Homework3_solution

Homework3_solution - W3211 Spring 2009 Suggested Solution...

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W3211 Spring 2009 Suggested Solution for Homework #3 . V ( x; y ) = x y 1 (1 ) 1 , since 0 1 . Hence, the demand funtion for x and y of U ( x; y ) and V ( x; y ) are same. Since V ( x; y ) is a Cobb-Douglas function, x = p x and y = (1 ) w p y . You can solve these through Lagrangian. 2. U ( w ) = 1 ( (1 ) 1 ) ± ( p x ) ± (1 ) w p y ² 1 ³ ± = w ± ± 1 p x p 1 y ² ± U "( w ) = ( 1) w ± 2 ± 1 p x p 1 y ² ± < 0 since 1 < 0 . So, he is risk-averse. Note that once we assume that both prices are equal to one, we have U ( w ) = w ± . 3. Let z be the probability that the widget is a success. EV(contract 1) = 100 ; 000 = z ± 10 ; 000 ; 000 + (1 z ) ± 0 = EV(contract 2) when z = 0 : 01 (a) EU(contract 1) = U (100 ; 000) = (100 ; 000) ± (b) EU(contract 2) = z ± U (10 ; 000 ; 000) + (1 z ) ± U (0) = z (10 ; 000 ; 000) ± (c) Both contracts are indi/rent to him if EU(contract 1)

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This note was uploaded on 12/21/2009 for the course ECON 1211 taught by Professor Govel during the Spring '08 term at Columbia.

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Homework3_solution - W3211 Spring 2009 Suggested Solution...

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