Economic growth and economic development 582

Introduction to Modern Economic Growth (3) What is the effect of the elasticity of demand on the relative incentives of the incumbent and the entrant to undertake innovation Exercise 12.8 (1) Prove Proposition 12.4 by providing an example in which there is excessive innovation incentives (2) What factors make excessive innovation more likely? Exercise 12.9 The discussion in the text presumed a particular form of patent policy, which provided ex post monopoly power to the innovator An alternative intellectual property right policy is licensing, where firms that have made an innovation can license the rights to use this innovation to others This exercise asks you to work through the implications of this type of licensing Throughout, we think of the licensing stage as follows: the innovator can make a take-it-or-leave-it-offer to one or many firms so that they can buy the rights to use the innovation (and produce as many units of the output as they like) in return for some licensing fee ν (1) Consider the competitive environment we started with and show that if firm is allowed to license its innovation to others, this can never raise its profits and it can never increase its incentives to undertake the innovation Provide an intuition for this result (2) Now modify the model, so that each firm has a strictly convex and increasing cost of producing, ψ1 (q), and also has to pay a fixed cost of ψ0 > to be active (so that the average costs take the familiar inverse U shape) Show that licensing can be beneficial for firm in this case and therefore increase incentives to undertake the innovation Explain why the results differ between the two cases Exercise 12.10 Derive the expression for the ideal price index, (12.9), from (12.8) and the definition of the consumption index C Exercise 12.11 Consider the maximization problem in (12.11) and write down the first-order conditions taking into account the impact of pi on P and C Show that as N → ∞, the solution to this problem converges to (12.12) Exercise 12.12 In the Dixit-Stiglitz model, determine the conditions on the function v (·) such that an increase in N raises the profits of a monopolist 568