Introduction to Modern Economic Growth (2) What is the value of ι that maximizes the equilibrium rate of economic growth? (3) Show that a policy of ι = does not necessarily maximize social welfare at time t = Exercise 13.13 Consider the formulation of competition policy in subsection 13.1.6 (1) Characterize the equilibrium fully (2) Write down the welfare of the representative household at time t = in this equilibrium (3) Maximize this welfare function by choosing a value of γ (4) Why is the optimal value of γ not equal to some γ ∗ ≥ 1/ (1 − β)? Provide an interpretation in terms of the trade-off between level and growth effects (5) What is the relationship between the optimal value of γ and ρ Interpret Exercise 13.14 Complete the proof of Proposition 13.4 In particular, show that the equilibrium path involves no transitional dynamics and that under (13.31), the transversality condition is satisfied Exercise 13.15 Characterize the Pareto optimal allocation in the economy of Section 13.2 Show that it involves a constant growth rate greater than the equilibrium growth rate in Proposition 13.4 and no transitional dynamics Exercise 13.16 Derive equation (13.35) Exercise 13.17 Consider the model of endogenous technological progress with limited knowledge spillover as discussed in Section 13.3 (1) Characterize the transitional dynamics of the economy starting from an arbitrary N (0) > (2) Characterize the Pareto optimal allocation and compare it to the equilibrium allocation in Proposition 13.5 (3) Analyze the effect of the following two policies: first, a subsidy to research; second, the patent policy, where each patent expires at the rate ι > Explain why the effects of these policies on economic growth are different than their effects in the baseline endogenous growth model 604