We study a two-country two-sector model of international trade in which one sector produces homogeneous products while the other produces differentiated products. The differentiated-product industry has firm heterogeneity, monopolistic competition, search and matching in its labor market, and wage bargaining. Some of the workers searching for jobs end up being unemployed. Countries are similar except for frictions in their labor markets, which include efficiency of matching, cost of vacancies, firing costs, and unemployment benefits. We study the interaction of labor market rigidities and trade impediments in shaping welfare, trade flows, productivity, and unemployment. We show that both countries gain from trade but that the flexible country - which has lower labor market frictions - gains proportionately more. A flexible labor market confers comparative advantage; the flexible country exports differentiated products on net. A country benefits from lowering frictions in its labor market, but this harms the country’s trade partner. And the simultaneous proportional lowering of labor market frictions in both countries benefits both of them. The model generates rich patterns of unemployment. In particular, better labor market institutions do not ensure lower unemployment, and unemployment and welfare can both rise in response to a policy change or falling trade costs.
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