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We present a dynamic comparative advantage model in which moderate reductions in import tariffs can generate sizable increases in trade volumes over time. A fall in tariffs has two effects. First, for given factor endowments, it raises the degree of specialisation, leading to a larger volume of trade in the short run. Second, it raises the factor price of each country's abundant factor, leading to diverging paths of relative factor endowments and a rising degree of specialisation. A simulation exercise shows that a fall in tariffs produces a disproportional increase in the trade share of output as in the data.