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# problem1 - Problem Set 1 Econ 210 Core Macro Monika...

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Problem Set 1 Econ 210 Core Macro Monika Piazzesi Stanford University Due Wednesday, September 29 in class one solution per group, please 1. Provide a proof for Proposition 6 on page 14 of Krueger (2002). 2. Suppose α = 0 , how does the Pareto optimal allocation look like? Suppose α = 1 , how does the Pareto optimal allocation look like? 3. Suppose you have an Arrow Debreu equilibrium for our Robinson/Friday economy. We want to construct a Security Markets equilibrium with the same consumption allocation as in the AD equibrium. (a) What is the interest rate in the SM equilibrium? Determine the interest rate in terms of preference parameters. (b) In the SM equilibrium, how many bonds does agent i buy in period t ? (c) Using the bond holdings from b., show that bond markets clear. (d) Show that these bond holdings satisfy a borrowing constraint. (e) Compute the natural debt limit for agent 1 and 2 explicitly. 4. Robinson and Friday save Friday’s father from the cannibals, and so now we have three agents on the island. Suppose the agents have utility functions X t =0 β t i ln c i t 1

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