Tariffs Part 2: Monopsony
The Case for Tariffs — Optimum Tariff Theory
Whilst many Economists think Trump’s Tariffs are insane, ugly even, there are many arguments in defence of tariffs. Here we focus on the case for a tariff as a means of maximising a country’s gains from trade. This is the optimum tariff theory (1).
In essence, as a monopsony buyer of certain imported goods, the USA may indeed benefit from tariffs.
So far we have made a tacit assumption in our analysis. This assumption is that country X is a small country such that its demand for electric cars is a small part of the total world demand for electric cars. This means that country X can buy any amount of the global supply of electric cars at the same price. This was why we could assume that the global supply of electric cars was perfectly elastic at the global market price Pw. Clearly, this assumption may be justified for many small economies: if New Zealand or Malta or Kenya buy more or less electric cars, they are unlikely to affect the global equilibrium price of electric cars. But it is unlikely to be true for larger economies. If the USA or China or Japan or Germany buy more or less electric cars, then this action will probably impact on the global equilibrium price of electric cars. If they buy more, price Pw will rise, and if they buy less, price Pw will fall. The effect of this is to change the effect of implanting a tariff. Indeed, it is possible that for such a larger country a tariff can yield a net welfare gain for the society. This is the case for an optimum tariff.
To understand this point, let us amend Figure 1.
In this diagram, assume first free trade, with country X accessing electric cars at the world price Pw. Total consumption of electric cars is OQ2, and of this quantity, Q1Q2 are imported. Consumer surplus is abPw. Now imagine that a tariff t is applied. Previously we assumed that the effect of this tariff is to raise domestic prices to Pw + t, with consumer surplus falling to acPw+t. However, this outcome was based on the assumption that the world price of cars did not change if country X consumed less electric cars. Now we assume that country X’s demand for electric cars is a significant component of the world demand for such cars; hence, as country X demands fewer cars the world price of electric cars falls to Pwt. What this means is that the terms of trade, which is the ratio of a country’s export prices to its import prices, have moved in favour of country X. Country X is paying less for imported electric cars than before and this, in itself, makes country X better off. In terms of Figure 1, since country X now faces a lower global price of electric cars, the domestic price after the tariff (i.e. Pwt + t) is lower than our previously assumed domestic price post tariff (Pw + t). The domestic price of electric cars has still risen due to the tariff, but it has risen by less. Thus, of the total amount of the tariff, about half is paid by domestic consumers, and half is paid by foreign suppliers who now receive a lower price for their car exports to country X (and indeed to other countries in general).
In terms of the welfare effects of the tariff, there is still a deadweight loss due to production and consumption distortions, as indicated by the two shaded triangles. These losses, however, are less than before since the post-tariff price has increased by less. Furthermore, there is an additional welfare benefit since the government’s revenue from the tariff has increased. This is because, while the absolute amount of the tariff has not changed (being t), imports are larger now since price has risen less meaning domestic consumption has fallen less and domestic production has risen by less. So, the quantity of trade taxed has increased. And of this tariff of t, where previously it was all paid by domestic consumers, now only half is paid by domestic consumers and the other half is paid by global car producers who receive a lower price for each car exported to country X. This welfare benefit accruing to the state is indicated by the shaded rectangle. As can be seen, if the shaded rectangle is larger than the two welfare-loss triangles, then the tariff can actually increase total social well-being. In this case, the positive effect of the tariff on the terms of trade offsets the negative effect of the tariff on the initial domestic price level.
This situation, where a tariff can shift the terms of trade in favour of the levying country, arises from the fact that a large country will be a monopsony purchaser of imported goods. A monopsony consumer is one whose consumption of a good is sufficiently large relative to a market to ensure that, when the consumer increases its purchases, the effect of its increased demand is to raise the equilibrium price of the product. This is what we are assuming here, though we have highlighted the point in reverse: as country X reduced its purchase of electric cars it lowered the global equilibrium price of cars. Likewise, when country X purchased more electric cars it raised the equilibrium price of cars. This is what we mean when we say that country X does not, in fact, face a perfectly elastic supply curve for electric cars. Only small economies face a perfectly elastic supply curve for imported goods and for such small countries an optimum tariff level is zero. But larger countries will tend to face an upward sloping supply curve for imports, and for such countries an optimum tariff will be positive. This point can be explained with reference to Figure 2.
