This paper builds a tractable partial equilibrium model to help explain the role of trade preferences given to developing countries, as well as the efficacy of various subsidy policies. The model allows for firm level heterogeneity in demand and productivity and lets the mass of firms that enter be endogenous. Trade preferences given by one country have positive spillovers on exports to others in this model. Preferences given by the European Union to Bangladesh in an industry raise profits, resulting in entry, and some of these firms also export to the United States. The parameters of the model are estimated using cross sectional customs data on Bangladeshi exports of apparel to the United States and European Union. Counterfactual experiments regarding the effects of reducing costs, both fixed and marginal, or of trade preferences offered by an importing country are performed. The counterfactuals show that reducing fixed costs at various levels has very different effects and suggest that such reductions are more effective in promoting exports when applied at later stages when firms are more committed to production. A subsidy of 1.5 million dollars to industry entry costs raises exports by only 0.4 dollars for every dollar spent, but when applied to fixed costs of production, it raises exports by 5 per dollar spent.