# S07 Prelim 2 answers - Econ313-1 Spring 2007 Talia Bar...

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Econ313-1 Spring 2007 Talia Bar Prelim 2 - suggested solution Question 1 (25 points. Consumer theory) Mr. Woodcock consumes two goods x and y . His preferences for bundles of these two goods are represented by the utility function u W ( x;y ) = ln x + 2 ln y: The price of x is p x and the price of y is p y = 1 : His income is m: max x;y [ln x + 2 ln y ] s:t:x;y & 0 p x x + y = m (b) (5 Points) If p x = 3 ; at what income m will Mr. Woodcock demand x = 25? Lets ±nd the demand for good x : 1

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MRS = p x p y ) y 2 x = p x ) y = 2 p x x p x x + y = m ) 3 p x x = m ) x = m 3 p x Now substitute p x = 3 and x = 25 m = 3 p x x = 9 25 = 225 : y in this case is y = 2 p x x = 2 3 25 = 150 : (c) (5 points) If m is the income level you found in part b, but p x ±s Marshallian demand for good x . Let us substitute m = 225 in the demand for good x x = m 3 p x = 225 3 p x = 75 p x : Hence the Marshallian demand is x = 75 p x : (d) (5 Points) Mrs. Cardinal faces the same prices as Mr. Woodcock, p x = 3 and p y = 1 : She consumes the bundle ( x;y ) = (25 ; 150) . Her utility function however is di/erent, u C ( x;y ) = A ln x + y and she possibly has a di/erent income level m C : Find the parameter A and the income level m C that are consistent with this information. If (25 ; 150) is her optimal bundle, then it is an interior solution to her utility maximiza- tion problem. Hence, MRS = p x p y ) A x = 3 ) A = 3 x ) A = 3 25 = 75 : 2
The bundle also needs to be on her budget line: p x x + y = m C ) 3 25 + 150 = m C ) m C = 225 : (e) (5 Points) Mr. Woodcock used to maximize utility and consume

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## This note was uploaded on 05/24/2008 for the course ECON 3130 taught by Professor Masson during the Spring '06 term at Cornell.

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S07 Prelim 2 answers - Econ313-1 Spring 2007 Talia Bar...

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