ONLINE APPENDIX to The Impact of a Firm ’ s Share of Exports on Revenue , Wages , and Measure of Workers Hired — Theory and Evidence

This Appendix provides the basic derivations of the multi-country trade model of heterogeneous firms presented in Hesse (2014). The ensuing presentation borrows from Dixit & Stiglitz (1977), Melitz (2003) as well as Helpman et al. (2010a) and its technical appendix, Helpman et al. (2010b). The preferences of a representative consumer are given by a C.E.S. utility function over a continuum of varieties indexed by ω: U = ω∈Ω y(ω) ρ dω 1 ρ , where y(ω) indexes the amount of variety ω and Ω represents the set of available varieties within the sector. These varieties are substitutes, implying 0 < ρ < 1 and an elasticity of substitution between any two varieties of σ = 1 1 − ρ > 1 ⇔ ρ = 1 − 1 σ = σ − 1 σ. (A.1) The consumer's constrained maximization problem may be solved by the Lagrangian L = U ρ − λ ω∈Ω p(ω)y(ω)dω − I , where U ρ is a strictly increasing transformation of U, p(ω) the price of variety ω, and I the con-sumer's income. The maximization problem yields the following first-order condition ∂L ∂y(ω) = ρy(ω) ρ−1 − λp(ω) = 0 .