10fB_ps04solutions

10fB_ps04solutions - Microeconomics ECON 100A Problem Set 4...

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

View Full Document Right Arrow Icon

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

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

Unformatted text preview: Microeconomics ECON 100A Problem Set 4 Solutions [THIS MATERIAL IS NOT ON THE MIDTERM] Due October 20, 2010 (Solutions Posted October 22, 2010) 1. Now, lets see if you can do the general perfect complements problem. Matt gets utility from X and Z. Matt always consumes X with Z. a. What type of utility function represents Matts preferences? Write down an expression for Matts utility. U=min{( 1 / ) X, ( 1 / ) Z} b. What is Matts utility maximizing combination of X*(P x , P z , Y) and Z*(P x , P z , Y)? Use the facts that (1) that there will be no excess X or Z (so 1 / X*= 1 / Z*) and (2) the utility maximizing bundle must be on the budget constraint (PxX*+PzZ* =Y). Substitute the expression for Z*= / X* from (1) into the budget constraint in (2) to get: Px(X*)+ Pz( / X*)=Y X*(Px+ / Pz) = Y and then solve for X*= z x p p Y + Finally, substitute this expression for X* into Z*= / X* to solve for Z*: Z*= ) ( z x p p Y + c. What is the Matts indirect utility function, i.e., V(P x , P z , Y)=U(X*(P x , P z , Y), Z*(P x , P z , Y))? U*(px, pz, Y)=min{ 1 / X*, 1 / Z* }=min{ ) ( , ) ( z x z x p p Y p p Y + + } d. Show that Roys identity holds for good x. Show that Roys identity holds for good x....
View Full Document

Page1 / 4

10fB_ps04solutions - Microeconomics ECON 100A Problem Set 4...

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

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