School of Economic Sciences - Washington State University

AppendicesAProofsAssumptions L i (M ij ) = L i Y j (M ij ) = Y j θ j (M ij ) = θ j .Justification. Suppose governor i may take at most one trade mission to country j. Furthersuppose the parameters and fundamentals, Y j , w i , and τ ij , are such that this governor chooses togo on the mission. I show this decision will not change to zero missions when both the benefit andthe cost of the mission go to zero,limb→0˜X ij M b ij − ˜X ij = 0 and limdi →0 d ig j (M ij − 1) = 0.The notation above matches that in the paper, yet should be viewed generally enough to hold inform when the assumptions do not hold. Let d i and b converge to zero along the same sequence.Compare the rates of convergence. Use l’Hôpital’s rule:limz→0˜X ij M z ij − ˜X ijzg j= limz→0˜Xij M z ij log M ijg j (M ij − 1)= ˜X ij log M ijg j (M ij − 1) > 0.Therefore near the limit, the convergence rate is equal. Since the governor chooses to go on a trademission initially and the rate of convergence is constant in the limit, the governor does not want tochange her mind at any point in the sequence.Lemma 1. Equilibrium aggregate exports from i to j as a function of trade missions,X ij (M ij ) = ˜X ij × M abij ,where a =γσ−1 − 1 > 0 and b > 0, is increasing in M ij.26