This paper develops a two-country macro model with endogenous tradability to study features of international economic integration. Recent episodes of integration in Europe and North America suggest some surprising observations: while quantities of trade have increased significantly, especially along the extensive margin of goods previously not traded, price dispersion has not decreased and may even have increased. These observations challenge the usual understanding of integration in the literature. We propose a way of reconciling these price and quantity observations in a macroeconomic model where the decision of heterogeneous firms to trade internationally is endogenous. Trade is shaped both by the nature of heterogeneity -- trade costs versus productivity -- and by the nature of trade policies -- cuts in fixed costs versus cuts in per unit costs like tariffs. For example, in contrast to tariff cuts, trade policies that work mainly by lowering various fixed costs of trade may have large effects on entry decisions at the extensive margin without having direct effects on price-setting decisions. Whether this entry raises or lowers price dispersion depends on the type of heterogeneity that distinguishes the new entrants from incumbent traders.