Tests2013.pdf - ECON 5113 Advanced Microeconomics Winter...

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ECON 5113 Advanced Microeconomics Winter 2013 Test 1 February 15, 2013 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 answers 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. Are the following consistent with economic theory? Explain (a) V ( p 1 , p 2 , y ) = p 2 1 y p 2 (b) Demand functions for one person: x 1 = D 1 ( p 1 , p 2 , y ) = y/ 2 p 1 , x 2 = D 2 ( p 1 , p 2 , y ) = 0 2. Let U : R n + ! R + is a continuous, increasing, twice continuously di erentiable and quasi-concave utility function. (a) Define the indirect utility function (b) State and prove the properties of the indirect utility function 3. Suppose that a consumer’s preference structure is represented by the utility function U ( x 1 , x 2 ) = x 2 1 + x 2 2 . (a) Find the Marshallian demand functions. (b) Find the Indirect Utility function. (c) Find the expenditure function. 4. Prove the following result must hold: @ x i ( p, y ) @ p j + x j ( p, y ) @ x i ( p, y ) @ y = @ x j ( p, y ) @ p i + x i ( p, y ) @ x j ( p, y ) @ y 5. Suppose that E ( p 1 , u ) = p 1 · x 1 and E ( p 2 , u ) = p 2 · x 2 . (a) Prove that ( p 2 - p 1 ) · ( x 2 - x 1 ) 0 . (b) What is the implicaton for Hicksian demand curves given the result in part a? 6. Suppose there are m individuals. Individual i has an indirect utility function given by: V ( p, y ) = a i ( p ) + b ( p ) y (a) Prove that aggregate demand for a particular good becomes independent of the income distribution across individuals. (b) Define a consumer’s Engel curve. What is the implication for the Engel curves of individuals given the form of the indirect utility function?
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ECON 5113 Advanced Microeconomics Winter 2013 Test 2 March 20, 2013 Answer ALL Questions Time Allowed: 1 hour 20 minutes
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