{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

HWIII.08 - HOMEWORK ECONOMICS 200A III DEMAND THEORY AND...

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

View Full Document Right Arrow Icon
HOMEWORK ECONOMICS 200A III. DEMAND THEORY AND DUALITY R. R. RUSSELL FALL 2008 1. Consider the following three utility functions: U ( x 1 , x 2 ) = ( x 1 ) 1 / 2 + x 2 , U ( x 1 , x 2 ) = x 1 + ln x 2 U ( x 1 , x 2 ) = ( x 1 - γ ) α x 2 , α > 0 . (a) Restricting prices to those that yield interior solutions, find the first-order conditions for maximizing these utility functions subject to a budget constraint, p · x = y , and check to see that second-order conditions are satisfied. (b) Without restricting prices to those that yield interior solutions, find the first-order conditions for maximizing these utility functions subject to the budget constraint. (Be careful here to consider different signs of γ and to restrict choices to those where the utility function is well defined.) (c) Derive the demand functions for each utility function and verify the requisite ho- mogeneity condition. (d). Derive the indirect utility function dual to each utility function and verify Roy’s Identity.
Image of page 1

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

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern