420KSpring10HW3answer - Homework 3, Spring 10 (Total 20...

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Homework 3, Spring 10 (Total 20 points) Due on Feb. 16, Tue. Q1 : (3 × 2): (a) When the interest rate is 4%, what is the present value of an asset that gives you $300 this period and $400 next period? (b) When the interest rate is 6%, what is the present value of an asset that perpetually gives you $300 every period? Answer : (a) 300 + 1 1 . 04 · 400 684 . 6 (b) 300 1 - 1 1 . 06 = 1 . 06 0 . 06 · 300 = 5300 Q2 : (4): Consider the two-period consumption/saving problem. The consumer’s preference over consumption streams is represented by u ( x 1 , x 2 ) = ln x 1 + 0 . 95 ln x 2 . When her earning stream is (40 , 30) and the interest rate is 4%, how much is her saving in the first period? Answer This is a special case of the standard consumption choice problem where p 1 = 1, p 2 = 1 1+ r , m = ω 1 + 1 1+ r ω 2 . Since MU 1 = 1 x 1 and MU 2 = 0 . 95 x 2 , we have MRS = x 2 0 . 95 x 1 . Since MRS = p 1 p 2 = 1 + r holds at optimality, we have x 2 0 . 9 x 1 = 1 + r = 1 . 04, which results in
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420KSpring10HW3answer - Homework 3, Spring 10 (Total 20...

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