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
and solving for x(i) implies
Taking wage rate w as given, ex ante of production, producer i chooses R&D labor input in period t to maximize
where future profits πt + 1(i) ≡ ( ...