Tests2010.pdf - ECON 5113 Advanced Microeconomics Winter...

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

View Full Document Right Arrow Icon
ECON 5113 Advanced Microeconomics Winter 2010 Test 1 February 12, 2010 Answer ALL Questions Time Allowed: 1 hour 20 minutes Instruction: Please write your answers on the answer book provided. Use the right-side pages for formal an- swers and the left-side pages for your rough work. Also, start each question on a new page. Read the questions carefully and provide answers to what you are asked only. Do not spend time on what you are not asked to do. Remember to put your name on the front page. 1. Suppose that U : R n + R + is a continuous, strictly increasing, and quasi-concave utility function which represents a preference relation . Show that satisfies (a) transitivity, (2) (b) locally nonsatiation, (3) (c) convexity. (3) 2. Suppose that a consumer’s preference structure is represented by the utility function U ( x 1 , x 2 ) = ax 1 + x 2 , where a > 0. (a) Find the Hicksian demand functions. (5) (b) Find the expenditure function. (5) 3. Let U : R n + R + be a continuous, increasing, and strictly quasiconcave utility function. (a) Define the indirect utility function associated with U . (3) (b) Prove that the indirect utility function is ho- mogeneous of degree zero in prices and in- come. (4) (c) Show that if U ( x ) is a homogeneous of degree one function then the corresponding indirect utility function can be written as: (4) V ( p , y ) = v ( p ) y. (d) Find the expenditure function associated with the indirect utility function in Part c. Clearly explain how and why you are able to obtain the expenditure function. (3) 4. A new highway project changes the rental rate of apartment in a suburb from p 0 to p 1 . A consumer with a well-defined preference structure has income y 0 . (a) Define a money metric indirect utility func- tion and explain how the money metric indi- rect utility function can be used to get the equivalent variation (EV) in this case. (3) (b) Define the equivalent variation (EV) of the consumer due to the price change using the indirect utility function. (3) (c) Express EV explicitly using the expenditure function. (3) (d) Express EV as a function of the Hicksian de- mand function. (3) 5. Let the observed consumption bundles of a con- sumer in period 0 and period 1 be x 0 and x 1 , given the price vectors p 0 and p 1 respectively.
Image of page 1

Info iconThis 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