Economic growth and economic development 639

Introduction to Modern Economic Growth for all q and t Consequently, the demand for the machine of quality q at time t is given by x (t | q) = q (t) LE (t) , and monopoly profits are π (t | q) = βq (t) LE (t) We can also write aggregate output as Y (t | q) = q (t) LE (t) , 1−β where we again condition on the quality of the machine available at the time, q This also implies that the equilibrium wage, determined from the production sector, is given by β q (t) 1−β When there is no need to emphasize time dependence, we will write this wage rate w (t | q) = as a function of machine quality, i.e., as w (q) Let us now focus on a “steady-state equilibrium” in which the flow rate of innovation is constant and equal to z ∗ Steady state here is an quote marks since, even though the flow rate of innovation is constant, consumption and output growth will not be constant because of the stochastic nature of innovation (and this is the reason why we not use the term “balanced growth path” in this context) This implies that a constant number (and thus a constant fraction) of workers, L∗R , must be working in research Since the interest rate is equal to r∗ = ρ, this implies that the steady-state value of a monopolist with a machine of quality q is given by V (q) = βq (L − L∗R ) , ρ + z∗ where we have used the fact that in steady state total employment in the final good sector is equal to L∗E = L − L∗R We also wrote V as a function of q rather than a function of both q and time, to simplify notation Free entry requires that when the current machine quality is q, the wage paid to one more R&D worker, w (q), must be equal to the flow benefits, ηV (λq), thus w (q) = ηV (λq) 625