{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

hw3_soln

# hw3_soln - Solution Homework Assignment 3 Econ 150b...

This preview shows pages 1–3. Sign up to view the full content.

Solution Homework Assignment 3 Econ 150b. Intermediate Microeconomics Fabian Duarte * February 5, 2008 1. Consider a consumer whose utility function is given by u ( x 1 , x 2 ) = ( α x ρ 1 +( 1 - α ) x ρ 2 ) 1 ρ (1) where ρ ε ( 0 , 1 ) is a parameter. Using any of the three methods we’ve seen in class, find the optimal consumption bundle as a function of prices ( p 1 , p 2 ) and income m . Plot the demand and Engel curves. (a) First method: We use two equations: MRS = - p 1 p 2 p 1 x 1 + p 2 x 2 = m So, first we calculate MRS , for that we need to calculate first partial derivatives u x 1 = 1 ρ ( α x ρ 1 +( 1 - α ) x ρ 2 ) 1 ρ - 1 ( αρ x ρ - 1 1 ) and u x 2 = 1 ρ ( α x ρ 1 +( 1 - α ) x ρ 2 ) 1 ρ - 1 (( 1 - α ) ρ x ρ - 1 2 ) then MRS = - α x ρ - 1 1 ( 1 - α ) x ρ - 1 2 = - p 1 p 2 (2) * [email protected] 1

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

View Full Document
then x 1 = ( 1 - α ) p 1 α p 2 · 1 ρ - 1 x 2 (3) Now, we replace x 1 in the second equation p 1 x 1 + p 2 x 2 = m and we get m = p 1 ( 1 - α ) p 1 α p 2 · 1 ρ - 1 x 2 + p 2 x 2 m = x 2 h‡ ( 1 - α ) α p 2 · 1 ρ - 1 p ρ ρ - 1 1 + p 2 i m = x 2 h ( 1 - α ) 1 ρ - 1 p ρ ρ - 1 1 + α 1 ρ - 1
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 4

hw3_soln - Solution Homework Assignment 3 Econ 150b...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online