms. The bus is probably even worse.* We subsidize it, however, at least in part for environmental reasons. Someone might take the bus instead of walking or instead of not making a trip, but there's an expectation that the subsidy will incent many people to use public transit instead of something more destructive — namely, driving a car. The standard Pigovian prescription would be to tax driving, and place a smaller tax on public transportation; it's easier, both for reasons of transaction costs and those of politics, to subsidize public transportation instead.

We also make it illegal to work for less than minimum wage. There are situations in which these laws have been used in clearly inappropriate ways against volunteers, but the intention of those who support these laws is not that somebody who could be making $5 per hour be unemployed instead; the hope is that forbidding someone to work for less than $7 per hour will induce more employers to pay $7 per hour, either because they previously gained more than $7 per hour in marginal benefit from the worker anyway, or, if the economic analysis is better, because making competitors unable to hire workers for less than $7 per hour will allow them to raise prices to where the workers are more valuable.

There are important differences between these cases, but both are situations in which the policy goal is pursued in a slightly round-about way, in a way that, in terms only of the immediate, proximate effect, is entirely perverse. With further analysis, each illustrates that, in the absence of an ability to pursue goals directly, that sort of perverse approach may be the next best option available; if you can't tax driving, taxing public transportation for its direct environmental impact is no longer a good idea, and if you can't transfer wealth from consumers at large to people with low-wages in more direct ways, outlawing their work altogether might ultimately benefit them in a similar way.

* In some stochastic, long-run sense. Obviously the fact that the subways run requires electricity; if they're already running on a given schedule, an additional rider contributes essentially nothing to that. If there's a 5% increase in ridership, though, after a period of time, it's likely that more trains will be run than if there's a 5% decrease in ridership. This is perhaps even more true of buses. When you decide to take a bus, let's suppose, given knowledge of which you could reasonably avail yourself, that increases the odds of them running another bus by some amount, and attribute to your bus ride the extra pollution from that extra bus, multiplied by the probability you contribute.

causality

The Washington Post asks whether it's time to bring back "old age" as a cause of death:

Many physicians find the task even harder when a very old person declines over a few weeks or months and then dies. The steps of that process often include muscular weakness that leads to inactivity and increased susceptibility to infection, or poor intake of food and fluid that leads to dehydration and electrolyte imbalances in the blood and a final fatal heart rhythm. The "underlying cause" is hard to find even with an autopsy.

There can be proximate causes, contributory causes, and interacting causes; sometimes one thing causes a chain of other things, but sometimes each of two (or more) causes are necessary for a death, and neither would have lead to the death by itself. I was thinking about this this past weekend, when several Bronx residents died of not wearing their seat belts. There were other causes as well, of course, but this seems to have been a necessary one.

This is a big issue in economics as well. Much of the housing boom involved people borrowing money that they could pay back, barely, if they got regular raises and never had a kid get sick or a car break down. Blaming a default in a situation like that on the car breaking down seems to be missing the cause that was more significant, or at least more reasonably susceptible to different behavior. And the same, naturally, applies to management plans that require that nothing go wrong.

different ways of working out the same thing -- tariffs

I've been thinking lately about a comment by physicist Richard Feynman that a good physicist should be able to work out a physics problem in several different ways. The same is true of economics; if we have different tools for analyzing problems then, to the extent that they're all correct, they should get the same answer to the same question. An example is the effect on a nation that is a large importer of a good placing an import tariff on that good.

One way to view this is initially to view the nation as a single entity, and to look at it as a monopsonist, or at least a market-moving buyer on the world stage. To optimize its own interests, it should reduce its purchases below what it would buy if it were a price-taker, thereby lowering the price on the units it does purchase. Efficient allocation of the reduced purchase among residents of the country should, for the usual reasons, be acheived by allowing them to trade at a single price within the country; the artificial reduction of quantity imported will increase the domestic price while reducing the world price, and the optimal tariff, from this standpoint, is the difference between the domestic price and the world price at the optimal consumption level.

Insofar as the country consists not of a unitary actor, perhaps this is better thought of as a buyers' cartel, but, to the extent that it's able to enforce internal cooperation, the external economics look the same. It is in the interest of each member of the cartel to cheat -- to buy more of the good at the world price, rather than the domestic price. As each individual does so, though, they bid up the price faced by everyone else, reducing the welfare of their fellow citizens by more than they increase their own welfare.

This gets us to a second way of viewing the same problem, in terms of pecuniary externalities. More buyers or sellers in a market may move the price up or down, but they won't have an effect on overall Marshallian welfare; they simply transfer it back and forth between buyers and sellers. As I've constructed this situation, though, we don't ascribe any value to the welfare of foreigners, who are net sellers, only to those of our fellow citizens, who are net buyers; a purchase, then, by placing upward pressure on the price, represents a welfare transfer away from our fellow citizens. An optimal Pigovian tax would impose this externality on the purchaser in the amount that it would fall, on net, on his fellow citizens; where the world price differs from the domestic price by the amount an additional unit purchased is likely to cost the fellow citizens in increased costs, the buyers will find their equilibrium, and it should be at the same optimal level inferred from the monopsony argument.

