PS3+solution

PS3+solution - Rice University Professor Diamond Economics...

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
Rice University Economics 370 Professor Diamond Microeconomic Theory SOLUTION TO PROBLEM SET 3: UTILITY AND DEMAND AND INCOME AND SUBSTITUTION EFFECTS I. Suppose that an individual’s indifference curves are described by straight lines with a slope equal to –b , and that, as usual, prices and income, p 1 , p 2 , m are determined exogenously. 1. What is the demand function for x 1 ? The budget line is x 2 m/p 2 slope=-p 1 /p 2 So, x 1 = m/p 1 if p p 1 < b p 2 m/p 1 x 1 0 if 1 > b p 2 p p 1 0 x 1 m/p 1 if = b 2 2. What is the demand function for x 2 ? x 2 = m/p 2 if p p 1 > b p 2 0 if 1 < b p 2 p p 1 0 x 2 m/p 2 if = b 2
Background image of page 1

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

View Full DocumentRight Arrow Icon
2 2 II. Suppose an individual’s utility function (defined over two goods) is expressed as u ( x 1 , x 2 ) = x 1 x 2 . 1. Derive the demand function for x 1 . 22 2 12 2 11 2 2 1 2 1 1 21 2 2 2 1 2 1 2 1 1 ,2 2 2 3 uu mu x x x xx p x x p x p p px m p p x m p m x p ∂∂ == = = += ⎛⎞ ⎜⎟ ⎝⎠ = 1 2. Derive the demand function for 1 2 33 pp m p = x 2 . 2 m p III. Suppose now that the utility function is u ( x 1 , x 2 ) = ln( x 1 ) + 2 ln( x 2 ) . x 1 and x 2 . 1. Again, derive the demand functions for both
Background image of page 2
4 12 11 2 112 1 21 22 1 2 1 2 1 2 1 1 1 2 , 2 2 2 3 2 33 uu mu 2 x xx p x p x x x p x p p px p x m p m x p pp m m p p ∂∂ == = ⎛⎞ += ⎜⎟ ⎝⎠ = = 2. Are your answers for II and III the same? Why or why not? Yes, the answers are the same. This is because a monotonic transformation of a utility function will yield the same demand curves, and f(x)=ln(x) is a monotonic transformation of x.
Background image of page 3

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

View Full DocumentRight Arrow Icon
Image of page 4
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 09/20/2008 for the course ECON 370 taught by Professor Diamond during the Spring '08 term at Rice.

Page1 / 8

PS3+solution - Rice University Professor Diamond Economics...

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online