Economic growth and economic development 566

Introduction to Modern Economic Growth even though ex post monopoly power (for example, generated by patents) can induce innovation, the incentives for innovation and the equilibrium allocations that result in the case of innovation are still inefficient Note also that Sb1I can be negative, so that a potentially productivity-enhancing process innovation can reduce social surplus because of the cost of innovation, µ However, it can be shown that if π ˆ I1 > 0, then Sb1I > 0, which implies that excessive innovation is not possible in this competitive environment (see Exercise 12.4) This will contrast with the results in the next subsection 12.3.4 The Value of Innovation to a Monopolist: The Replacement Effect Let us now analyze the same industry as in the previous subsection, but first presuming that firm is already a monopolist with the existing technology Then with the existing technology, this firm would set the monopoly price of ψ pˆM ≡ − εD (p)−1 and make profits equal to ¡ M¢ ¡ M ¢ π ˆN ˆ pˆ − ψ = D p If it undertakes the innovation, it will reduce its marginal cost to λ−1 ψ and still remain the monopolist Therefore, its profits will be given by π ˆ I1 as in (12.3), with the monopoly price pM given by (12.2) Now the value of innovation to the monopolist is ∆ˆ πI1 = π ˆ I1 − π ˆN ¡ M¢ ¡ M ¢ ¡ ¢¡ ¢ = D p p − λ−1 ψ − D pˆM pˆM − ψ − µ Proposition 12.3 We have that ∆ˆ π I1 < π I1 < π ˆ I1 , so that a monopolist always has lower incentives to undertake innovation than a competitive firm Proof See Exercise 12.6 Ô This result, which was first pointed out in Arrow’s (1962) seminal paper, is referred to as the replacement effect The terminology reflects the intuition for the 552