Dollars and Jens
Wednesday, July 16, 2008
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 achieved 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.

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