In this diagram, the downward sloping demand line is country X’s demand curve for imported cars. The global supply curve for electric cars is an upward sloping world supply line — as country X buys more cars on the global market it raises the world price of electric cars. The free-trade equilibrium price of cars is Pw, and country X imports QNT of cars. However, QNT is not the efficient welfare-maximising consumption of cars by country X. The reason is that, as country X buys more cars, it shifts the terms of trade against itself, driving up the global price of cars. This means that the marginal cost of a car for country X is not the price of the car. The marginal cost of a car is the price of that car plus the increase in the price of all the cars it is already importing. For example, suppose country X imported 1000 electric cars a year at a price of $10,000 a car. The total cost of importing those cars is 1000 x 10,000 = $10,000,000. Now imagine that country X wishes to buy an additional car per year, and this raises the global price of cars from $10,000 to $10,100. Hence the marginal cost of that car is $10,100 plus the extra $100 for all the 1,000 cars it was already importing, which now all cost $10,100 instead of $10,000. Hence the cost of the extra car is $10,500 + (1,000 x 100) = $10,500 + $100,000 = $110,500. This is a rather extreme example, but it makes the point. It means that the last car purchased by country X cost the person who bought it $10,500, but it cost country X as a whole £110,500. Such a purchase represents a deadweight welfare loss: the benefit to the marginal consumer of the last car purchased is measured by its price, which is $10,500; but its cost to country X’s population as a whole is $110,500. Clearly the marginal cost far exceeds the marginal benefit — the car has reduced the welfare of country X. In Figure 2the marginal cost of buying more cars is the MC line above the supply line. The optimum quantity of cars for country X is Qo, where the demand (marginal benefit) line intercepts the MC of cars line. By consuming at QNT the society incurs a deadweight social welfare loss of abc. In effect, the society is consuming too many imported cars and should reduce its consumption to Qo. As Abba Lerner expressed the point in his The Economics of Control:(2)
If the country chooses to disregard entirely the effects on the rest of the world economy, it imports and exports less … Instead of importing goods up to the point where the price of the import (including the cost of transport) equals the domestic price, it will import only up to the point where the marginal cost to the country of importing another unit — the increase in the total amount spent on the importation of the goods — equals the domestic price … If the elasticity of supply of a good is infinite, so that the price does not rise at all when more of it is bought, the marginal cost to the nation is equal to the price per unit … But if the country’s purchases have some influence on the price, so that when it buys more the price, which is the average cost, rises, then the marginal cost is greater than the price, or average cost, and there is a divergence from the optimum allocation of resources.
To reduce imports of cars to the efficient quantity Qo the country can impose an optimum tariff, indicated by t in the diagram. What this tariff does is raise the import price of cars to reflect the actual marginal social cost of purchasing the cars so that the MC line now intersects the demand line at Q0. This is the social welfare maximising import of electric cars. The deadweight loss has been eliminated. Because country X is purchasing fewer cars the global price of electric cars falls to Pwt. Since country X is now paying less for cars (the terms of trade effect) the burden of the tariff is split between domestic consumers and foreign suppliers. Domestic consumers pay (Pwt+t — Pw) of the tariff per car, and importers pay (Pw — Pwt). The government’s revenue from the tariff is t x Qo.
Calculating the Optimal Tariff (3)
The size of the optimum tariff depends upon the elasticity of supply of the global supply of the product the country imports — in our example, electric cars. The more inelastic the supply line the greater will be the terms of trade effect of the country’s imports from the global market and the larger will be the optimum tariff. To see this, consider Figure 2. The point of the tariff is to ensure that the domestic price to consumers is equal to the marginal cost of purchasing cars on the global market. This occurs of when the price of cars after the tariff is Pwt+t. The amount of the tariff which secures this result is (Pwt+t) — Pwt. This is the amount t indicated. The rate of the tariff relative to the global purchase price of cars is:
Pwt+t — PwtPwt
Viewed from the perspective of country X, Pwt+t is equal to the Marginal Cost to country X of buying the product, while Pwt is the price P of imported cars when Qo cars are imported. Hence, we can re-write the rate of the tariff as:
MC-PP
The Total Cost for country X of purchasing cars on the global market is:
TC = PQ
where P is the world supply price of electric cars as expressed by the world supply curve. P is a positive function of Q, that is:
P = f(Q)
Hence, the Marginal Cost to country X of purchasing additional units of cars is:
dTCdQ = d(PQ)dQ
Using the product rule, this can be written:
dTCdQ = P dQdQ + Q dPdQ
dTCdQ = MC = P + Q dPdQ
It follows that:
MC — P = P + Q dPdQ — P
MC — P = P — P + Q dPdQ
MC — P = Q dPdQ
Dividing both sides by P to get the optimal tariff rate, we have:
MC-PP = QP dPdQ
MC-PP = 1PQdQdP
PQ dQdP is the expression for Price Elasticity of Supply when Q = f(P). But since we are assuming that P = f(Q) we re-write the formula for Price Elasticity of Supply as:
PQ 1dP/dQ
Therefore we arrive at the following equation:
MC-PP = 1PQ 1dP/dQ
Which can be written:
MC-PP = 1εs
where 𝜀s = price elasticity of supply.
