MIdterm2008 - Midterm Exam, Econ 210A, Fall 2008 1) Elmer...

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Unformatted text preview: Midterm Exam, Econ 210A, Fall 2008 1) Elmer Kink’s utility function is min { x 1 , 2 x 2 } . Draw a few indifference curves for Elmer. Find each of the following for Elmer: • His Marshallian demand function for each good. • His Indirect utility function. • His Hicksian demand function for each good. • His Expenditure function. • Verify that Roy’s Law applies in Elmer’s case. 2) Consider the function f ( x 1 ,x 2 ) = ax 1 + bx 2 + cx 2 1 + dx 1 x 2 + ex 2 2 . (a) Write down the Hessian matrix for this function. (b) For what values of the parameters a , b , c , d , and e is f a concave function? (c) For what values of these parameters is f a convex function? (d) For what values of these parameters is f neither concave, nor convex? (e) For what values of these parameters is f both concave and convex? 3) Prove that a concave function must be quasi-concave. Give an example of a quasi-concave function that is not concave. (Be sure to show that your example is quasi-concave and that it is not concave.)example is quasi-concave and that it is not concave....
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This note was uploaded on 02/01/2011 for the course ECONOMY 6 taught by Professor Fallahi during the Spring '10 term at Cambridge.

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MIdterm2008 - Midterm Exam, Econ 210A, Fall 2008 1) Elmer...

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