I develop a model of agriculture on heterogeneous land to study the relation between trade, productivity, and welfare in Peru, where farmers face high internal and external trade costs. I quantify the model with new data on crop prices, yields, and land allocations. I then measure the effects of changes to trade opportunities. A policy of paving roads raises aggregate productivity (4.9%) and the median farmer’s welfare (2.7%), but increased competition from remote suppliers harms 20% of farmers. An increase in international grain prices spreads unevenly across regions, benefiting farmers but hurting urban consumers close to ports.

We study how migration shapes aggregate and regional comparative advantage, exploiting a large migration of farmers to Brazil’s West between 1950 and 2010. Migration allowed workers to sort according to their own comparative advantage, reallocating knowledge and raw labor to high-productivity regions. In a quantitative model, we find that migration cost reductions reshaped Brazil’s comparative advantage and contributed to its rise as a leading commodity exporter—accounting for 25% of the observed changes in specialization. Road expansions were key drivers of migration. Migration opportunities, moreover, account for a substantial share of the gains from trade.