Thus, the lower is the elasticity of supply, the larger will be the optimal tariff. For example, if the elasticity of supply is 2, then the optimal tariff rate will be 1/2 = 0.5 = 50%. If the elasticity of supply is 0.5, then the optimal tariff rate will be 2 or 200%. Only when elasticity of supply is infinite (which is the standard small-economy assumption of neoclassical theory) will the optimal tariff be zero.
Statistical Estimates
Several attempts have been made to calculate optimum tariff rates for large importing economies. In 2021, Douglas Irwin and Anson Soderbery estimated that optimal tariffs for the US in the early 1930s were 17.5 per cent. An important 2011 study for the National Bureau of Economic Research by Ralph Ossa of the University of Chicago, calculated optimal tariffs for a series of countries, including the US, China, India and the EU (4). He concluded that the optimal tariff rate for such economies averaged around 60 per cent, with welfare gains for the countries concerned ranging from 1 to 4 per cent of GDP. Table 1 summaries some of his results.
An optimal tariff of 60 per cent implies an elasticity of supply of imports to the large economy of about 1.7. The figures for the optimal tariff are quite high: such tariff rates are far in excess of Trump’s recent 10 per cent tariff on China and even his 25 per cent tariffs on iron and steel imports. Such tariffs would raise US import prices to consumers by about 30 per cent, this cost being offset by greater domestic production and higher government revenues. Yet the net welfare gains are relatively small — in the US case, about 2.3 per cent of GDP.
Broda, Limao, and Weinstein, writing in 2007, sought to estimate the supply elasticity for an extensive sample of 12,000 traded goods (5). They found that the median price elasticity of supply was 0.6 — which is to say, a 1 percent increase in the price of a good leads to a 0.6 percent increase in the volume of exports, which is in accordance of what optimum tariff theory predicts. Indeed, even small countries will have some influence over the price at which they import products. While this influence will be negligible in the case of homogeneous goods like oil, wheat, and natural gas, this influence is significant for differentiated goods, such as particular types or makes or brands of goods. The following chart highlights the significance of America’s import demand in the market for certain makes of car: there can be no doubt that if the US increases its purchases of Honda, Hyundai, Nissan, or Porsche cars it will tend to raise the price of those models.
Having calculated these elasticity of supply figures, the authors then looked at the tariff policies of 15 countries who were not members of the World Trade Organisation and were thus free to set their own tariffs (including, at the time the article was written, China) in order to see whether these countries, as optimal tariff theory would predict, set higher tariffs for those goods where their market-power in purchasing was greater. Their study suggested that they did.
We find that the typical country sets tariffs 9 percentage points higher in goods where it has medium or high market power relative to those with low market power. These goods represent two-thirds of each country’s sample. The effect is important in 13 of the 15 non-WTO countries; in China it is 35 percentage points. (7)
Thus they conclude that non-members of the WTO ‘systematically set higher import tariffs on goods in which they have market power, i.e. goods that are supplied inelastically.’ (8). They found also that the United States, although subject to the WTO with regard to tariffs, still erected higher non-tariff barriers to trade on those items in which they faced the most inelastic supply lines (9). This, say Broda, Limao, and Weinstein, emphasises the importance of WTO trading rules, since in their absence large economies like the US would almost certainly charge significantly higher tariffs — a conclusion recent events confirm.
