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.