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We study the incidence of offshoring, or trade in tasks, on firms' productivity and on manufacturing employment in a standard economic-geography model with iceberg trade costs and a continuum of tasks. In a two-countries world where one country has a Hick's neutral technological edge over the other, tasks in which the productivity edge more than offsets offshoring costs get offshored, giving rise to global disintegration of the production process. Offshoring raises firms' productivity and the number of manufacturing firms in the offshoring countries, thereby reducing costs of living. The general equilibrium incidence of offshoring on labor demand is shown to depend on offshoring costs and trade costs. For high enough offshoring costs, interior equilibria where both countries still produce manufactured goods are likely to be sustained. In this case, offshoring will boost labor demand for low enough trade costs. If, on the other hand, offshoring costs are low enough, core-periphery equilibria with all manufacturing in the offshoring country are likely to emerge. In this case, manufacturing labor demand is positively affected by offshoring as long as offshoring costs are not too low. In a threecountries extension, we show that a country would suffer welfare and employment losses from the adoption of policies that limit its firms' possibility to go offshore while similar countries allow offshoring.