Regular Grind

When I was a computer programmer, I had a coworker who often preferred very different kinds of solutions to problems than I did. If I proposed a design of some sort that was different from what he would typically do, he would frequently use the word "just" (in the sense of "merely" or "simply") as, it felt to me, something of a cudgel; he would be saying something that sounded to my ear like "Why would you take Tylenol for a headache when you could just self-administer brain surgery?" I don't know whether it was an attempt on his part, conscious or unconscious, to make me think that, well, yeah, brain surgery does sound simpler, but it always sounded clumsily tendentious to me.

In more subtle contexts, though, such verbal patterns do affect our thinking, and often our own language places constraints on our own thoughts. As George Orwell noted, sloppy language is often indicative of sloppy thinking, and wordplay is sometimes used as a substitute for thinking or argument. Oratory involving slippery homonyms usually strikes me as disingenuous, but it may often be that the speaker has confused himself before offering his confusion to others; he's not making a bad argument in an attempt to persuade people of something he believes for other reasons, but is instead sharing his own sloppy reasoning processes.

Homonyms are, I think, one of the more prolific sources of this kind of confusion, but consider how much damage can be done by the simple (and ubiquitous) word "the". Prepending a noun-phrase with the definite article can imply both existence and uniqueness in a way that the listener often won't even bother to question. Consider a famous "paradox" from mathematical set theory: does "the" set of sets that do not contain themselves contain itself? If I mention "the set that contains 2 and 5", the average listener, without even realizing it, will mentally add the restriction "and contains no other elements" to make the set unique; if I say "the set that contains 2 and 5 but not 4", the listener will be thrown off by the explicit restriction, and may realize that, but for the "the", there's no reason to believe that this set has been fully specified. As for existence, a more explicit contradiction — "the set that contains 4 but not 4" — might engage a similar awareness, but a broader description of a set ("the set that contains all sets that do not contain themselves, and has no other elements") seems to make people feel as though there ought to be one and only one set meeting that description, and that one's inability to answer binary questions about it (does it contain itself?) is a paradox. The careless listener assumes the question should have the answer "yes" or the answer "no", when in fact it is simply ill-posed; the phrase "the set that contains all sets that do not contain themselves, and has no other elements", like "green day" or "too much garlic", obeys all the rules of syntax but corresponds to no actual or even imaginable construct.

This, in fact, is a slightly broader phenomenon; it is the "will you stop beating your wife?" question. Putting an assumption at the heart of a question can evade the detection of the assumption; the listener (and perhaps speaker) will be busy setting off to answer the question when the question itself actually makes no sense. Listeners are used, perhaps, to looking for false statements; when a statement isn't even coherent enough to be wrong, they may accept whatever is necessary to fit it into their expectations. Listeners should be more careful about analyzing what they hear — and speakers, at least those who intend good faith, should be careful about constructing what they say.

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.