Introduction to Modern Economic Growth ¯ ∈ (0, ∞) such that Φ0 (h) = for all h ≥ h ¯ Φ0 (0) < ∞ and that there exists h The assumption that Φ0 (0) < ∞ implies that there is no Inada condition when hi (ν, t) = The last assumption, on the other hand, ensures that there is an upper bound on the flow rate of innovation (which is not essential but simplifies the proofs) Recalling that the wage rate for labor is w (t), the cost for R&D is therefore w (t) G (zi (ν, t)) where (14.40) G (zi (j, t)) ≡ Φ−1 (zi (j, t)) , and the assumptions on Φ immediately imply that G is twice continuously differentiable and satisfies G0 (·) > 0, G00 (·) > 0, G0 (0) > and limz→¯z G0 (z) = ∞, where ¡ ¢ ¯ is the maximal flow rate of innovation (with h ¯ defined above) z¯ ≡ Φ h We next describe the evolution of technologies within each industry Suppose that leader i in industry ν at time t has a technology level of (14.41) qi (ν, t) = λni (ν,t) , and that the follower −i’s technology at time t is (14.42) q−i (ν, t) = λn−i (ν,t) , where, naturally, ni (ν, t) ≥ n−i (ν, t) Let us denote the technology gap in industry ν at time t by n (ν, t) ≡ ni (ν, t) − n−i (ν, t) If the leader undertakes an innova- tion within a time interval of ∆t, then the technology gap rises to n (ν, t + ∆t) = n (ν, t) + (the probability of two or more innovations within the interval ∆t is again o (∆t)) If, on the other hand, the follower undertakes an innovation during the interval ∆t, then n (ν, t + ∆t) = In addition, let us assume that there is an intellectual property rights (IPR) policy of the following form: the patent held by the technological leader expires at the exponential rate κ < ∞, in which case, the follower can close the technology gap 633