VoxEU Column International trade

Trump’s China tariffs: Lessons from first principles of classic trade policy welfare analysis

Traditional analysis of tariffs in a partial equilibrium setting can tell us much about the welfare consequences of the US-China trade war. The column argues that, as tariffs ratchet up, welfare costs for both sides increase disproportionately. The cost of trade diversion in the US to less-efficient suppliers likely overwhelms any terms-of-trade gain the US might enjoy. In all cases, exporters in the rest of the world benefit.

Textbooks on international trade devote considerable space to basic welfare analysis of tariffs in a partial equilibrium setting. The analysis demonstrates the basic economic mechanisms through which tariffs cause economic losses. It has important implications for the large and discriminatory tariffs currently used by the US.

The small country case

The starting point, usually called the ‘small country case’, is usually the case when the imposition of a tariff does not affect the world (net of tariff) price. This analysis is usually focuses on the areas under the demand and supply curves due to the price changes induced by the tariff (for an example see Krugman and Obstfeld 1991: 1988).

Two conclusions, seldom mentioned in textbooks, follow:

Conclusion 1: The welfare loss from tariffs is convex in the tariff rate

In other words, the cost of increasing a tariff from 10% to 20% is higher than the cost of increasing a tariff (on the same goods) from zero to 10%. The economic intuition behind this general result is that when a tariff is increased from zero to some positive value, it displaces only demand and supply, which was operating at close-to-world-market prices. This means that the welfare from the initial foreign supply and domestic demand displaced by a ‘small’ tariff is second-order small. 

In contrast, when a tariff is increased from a positive value to an even higher one, the marginal units of supply and demand displaced will already have, as a starting point, a difference between the world market and the domestic price. In technical parlance this means that increasing a tariff from zero to a small positive number leads to welfare losses in the form of triangles, whereas increasing a tariff from a positive level even further leads to welfare losses in the form of ‘rectangles’. 

When there are linear demand and supply curves one can be more specific: the welfare loss of a tariff (for a small country) is proportional to the square of the tariff rate. This implies that a tariff rate of 25% involves a welfare loss which is 25 times higher than a tariff on the same good of 5%. 

These principles imply that, if we are interested in welfare losses, we should not be looking at the average tariff rate. With linear demand and supply functions the welfare loss from a tariff structure should be proportional to the squares of the tariff rates; with the factor of proportionality given by the size of imports and the slopes of the demand and supply functions). 

This principle of the more than proportional increase in the welfare loss has important implications: 

  • US trade war tariffs are additional. Admittedly, existing tariffs were low.  
  • Many tariffs were imposed in two steps. First 10%, then 25%. Convexity implies that the welfare cost of the second step must be much larger. In August 2019, President Trump further increased tariffs on many goods to 30% (the reason given was that the Chinese government has not met US demands when faced with 25% tariffs). Again, convexity implies that this last step might be more costly than the previous ones, although it increases the tariff rate by ‘only’ 5 percentage points. Bown and Irwin (2018) show that, in many cases, US import tariffs could reach 40% if the US were to leave the WTO.
  • Average tariff rates are misleading. The US will soon levy a tariff of 30% on most imports from China, that is on one-fifth of total US imports. This is often characterised as an average tariff rate of 6% (one-fifth of 30%). But an average tariff of 5% on all imports would lead to much lower welfare losses:
    • The welfare loss due to a tariff of 5% on all imports should be proportional to the square of 5, or 25 units.
    • The welfare loss due to a tariff of 30% on one-fifth of imports should lead to a welfare loss proportional to the square of 30 and multiplied by one-fifth, or 180 units. That is, it is more than six times as high.

The analysis could of course also be applied to the Chinese reaction, which have included tariffs on US goods. The rates chosen by China were initially  less than half of the US rates, between 5% and 10%. This would have implied that welfare costs for China about a quarter of those for the US, per unit of pre-tariff trade. More recently, however, China has also ratcheted up its tariffs to levels similar to that of the US.

However, Chinese imports from the US are much smaller. The amount of imports subject to Chinese tariffs is about one-third of the goods subject to US tariffs, which implies that the total welfare loss for China is an order of magnitude lower. 

