final_exam - Economics 202A Final Exam Instructions You...

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Economics 202A Final Exam December 15, 2007 Instructions: You have 1 hour and 35 minutes. Answer all 3 questions, each of which carries an equal weight. Notice that within question 2, you have a choice between two options. There is no extra credit for picking both of those options { you may only pick one. Take the °rst 5 minutes to look over all 4 pages of the exam before you start. That way you can better pace yourself. If you get stuck, go on to something you can answer more easily and return to the di±cult bits later on. Good luck, and happy holidays! 1. A representative consumer maximizes Z 1 0 u [ c ( t )] e ° °t d t subject to _ a = y + ra ° c; a (0) given ; where y and r are constant through time, y is perishable output, and a rep- resents a stock of interest-bearing real °nancial assets. We do not necessarily impose that the subjective discount rate ° is equal to the market real interest rate r . A no-Ponzi condition also is imposed on the problem. (a) Use the Maximum Principle to write down the necessary conditions for this maximization problem, based on the Hamiltonian. (b) For the isoelastic function u ( c ) = c 1 ° 1 ° ° 1 1 ° 1 ± ; derive from the Maximum Principle °rst-order conditions the Euler equation relating the proportional growth rate of consumption c to the parameter ± and the di±erence r ° ° .
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