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On Tariffs and Constant Returns to Scale

Warning: Wonky

On Facebook, GMU Econ alum Jon Murphy asked the following question about the penultimate paragraph in my letter of earlier today on the silly notion that tariffs aren’t a tax on consumers. First, here’s that paragraph:

Economic pedants will note that, under what economists call “constant returns to scale,” it’s possible that in the long run prices paid by consumers for protected goods will be no higher than before the tariffs were imposed. The reason is that the tariffs attract into protected industries enough new resources to bring the prices of goods sold by protected industries back down to pre-tariff levels. But these resources must be drawn away from other domestic industries, causing prices that consumers pay for non-protected goods and services to rise.

And here’s Jon’s question about this paragraph:

If there are constant returns to scale, why would a tariff be necessary? Why wouldn’t producers already produce at the lower price if that’s the competitive price? I don’t understand why tariffs are needed to attract resources in.

Jon’s question is good. I responded to him on Facebook – a response that I use as the basis for what I write below.


In my letter I debated whether or not to include the paragraph that sparked Jon’s question, knowing that what I describe in that paragraph is an unrealistic limiting possibility. But I chose to include the paragraph precisely to ward off what I intentionally call “pedants,” as well as to enable me to make the point that, as a result of tariffs, prices of outputs even in many non-protected industries will rise.

The best way to convey the meaning of “constant returns to scale” is a simple example. Suppose Acme, Inc. can annually produce one million widgets, at a cost of $10 per widget, using a certain size (“scale”) of factory and combination of resources. Constant returns to scale prevail if Acme builds a second identical factory that enables it annually to produce an additional one million widgets at a cost of $10 per widget.

Now to the tariff. The initial effect of an import tariff on widgets is to reduce the supply of widgets available for sale in the home country. This reduction in supply causes the price of widgets in the home country to rise. (This effect, it must be emphasized, is precisely what proponents of protective tariffs hope and expect to happen.) This higher price attracts additional home-country resources into the production of widgets, causing the price of widgets to fall somewhat below the peak that it hit just after the tariff was imposed – or, put differently, below the price that widgets would sell for in the home country if, despite the imposition of the tariff, additional resources were somehow prevented from being drawn into the domestic widget industry.

Realistically, the new ‘equilibrium’ price of widgets in the home-country will remain higher with the tariff than it was before the imposition of the tariff. But there can be no doubt that the tariff-induced higher price of widgets, by drawing more workers and other resources into the domestic widget industry, modifies the price hike in widgets.

The question now is: By how much does the drawing of additional resources into the domestic widget industry modify the tariff-induced price hike of widgets? In the limit, the equilibrium price of widgets will fall back, despite the tariff, to what it was before the tariff was imposed. “In the limit” is a key qualification, and one that I ought to have emphasized in my letter. Like many results that are ‘in the limit,’ this one is unrealistic but theoretically – merely theoretically – possible. Yet unrealistic theoretical possibilities are the stock in trade of pedants and clever sophomores, which is the chief reason I mentioned this limiting possibility in my letter.

This limiting possibility will occur, theoretically, if there are constant and non-lumpy returns to scale in the industry. (By “non-lumpy,” I mean the absurdly unrealistic possibility that the scale of the industry’s operation can be increased or decreased by any amount – 5%, 5.1%, 10%, 100%, 500%, whatever% – with the per-unit cost of production remaining unchanged.)

Allow me now to get even wonkier. Think of it this way: There’s an equilibrium price and quantity of output in a constant-returns-to-scale American widget industry. Production beyond this quantity is unprofitable. Now let demand for widgets increase because the price of a domestically produced substitute good – gidgets – rises. More resources are drawn into the American widget industry. Because the American widget industry is characterized by constant returns to scale, the initially higher widget price caused by the increase in widget demand will result, eventually, in the price of widgets being the same as it was before the increase in widget demand.

Now change the hypothetical a bit: Let demand for the domestic output of widgets increase, not because of an increase in the price of gidgets, but because a tariff raises the price of a different substitute good for widgets – namely, imported widgets. Because we’re assuming constant and non-lumpy returns to scale, the higher widget price (caused by the tariff) will attract enough additional domestic resources into the American widget industry to bring the price of the widgets back down to the pre-tariff level.

It’s worth pausing here to remind you that the withdrawal of resources from non-widget industries into the widget industry will raise the prices that American consumers pay for many goods other than widgets.

Again, the assumption of non-lumpy constant returns to scale is ridiculously unrealistic. Resources in reality are too heterogeneous to make the assumption of what we might call “constant constant returns to scale” realistic. (To make this assumption is, effectively, to assume away comparative advantage.) In reality, a U.S.-government-imposed tariff on widget imports will cause consumers in the U.S. to pay higher prices for widgets not only immediately after the tariff is imposed but for as long as the tariff remains in force. And also, the prices of some non-tariffed goods and services will also rise because the widget tariff will draw some resources out of non-widget American industries into the American widget industry.