2011_questions_final

2011_questions_final - Final Exam Questions Econ 600 Summer...

Info icon This 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 Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Final Exam Questions Econ 600, Summer 2011 Leland Crane and Jonathan Kreamer Read the entire exam before starting. Show your work and clearly mark your nal answer for each question. Good luck! 1. (10 points) Let f : R → R and g : R → R . Let h : R → R be de ned as h ( x ) = min ( f ( x ) ,g ( x )) . (a) If f and g are concave, is h concave? Prove or o er a counter-example. (b) If f and g are quasiconcave, is h quasiconcave? Prove or o er a counter-example. 2. (5 points) Suppose that f : R → R is continuous and invertible. Prove that f is either strictly increasing or strictly decreasing. 3. (5 points) Suppose f : A ⊂ R n → R is strictly quasi-concave and has a local minimum at x ? ∈ A . Prove A is not open. 4. (15 points) Let U ( y ) = max x f ( x ) s.t. x ≤ G ( y ) where f and G are concave. Prove that U is concave. 5. (15 points) Let f : R → R . Suppose you are given that on the interval [ x 1 ,x 2] , the absolute value of the derivative of f never exceeds some positive constant...
View Full 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