Conclusion 2: The welfare loss from a discriminatory tariff is higher than if the same tariff covers all imports

A country-specific tariff is conceptually equivalent to levying a general tariff on all imports while providing a production subsidy for competing producers from the rest of the world –t that is, all the countries not covered by the tariffs (Gardner and Kimbrough 1990). Current US tariffs are levied only on imports from China, implying that a production subsidy goes to European, Asian and other competitors. US consumers pay this subsidy in the form of higher prices. It follows immediately that the welfare cost to the US from tariffs of China is higher than if the US were to impose tariffs on all imports. 

The indirect harmful consequences of country-specific tariffs are the main reason that the 'most favoured nation' principle is a cornerstone of the global trading system (Hashimzade et al. 2011).

The large country case

The small country case is not a useful framework in which to analyse discriminatory tariffs because, with homogeneous goods, any discriminatory tariff in a small country would just lead to a complete re-routing of imports: US imports from China would collapse to zero, and be fully substituted by imports from the rest of the world. This is actually what is happening the other way round, i.e. for US agricultural exports, like Soybeans. China’s tariffs on these commodities has led to a collapse of Chinese imports from the US, which are fully substituted by exports from other producers, the Brazil (whereas US exports of soybeans to markets formerly served by Brazil, like the EU, are soaring). 

Standard theory implies that a large country might benefit from imposing an import tariff if the lower import demand caused by the tariff induces foreign producers to lower their price. If there is no retaliation, this can lead to a situation in which the home country gains because the terms-of-trade benefit outweighs the consumer and producer welfare losses described above (again, see Krugman and Obstfeld 1991: 191). 

The so-called ‘optimal’ tariff is the point at which the terms-of-trade gain from any further small increase in the tariff rate just balances the traditional welfare losses. There is little empirical evidence to support the concept of optimal tariffs (Bowen 2015), but this is the best argument that can be made for Trump tariffs.

But the effects mentioned above also have a bearing on this argument:

  • The optimal tariff is finite. This has a simple logical implication: as the tariff rate increases and gets closer to the optimal rate, the (potential) welfare gain from increasing the tariff further must start to fall: the welfare gain from the ‘large country tariff’ is a concave function of the tariff rate (Suranovic 2005). The higher the tariff, the lower the marginal welfare. When the actual tariff is above the optimal one, marginal welfare is negative.
  • The optimal discriminatory tariff is smaller than the optimal non-discriminatory one. This result follows from conclusion 2 in the small country case. The difference in the welfare consequences of a discriminatory tariff and one erga omnes depends in the first instance on the elasticity of supply coming from the producers located in the countries not covered by the tariff. The size of the ‘trade diversion’ as a result of the discriminatory tariff is thus decisive. 
  • Killing bilateral trade maximises welfare losses. If a tariff is so high that it completely chokes off bilateral trade, the country imposing it can only lose. This follows immediately from the fact that, in this case, tariff revenues will be zero and the home country can only import at a higher cost from the rest of the world. Reaching the point at which bilateral imports go to zero maximises the welfare cost of a discriminatory tariff. Higher tariff rates would be meaningless.

Table 1 summarises this analysis:

Table 1 Welfare consequences of discriminatory tariffs imposed by US on imports from China (large country case)

Source: author's calculations, assuming the US imposes a tariff only on Chinese goods.

The potential for trade diversion in the US-China case

Trade diversion – switching to competing, but higher-cost supply from the rest of the world – thus plays a crucial role in the cost-benefit analysis of discriminatory tariffs. In the current trade war between the US and China, it is likely that trade diversion will be substantial. 

We can estimate the potential for trade diversion in two ways:

  • China provides about one-quarter of US imports. Supply from the rest of the world (EU, Canada, Mexico, other Asia) is three times as large.
  • China accounts for about one-fifth of global exports. (Not counting the US, and counting only manufacturing goods, which are the ones on which the US is levying tariffs). Other potential sources of exports to the US are four times as large as China. There are, of course, products in which China is the main global supplier. But production can migrate to other countries with low wages. For example, smartphone exports from Vietnam are booming.

