On the Optimal Tariff and the Law of Demand

In his 1987 Economic Review article detailing the history of optimal tariffs, Thomas Humphrey writes:

“[The optimal tariff model] assumes unrealistically (1) that foreign countries will not retaliate with tariffs of their own, (2) that elasticities of supply and demand in foreign trade are not so large in the long run as to render the tariff ineffective, (3) that the optimum tariff rate can be precisely identified and skillfully administered, and (4) that politicians can resist pressures to raise tariff rates above the optimum level” 

All four of these objections of the optimal tariff model are difficult to overcome when addressing the model as a policy procedure. I have written on some of these other points before (as have many people far smarter than I). However, I want to focus on point #2 and I’ll try to keep this not wonky.

That the optimal tariff model depends on elasticities of supply and demand is not controversial. Indeed, that is how the calculation of the tariff works. However, given condition (2) above, we can see the optimal tariff is, at best, a short-run policy. This follows from the Law of Demand.

Most people tend to think of the Law of Demand in its common form: all else held equal, an increase in the price of a good will reduce the quantity demanded of that good. But there is a second Law of Demand: the longer a price remains relatively high, the more elastic the demand for a good becomes.

Given that the goal of a tariff is to increase the relative price of a good, then as long as the tariff remains in place, the more elastic demand for that good becomes. Indeed, if the tariff remains in place and, again, everything else held equal, over enough time, the tariff could cause the demand curve for a good to become perfectly elastic. A perfectly elastic demand curve would indicate no consumer welfare gains from the trade. The elimination of consumer welfare would then mean that the tariff is a net welfare loss for the country in question. So, an optimal tariff cannot persist in the long run, only in the short run given the Second Law of Demand.

Some might object by saying: “But wait, Jon, you sly and handsome devil! That would just mean the optimal tariff would need to be reduced. There’s no reason to think the tariff would eventually become a net welfare loss.”

Indeed, it may very well be that some benevolent government can milk the tariff for everything its worth by constantly adjusting the optimal tariff as the elasticities change. However, this is where public choice comes into play. As Gordon Tullock discussed in 1975, government support of firms is very difficult to remove. Domestic producers have capitalized on the gains the tariff has provided them. To remove the tariff is not to eat up “extra normal” profit for monopolizing firms, but rather to eat into normal profit for them. These firms are legitimately harmed, profit-wise, by the removal or alternations of these protections like an optimal tariff. Any adjustment to an optimal tariff, even if demanded by the economic scenario is likely to be fought tooth-and-nail by affected firms. The resulting stagnation will likely result in an optimal tariff that is too high! Any short-run gains from the optimal tariff (assuming all the above conditions are met) would likely be eaten up by this un-optimal tariff that results from the changing elasticity and lack of change in the statuary tariff.

In a general-equilibrium theoretical framework, an optimal tariff makes perfect sense. But, once public choice enters the fray, the reasonableness of an optimal tariff goes out the window. And, as my professor Garett Jones likes to say: in a knockdown fight between general equilibrium and public choice, public choice wins every time.

HT to Dallas Weaver, whose comment on this Cafe Hayek blog post inspired this post.