Economic growth and economic development 642

Introduction to Modern Economic Growth each of them to innovate Each firm ignores its effect on the aggregate rate of innovation, thus takes η (LR ) as given (this assumption is not important as shown by Exercise 14.20) Consequently, when the current machine quality is q, the free entry condition takes the form η (LR (q)) V (λq) = w (q) , where LR (q) is the number of workers employed in research when the current machine quality is q Let us now look for an equilibrium with the following cyclical property: the rate of innovation differs when the innovation in question is an odd-numbered innovation versus an even-numbered innovation (say with the number of innovations counted starting from some arbitrary date t = 0) This type of equilibrium is possible when all agents in the economy expect there to be such an equilibrium (i.e., it is a “self-fulfilling” equilibrium) Denote the number of workers in R&D for odd and even-numbered innovations by L1R and L2R Then, following the analysis in the previous subsection, in any equilibrium with a cyclical pattern the values of odd and even-numbered innovations (with a machine of quality q) can be written as (see Exercise 14.18): V (λq) = (14.28) βq (L − L2R ) βq (L − L1R ) and V (λq) = , ρ + η (L2R ) L2R ρ + η (L1R ) L1R and the free entry conditions take the form ¡ ¢ ¡ ¢ η L1R V (λq) = w (q) and η L2R V (λq) = w (q) , (14.29) where w (q) is the equilibrium wage with technology of quality q The reason why η (L1R ) multiplies the value for an even-numbered innovation is because L1R researchers are employed for innovation today, when the current technology is oddnumbered, but the innovation that this research will produce will be even-numbered and thus will have value V (λq) Therefore, we have the following two equilibrium conditions: (14.30) ¡ ¢ λ (1 − β) q (L − L1R ) ¡ ¢ λ (1 − β) q (L − L2R ) = and η LR = η LR ρ + η (L2R ) L2R ρ + η (L1R ) L1R 628