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Homework 3, Spring 08 answer (Total 20 points) Due on Feb. 11, Tue. Q1 : (3 × 2): (a) When the interest rate is 5%, what is the present value of an as- set that gives you \$140 this period and \$420 next period? (b) When the interest rate is 4%, what is the present value of an asset that perpetu- ally gives you \$300 every period? Answer : (a) It is 140 + 420 1 . 05 = 140 + 400 = 540. (b) Recall that ω t =1 ( 1 1+ r ) t - 1 = ω 1 1 - 1 1+ r = ω (1+ r ) r . Hence it is 300 · 1 . 04 0 . 04 = 7800. — One may use the approximate formula ω r , which delivers 300 0 . 04 = 7500. Q2 : (4): Consider the two-period consumption/saving problem. Marina’s prefer- ence over consumption streams is represented by u ( x 1 ,x 2 ) = ln x 1 + 0 . 9ln x 2 . When her earning stream is (37 , 21) and the interest rate is 5%, how much is her saving in the ﬁrst period? —- Perform the solution process . Answer

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