Of course, if we valued foreigners' welfare equally to that of domestic citizens, there would be no externality to tax; that Pigovian tax, to first order, represents welfare that would otherwise be gained by foreigners from the additional unit purchased. The tax is economically incident, in part, on the foreigners, and this offers a third treatment of the problem: we wish to impose a tax such that the amount of revenue effectively derived from the foreign exporters from a marginally higher or lower tax would be offset by further welfare losses associated more directly with the lower domestic use of the good at higher prices. This is another standard paradigm into which the problem can be put and, yet again, it should yield the same result. This is the paradigm that makes it most easily apparent, though, that it is also in the interest of a large net exporter of a good to tax that good -- driving up world prices, with the tax falling partly on foreigners -- rather than to try to subsidize it, as is more often what mercantilist impulses seem to lead nations to implement.

Note that this is all without regard to any other Pigovian taxes one might impose on the product for other externalities; if consumers of the good, besides bidding up prices and effecting a transfer of wealth out of the country, also impose other negative externalities on their fellow citizens, even higher Pigovian taxes would be justified. The arguments above do not suppose such externalities, and are independent of them.

This is all under the ceteris paribus assumption, and the assumption that the welfare of the exporters is to be ignored. If a tariff is likely to lead to a trade war, that could well cost more than the net benefit of the tariff; if, conversely, a free trade regime can be negotiated and all parties are likely to adhere to it, that is likely to improve welfare for each country more than if each country separately starts taxing trade in attempts to optimize its own welfare by itself. On the other hand, if many of the exporters of a particular good are actually using proceeds from the sales to actively harm a country's interest, so that the importing country might view the exporters' economic welfare as negative, then the arguments apply all the more strongly.

GDP

One of the proximate instigators of this blog was the off-handed credit offered by an economist to feminists for continuing to remind people that non-traded goods and services — in their favorite example, unpaid housework — isn't included in the GDP. In principle, if my neighbor and I each mow our own lawns, that isn't in GDP, but if we each pay each other to mow our lawns, it is, even though, in practice, it's likely to be missed. There are related nonpecuniary (or partially nonpecuniary) transactions that will similarly be excluded; if I choose a low-paying job over a high-paying one, it seems that my share of GDP should be higher than if I were forced to take the high-paying job that I would like less. And that gets closer to the main problems I wanted to highlight.

The first point is that economic concepts of value are essentially relative; the value of a thing only makes sense in comparison to not having the thing. In particular, trying to assign a value to "everything in the world" requires comparing it to a world with nothing in it; in mathematical terms, value forms an affine space. (This is also one of the problems with occasional valuations of the environment.) If we want to value the goods and services we produce in a year, we're comparing it to a world in which we aren't producing any goods and services.

The next point, though, is that the extent to which some good enters into GDP is its quantity times its price; for example, apples contribute to GDP in an amount equal to the sum of the prices of each apple. The price of an apple, though, is the amount of benefit it provides in the current world, where there are lots of apples. If there were a single apple, someone somewhere would be willing to pay a lot of money for it, and that would set its price; the loss if there were no apples would be considerably greater than simply their price times their quantity. (It would be even greater if there were no oranges, either.) A similar problem is with the measure we use for GDP; we measure it in dollars. Economists, of course, try to factor out inflation, to produce a "constant-dollar" measure; this doesn't solve the problem when we're trying to trade all goods and services. The value of a dollar is calibrated against what it can buy; a real value is a price in terms of real goods, and it's hard to make sense of figuring out what we would be willing to trade for everything if nothing existed. To some degree of approximation, we can imagine trading a multiple of one year's product against a multiple of another year's product, but the two multiples aren't likely to scale perfectly linearly against each other. It's specious to think of GDP as the value of all the goods and services; it's more nearly a thousand times the value of one one thousandth of all goods and services.

Finally, there are attempts by some people to correct the broken window fallacy; when a window is broken, we have to replace it, and the cost of the replacement is counted in GDP, even though it simply gets us back to where we started. There is probably some value to this point, but many goods and services are intended to be nondurable, and are valued in their continued consumption for keeping our equilibrium against the forces of entropy at a more favorable level than they would be otherwise; indeed, virtually all goods are, at best, finitely durable, and the value of a durable good lies in its expected ability to provide some nondurable value on an ongoing basis, subject to whatever maintenance it's subject to, until it inevitably wears out — or is broken. If we're going about smashing windows to improve the economy, we've made a logical error, but so long as the rate of window-smashing is more or less in line with the reasonable expectations people had when they decided to buy the windows, I'm inclined to say that that was included in the value of the windows as it's recorded in the GDP when the window was purchased.

It's kind of nice to think of GDP as the value of all the goods and services we produce; modulo some concerns about how we count our leisure, our social interactions, and other nonpecuniary pleasures of life, per capita GDP is more nearly what it purports to be, even if it can't be measured perfectly. Ultimately, the hope is that any errors we make are systematic, and that GDP, as measured, performs well at whatever we try to use it for; from that standpoint, it really does seem to do a reasonable job at measuring economic growth, and, ultimately, that's probably good enough.