• Kristian BehrensUniversite du Quebec a Montreal
• Yoshitsugu KanemotoGRIPS
• Yasusada MurataNihon University

We generalize the formulae for welfare changes by Arkolakis, Costinot, and Rodríguez-Clare (2012) and Melitz and Redding (2014a) to allow for various cardinalizations of the subutility functions for varieties. Despite the same macro restrictions and the same equilibrium allocations, our new formula coincides with the original ones if and only if the number of varieties is invariant to foreign shocks. When product diversity responds to foreign shocks, different cardinalizations generate different welfare changes, thus revealing a fundamental
difficulty in quantifying welfare gains implied by new trade models.