Both approaches thus suggest that that potential supply from other sources (at costs higher than those of previous Chinese suppliers) should be large, relative to the imports from China displaced by the tariffs. In these conditions, it becomes highly likely that the cost of trade diversion as US importers switch to less-efficient suppliers overwhelms any terms-of-trade gain the US might enjoy. 

The optimum tariff argument makes sense only if the market of the country imposing the tariff (the US) is large enough for exporters that they feel constrained to lower their price. The GDP of the US is large – in current-dollar terms it remains the largest in the world – but it represents only a fraction of global GDP. And the share of the US market in overall Chinese exports is 15-20%, roughly the share of the US in global GDP. This might explain why most empirical estimates suggest that Chinese suppliers have not reduced their prices on the US market (Amity et al. 2018).

Beyond partial equilibrium 

I am merely drawing lessons from standard, classroom trade analysis of tariffs in a partial equilibrium setting. But in a general equilibrium setting, the overall conclusions are unlikely to change, as Gardner and Kimbrough (1990) have shown. And even in the partial equilibrium approach, tariffs can be more costly than suggested by standard welfare analysis if they discourage entry (Caliendo at al. 2017). 

The US trade war against China involves, of course, much more than tariffs. For example, disadvantaging leading Chinese technology firms is clearly designed to interrupt the flow of ideas, which represents a third wave of globalisation (Baldwin 2018). These aspects can only add to welfare losses.

In the real world setting, other factors change. The exchange rate might move, or the Chinese government might alter other elements of trade policy, for example, VAT rebates on exports (Garred 2019). 

Trade diversion has also macroeconomic consequences. Because rest-of-world (non-Chinese) producers can raise their prices by up to 25% and still remain competitive in the US, prices for many consumer goods in the US are likely to increase. The indirect effect of Trump tariffs on consumer prices is therefore likely to be much greater than San Francisco Fed's recent estimate of a direct impact of only 0.1% (Hale et al. 2019)

In a general equilibrium analysis, a tariff has little effect on the trade balance, which is determined by the overall difference between spending and income. By contrast, the partial equilibrium analysis presented here does imply that a tariff leads to an improvement in the balance of trade (at least, in the good on which the tariff is being levied). The partial equilibrium analysis therefore supports the idea that a tariff war can reduce a trade deficit, especially a bilateral trade deficit. But this approach also implies that the (purely economic) welfare cost of the discriminatory tariffs to achieve this goal is large.


Amiti, M with S J Redding and D Weinstein (2019), "The Impact of the 2018 Trade War on U.S. Prices and Welfare” NBER working paper 25672.

Baldwin, R (2018), The Great Convergence: Information Technology and the New Globalization, Harvard University Press.

Bowen, L (2015), "Rethinking the Optimal Tariff Theory", Chicago Policy Review, 15 January.

Bown, C P and D AIrwin (2018), “What Might a Trump Withdrawal from the World Trade Organization Mean for US Tariffs?”, PIIE policy brief 18-23. 

Caliendo, L, R Feenstra, J Romalis, and A Taylor (2017), “Theory and evidence for the last two decades of tariff reductions”,, 26 April.

Gardner, G W and K B Kimbrough (1990), “The Economics of Country-Specific Tariffs", International Economic Review 31(3): 575-588.

Garred, J (2019), "The persistence of trade policy beyond import tariffs”,, 9 July. 

Hale, G, B Hobijn, F Nechio, and D Wilson (2019), "Inflationary Effects of Trade Disputes with China", Federal Reserve Bank of San Francisco Economic Letters 2019-07.

Hashimzade, N, H Khodavaisi, and G D Myles (2011), "Uniform Versus Discriminatory Tariffs", Review of Development Economics 15(3): 403-416.

Krugman, P R and M Obstfeld (1991), International Economics Theory and Policy, 2nd ed, HarperCollins.

Suranovic, S M (2004), "The Optimal Tariff", International Trade Policy and Theory 90(9).

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