Conclusion
Most students of economics are surprised to learn that for most reasonably-sized economies the optimum level of tariffs is positive. Economists are trained in the virtues of free-trade, and the welfare gains from trade are a core part of any introductory economics course. Yet, as with so many welfare results in economics, these gains from trade are predicated upon a world of perfect competition. If the world consisted of large numbers of small countries, each facing a perfectly elastic supply curve for imports, then an optimum tariff would indeed be zero. But, as economists increasingly recognised during the twentieth century, such results do not apply when the reality of imperfect competition is faced. One such market imperfection is monopsony. (10). A monopsony exists when the purchasing decisions of a consumer affect the market price of a good. Large firms and employers are usually monopsonists and so are large economies when they access global supply chains. As soon as this is the case, the cost to the country of purchasing greater imports exceeds the market price of the traded product since the act of purchasing the product turns the terms of trade against the consuming country, raising its import prices relative to its export prices. In such cases the social welfare maximising level of imports will be less than the free-market level of imports. The degree to which this is so depends on the price elasticity of supply of the imported product. So long as the price elasticity of supply is less than infinite, then the optimal welfare maximising tariff rate will be positive. This result is clear. As Paul Krugman and Maurice Obstfeld (both economists supportive of free-trade) acknowledge:
“Although economists often argue that deviations from free trade reduce national welfare, there are, in fact, some theoretical grounds for believing that activist trade policies can sometimes increase the welfare of the nation as a whole … It is possible … that in some cases the terms of trade benefits of a tariff out-weigh its costs, so there is a terms of trade argument for a tariff … The terms of trade argument against free trade, then, is intellectually impeccable but of doubtful usefulness.”
Intellectually impeccable but of doubtful usefulness. Why do Krugman and Obstfeld arrive at this conclusion? The reason is that, while it would be in the interest of one country to enact an optimal tariff, if many countries so acted the result would be a collective loss of the gains from trade which would damage the world economy as a whole. If other countries responded to country X’s implementation of tariffs on, say, electric cars, by imposing tariffs on products country X exported to them, then this would lower the prices country X received for its products and turn the terms of trade against them. As Lerner remarked, if all countries for whom optimum tariffs were positive went ahead and imposed them, then ‘the particular benefits cancel out while the general loss through the restrictions of international trade remains. If all countries persist in trying to exploit each other in this way, international trade would be completely destroyed with all the benefits that could have come from it.’ Even so, the optimal tariff remains the dominant strategy for any one country: if all other large economies forswear tariffs, then any country introducing such a tariff would gain, and if all countries implemented tariffs, any given country would be better off doing so too. To prevent this a world commitment to free trade is required; but it is just such a commitment that is lapsing in the current world economy. However ugly most economists believe tariffs to be, they can probably expect to see more of them.
- The first economist to articulate the argument for an optimum tariff was Robert Torrens in his 1824 Essays on the Production of Wealth. For this and subsequent developments of the theory see T.M. Humphrey, ‘Classical and Neoclassical Roots of the Theory of Optimum Tariffs’, Federal Reserve Bank of Richmond, Economic Review (July-August, 1987).
- A. Lerner, The Economics of Control: Principles of Welfare Economics (Macmillan, New York, 1944), p. 357.
- This method of deriving the optimum tariff is based on J. Sloman, A. Wride, and D. Garratt, Economics (Pearson, Harlow, Ninth Edition, 2015), pp. 723–4. I am grateful to Ryan Das for assisting me in re-working Sloman’s calculations.
- R. Offa, Trade Wars and Trade Talks with Data, NBER Working Paper №17347 August 2011, Revised January 2014. For a review of the evidence see F. Ferry, ‘What are the Best Tariffs for the U.S.? Economists Say: From 14% to 60%’ (October 2023), prosperousamerica.org.
- Broda, Limao, Wall Street Journal, 20 February 2025and Weinstein, ‘Optimal Tariffs: The Evidence’, p. 33.
- Wall Street Journal, 20 February 2025
- Ibid., p. 4.
- Ibid., p. 1.
- Ibid., p. 33.
- For an extended treatment of the effects of Monopsony in product markets, see my ‘Monopsony in Product Markets: An Economic Analysis’, Haberdashers’ Occasional Paper Number 67 (2023), OP67StJohnMonopsonyinProductMarkets.pdf
