Economic growth and economic development 560

Introduction to Modern Economic Growth is useful to start our investigation of the value of innovation in partial equilibrium, where much of the industrial organization literature starts Throughout this section, we consider a single industry Firms in this industry have access to an existing technology that enables firms to produce one unit of the product at the marginal cost ψ > The demand side of the industry is modeled with a demand curve Q = D (p) , where p is the price of the product and Q is the demand at this price Throughout we assume that D (p) is strictly decreasing, continuously differentiable and satisfies the following conditions: D (ψ) > and εD (p) ≡ − pD0 (p) ∈ (1, ∞) D (p) The first ensures that there is positive demand when prices equal to marginal cost, and the second ensures that the elasticity of demand, εD (p), is always greater than 1, so that when we consider monopoly pricing, there will exist a well-defined profitmaximizing price Moreover, this elasticity is less than infinity, so that the monopoly price will be above marginal cost Throughout this chapter and whenever we analyze economies with monopolistic competition, oligopolies or potential monopolies, equilibrium refers to Nash equilibrium or subgame perfect Nash equilibrium (when the game in question is dynamic) 12.3.1 No Innovation with Pure Competition Suppose first that there is a large number of firms, say N firms, with access to the existing technology Now imagine that one of these firms, say firm 1, also has access to a research technology for at process innovation In particular, let us simplify the discussion and suppose that there is no uncertainty in research, and if the firm incurs a cost µ > 0, it can innovate and reduce the marginal cost of production to ψ/λ, where λ > Let us suppose that this innovation is non-rival and is also non-excludable, either because it is not patentable or because the patent system does not exist Let us now analyze the incentives of this firm in undertaking this innovation We first look at the equilibrium without the innovation Clearly, the presence of a large number of N firms, all with the same technology with marginal cost ψ, implies 546