Econ100A Midterm 2 Solutions

Econ100A Midterm 2 Solutions - Microeconomics, ECO 100A,...

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Microeconomics, ECO 100A, Spring 2011, Dr. Famulari KEY: Midterm 2 (8 am Class): 225 points total Question 1. (25 points total) Suppose a consumer gets utility from x and y. Suppose Py increases. Illustrate the total effect, substitution effect, and income effect of this price change assuming that y is an inferior good and the law of demand holds for Y. y > y” (Law of demand holds). y’ < y” (y is an inferior good). Question 2 (50 points total). Luka gets utility from commodities X and Y and his preferences can be represented by the utility function, U(x,y)= 3x 2 y 3 . Luka minimizes his expenditures subject to achieving utility level, U . A. (15 points) What are the first order conditions for Luka’s expenditure minimization problem? ) 3 ( 3 2 y x U y p x p L y x - + + = λ 0 3 ) 3 ( 0 9 ) 2 ( 0 6 ) 1 ( 3 2 2 2 3 = - = = - = = - = y x U L y x p y L xy p x L y x B. (15 points) What are Luka’s compensated demand functions, X C (p x , p y , U ) and Y C (p x , p y , U )? Dividing the first two equations and rearranging: U U’ I P y I P y y” y’ B A A’ x x’ x”
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Substitute back into the utility constraint and solve for x: 5 3 5 1 3 5 3 5 3 2 ) 3 2 ( ) 3 ( ) 3 2 )( 3 ( ) 2 3 ( 3 ) 2 3 ( 3 x y c x y y x y x p p U x p p U x p p x p xp x U = = = = Solve for y: y x C p p y 2 3 = 5 2 5 1 5 3 5 1 ) 2 3 ( ) 3 ( ) 3 2 ( ) 3 ( x y c x y p p U y p p U = C. (20 points) What is the definition of a net complement? Does Luka consider X and Y to be net complements? Take the appropriate derivative to prove your answer.
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Econ100A Midterm 2 Solutions - Microeconomics, ECO 100A,...

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