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Handbook of the Economics of International Migration by Paul W. Miller, Barry Chiswick

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Appendix Solution of the Model in Section 5.1.2

We now prove the claims in Section 5.1.2 by fully solving the vertical innovation model. Combining p(i) = r/α with

pi=αBAi)xi1αLYβZ1αβ=Yxi

si183_e  (18.67)

and solving for x(i) implies

xi=AiBα2rLYβZ1αβ11α

si184_e  (18.68)

Taking wage rate w as given, ex ante of production, producer i chooses R&D labor input in period t to maximize

Πt+1iπt+1i1+rwtltiwtf

si185_e  (18.69)

where future profits πt + 1(i) ≡ ( ...

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