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5 Appendix

5.1 Optimality of technologies

Consider first the case of no IPRs protection in S, (θ = 0). Total production in the
North is equal to Yn = WnLn/ β. Using (9):

Max^_a^j^yY^ = Ln {ʃ [а (г) Φn(i)]^σ di^∙      s.t. J а (г) di = а

The solution to this program has to satisfy the following first order conditions
(FOCs), ∀i ∈ [0,1]:

^LN I    ^{[a (i) φ}N^(г)Г ^dij> ^{[a (i) φ}N^(г)Г ^{1 φ}N⁽ⁱ⁾ = ^λ

where λ is the lagrange multiplier associated to the constraint. Taking the ratio of
any two FOCs and using An(i) = а (i) Φ_n(г) yields equation (13). This proves that
the sectoral profile of the endogenous technology maximizes Northern output and
wage and hence it is optimal for the North.

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