This paper examines the efficacy of second-best trade restrictions at correcting sectoral misallocation due to scale economies or profit-generating markups. To this end, we characterize optimal trade and industrial policies in an important class of quantitative trade models with scale effects and profits, estimating the structural parameters that govern policy outcomes. Our estimates reveal that standalone trade policy measures are remarkably ineffective at correcting misallocation, even when designed optimally. Unilateral adoption of corrective industrial policies is also ineffective due to immiserizing growth effects. But industrial policies coordinated internationally via a deep agreement are more transformative than any unilateral policy alternative.