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Introduction to Modern Economic Growth (2) Now suppose that the flow rate of success of R&D is φη/q for an incumbent as opposed to η/q for an and turned Show that for any value of φ, the incumbent will still choose zero R&D Explain this result Exercise 14.2 The baseline endogenous technological change models, including the model of competitive innovations in this chapter, assume that new products are protected by perpetual patents This exercise asks you to show that this is not strictly necessary in the logic of these models Suppose that there is no patent protection for any innovation, but copying an innovator requires a fixed cost ε > Any firm, after paying this cost, has access to the same technology as the innovator Prove that in this environment there will be no copying and all the results of the model with fully-enforced perpetual patents apply Exercise 14.3 Complete the proof of Proposition 14.1 In particular, verify that the equilibrium growth rate is unique, strictly positive and such that the transversality condition (14.15) is satisfied Exercise 14.4 Prove Proposition 14.2 Exercise 14.5 Derive equation (14.24) Exercise 14.6 Show that condition (14.5) is sufficient to ensure that a firm that innovates will set the unconstrained monopoly price [Hint: first suppose that the innovator sets the monopoly price ψq/ (1 − β) for a product of quality q Then, consider the firm with the next highest quality, λ−1 q Suppose that this firm sells at marginal cost, ψλ−1 q Then find the value of λ such that final good producers are indifferent between buying a machine of quality q at the price ψq/ (1 − β) versus a machine of quality λ−1 q at the price ψλ−1 q.] Exercise 14.7 Analyze the baseline model of competitive innovations in Section 14.1 assuming that (14.5) is not satisfied (1) Show that monopolists will set a limit price (2) Characterize the BGP equilibrium growth rate (3) Characterize the Pareto optimal allocation and compare it to the equilibrium allocation How does the comparison differ from the case in which innovations were drastic? 648