world of economics


  • Optimal tariffs allow a country to exploit its market power in international trade. A country can improve its terms of trade by unilaterally restricting its exports if it faces a downward-sloping demand for them or restricting its imports if it faces an upward-sloping foreign export supply. This argument against unilateral free trade is over 150 years old but it remains central to modern theories that explain trade agreements and their rules. This, along with recent evidence that prior to such agreements countries exploit their market power in trade, shows that optimal tariffs may be an important positive theory of protection.
  • When a large nation imposes a tariff, the volume of trade declines but the nation’s terms of trade improve. The decline in the volume of trade, by itself, tends to reduce the nation’s welfare. On the other hand, the improvement in its terms of trade, by itself, tends to increase the nation’s welfare.
  • The optimum tariff is that rate of tariff that maximizes the net benefit resulting from the improvement in the nation’s terms of trade against the negative effect resulting from reduction in the volume of trade. That is, starting from the free trade position, as the nation increases its tariff rate, its welfare increases up to a maximum (the optimum tariff) and then declines as the tariff rate is raised past the optimum. Eventually the nation is pushed back toward the autarky point with a prohibitive tariff.
  • However, as the terms of trade of the nation imposing the tariff improve, those of the trade partner deteriorate, since they are the inverse, or reciprocal, of the terms of trade of the tariff-imposing nation. Facing both a lower volume of trade and deteriorating terms of trade, the trade partner’s welfare definitely declines. As a result, the trade partner is likely to retaliate and impose an optimum tariff of its own.
  • While recapturing most of its losses with the improvement in its terms of trade, retaliation by the trade partner will definitely reduce the volume of trade still further. The first nation may then itself retaliate. If the process continues, all nations usually end up losing all or most of the gains from trade.
  • Note that even when the trade partner does not retaliate when one nation imposes the optimum tariff, the gains of the tariff-imposing nation are less than the losses of the trade partner, so that the world as a whole is worse off than under free trade. It is in this sense that free trade maximizes world welfare.

Illustration of the Optimum Tariff and Retaliation

Figure 1
  • Suppose that with the optimum tariff, Nation 2’s offer curve rotates to 2*.
  • If Nation 1 does not retaliate, the intersection of offer curve 2* and offer curve 1 defines the new equilibrium point E*, at which Nation 2 exchanges 25Y for 40X so that PX /PY = P W = 0.625 on the world market and for Nation 2 as a whole.
  • As a result, Nation 1’s (the rest of the world’s) terms of trade deteriorate from PX /PY = PW = 1 to PX /PY = PW = 0.625, and Nation 2’s terms of trade improve to PY /PX = 1/PW = 1/0.625 = 1.6.
  • With the tariff associated with offer curve 2*, not only does the improvement in Nation 2’s welfare resulting from its improved terms of trade exceed the reduction in welfare due to the decline in volume of trade, but it represents the highest welfare that Nation 2 can achieve with a tariff (and exceeds its free trade welfare).
  • However, with deteriorated terms of trade and a smaller volume of trade, Nation 1 is definitely worse off than under free trade. As a result, Nation 1 is likely to retaliate and impose an optimum tariff of its own, shown by offer curve 1*.
  • With offer curves 1* and 2*, equilibrium moves to point E**. Now Nation 1’s terms of trade are higher and Nation 2’s are lower than under free trade, but the volume of trade is much smaller.
  • At this point, Nation 2 is itself likely to retaliate, and in the end both nations may end up at the origin of Figure 1, representing the autarky position for both nations. By so doing, all of the gains from trade are lost.
  • Note that we have been implicitly discussing the optimum import tariff. More advanced treaties show, however, that an optimum import tariff is equivalent to an optimum export tariff.
  • Finally, note that the optimum tariff for a small country is zero, since a tariff will not affect its terms of trade and will only cause the volume of trade to decline.
  • Thus, no tariff can increase the small nation’s welfare over its free trade position even if the trade partner does not retaliate. Finally, recent empirical research by Broda, Limao, and Weinstein (2008) indicates that nations do indeed impose higher tariffs on goods with lower export elasticity (i.e., in which the nations have more market power).


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