{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

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

This preview shows pages 1–2. Sign up to view the full content.

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 x 2 = 1 . 04 · 0 . 95 x 1 . Plug this into the budget constraint x 1 + 1 1 . 04 x 2 = 40 + 1 1 . 04 · 30 = 68 . 85, the we have x 1 + 1 1 . 04 · 1 . 04 · 0 . 95 x 1 = 1 . 95 x 1 = 68 . 85. Hence x 1 = 30 . 31,

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online