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# MT1P2 vA - ECO 320L Fall 2010 Professor Beatrix Paal...

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ECO 320L Fall 2010 Professor Beatrix Paal Midterm 1 -- Problems (cont'd) name: 9/27/2010 65 points + 8 extra credit points 4. (_____ of 21 points) A consumer has labor income of 54 units of goods in the current period and 90 units of goods in the future period. Her initial asset position is –6 units of goods, or, in other words, she starts the current period with a debt. Per capita taxes are 3 units of goods in the current period, and there are no taxes in the future. The real interest rate is 25%. The consumer's utility function is ( , ) ln 2ln = + f f u c c c c a. (_____ of 4 points) Calculate the present value AND the future value of the consumer's lifetime resources. SHOW YOUR WORK. b. (_____ of 3 points) Write down the consumer's optimization problem, using numerical values wherever you can. What are the choice variables? Version A Page 4 PDF Created with deskPDF PDF Writer - Trial :: http://www.docudesk.com

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c. (_____ of 6 points) Derive the optimal consumption plan (both c and cf) of the consumer. SHOW YOUR WORK. (Hint: Prove that c*=39 and cf*=97.5) d. (_____ of 4 points) Using your results from part c), calculate the consumer's saving and net lending at the end of the current period. Calculate her future assets. Is this consumer a borrower or a lender?
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