School of Economic Sciences - Washington State University

hold.• Good 0: q ∗ j (0) > 0, p∗ (0)w j (0) = w ∗ j , and q∗ j (0) = w j(0)l ∗ j (0), ∀j and ∑ Jj=1 q∗ j (0) = ∑ Jj=1 x∗ j (0).• Given prices, labor endowment, wages, profits, and the set of available goods, the representativeconsumer in each country maximizes (1) by choosing x ∗ (0) and x ∗ (ω) such thatp ∗ j (0)x j(0) + ∫ Ωp ∗ ∗ j (ω)x j(ω)dω ≤ wj ∗N j + Π ∗ j and x j(0), x j (ω) ≥ 0 ∀ω ∈ Ω ∗ j .j• Given wages, transportation and fixed costs, and the demand function for its good in eachcountry, each monopolistic competitor chooses p ∗ j (ω) to maximize ∑ Jj=1 p j(ω)q ∗ j (ω) − c∗ j (ω).• Individual goods and labor clearing condition: qj ∗(ω) = x∗ j (ω) and q∗ j (ω) = φ(ω)l∗ j (ω), ∀j∀ω.• Country labor clearing condition: ∑ Jk=1(l∗k(0) + ∫ L jk(l ∗ k (ω) + f jk) dω ) = N j , ∀j where L jk isthe measure of country j firms exporting to k.• Country profits condition: ∫ L j( ∑ Jk=1 π∗ k (ω)) dω = Π ∗ j , ∀j.• Ω ∗ j determined by L j and { ˆφ ∗ ij }J i=1 where ˆφ ∗ ij = sup {πij ∗ (φ) = 0}.φ≥1With a continuum of varieties, the equilibrium is identical under either Bertrand competitionor Cournot competition. Chaney (2008) proves the existence of this equilibrium for γ > σ − 1 > 0.Henceforth, all variables are assumed to be at their equilibrium values and thus the stars aredropped. Equilibrium properties include the following.Firms from i selling in country j set the price p j(φ(ω))= pij (φ) =σσ−1w i τ ijφ. For some firms,their productivity is low enough that there does not exist a price such that π ij (φ) ≥ 0. Thereforefor each (i, j) there exists a threshold productivity, ˆφ ij such that firms in i with φ < ˆφ ij choose notto export to j. Among other fundamentals and parameters, this threshold productivity dependson the fixed cost to export f ij :( σˆφ ij =µγγ − (σ − 1)) 1γ× Y− 1 γj( )wi τ ij× (w i f ij ) 1σ−1 . (4)θ jAs f ij increases, the threshold productivity is larger. Notice because f ii = 0, all L i firmsproduce domestically. Using (2), the measure of firms in i exporting to j is L ij = L i(1 − H( ˆφij ) ) .7