We estimate the aggregate export and import price elasticities implied by a Constant Elasticity of Substitution (CES) demand system, for more than 30 countries at various stages of development. Trade elasticities are given by weighted averages of sector-specific elasticities of substitution, that we estimate structurally. Both weights and substitution elasticities can be chosen to compute the response of trade to specific shocks to relative prices, bilateral or global. We document considerable, significant cross-country heterogeneity in multi-lateral trade elasticities, which is virtually absent from estimates constrained to mimic aggregate data. The international dispersion in import price elasticities depends mostly on preference parameters, whereas export price elasticites vary with the composition of trade. We simulate the demand-based response of trade to specific exogenous shifts in international prices. We consider shocks to EMU-wide, US or China's relative prices, as well as country-specific shocks within the EMU zone. The trade responses to an external EMU-shock are considerably heterogeneous across member countries; in contrast, a within-EMU (Greek, Portuguese, German) shock to relative prices has largely homogeneous consequences on Eurozone trade patterns. PRELIMINARY AND INCOMPLETE.