{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Supplement%209

# Supplement%209 - On Preference Relations Recall that[see...

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

On Preference Relations Recall that [see Handout #9 ] that a basic role is played by MRS de°ned as the absolute value of the slope of an indi/erence curve. Consider the following optimization problem of the consumer [in what follows p x > 0 ; p y > 0 and m > 0 ] : max f u ( x; y ) g subject to the constraint p x ° x + p y ° y = m , and x ± 0 ; y ± 0 To look for an optimal solution ( x ° ; y ° ) with x ° > 0 ; y ° > 0 , we can use the budget equation to get x = m ² p y ° y p x (1) and, upon substitution get the problem max n u ° [ m ± p y ² y ] p x ; y ±o on 0 < y < m p yy This is a maximization problem with a single variable y and if an optimal y ° exists; the following °rst order condition must hold [using the "relevant rules from calculus"]: u x ° [ ² p y =p x ] + u y = 0 or, u x =u y = p x =p y or, ( MRS ) u = p x =p y (2) Given a speci°c functional form of u we may be able to solve for ( x ° ; y ° ) as in the Cobb-Douglas case. Now, we interpret u ( x; y ) > u ( b x; b y ) as " ( x; y ) is preferred to ( b x; b y ) " : In terms of the usual diagram u ( x; y ) > u ( b x; b y ) means ( x; y ) is on a "higher"

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 ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern