# hw3 - H = 16 hours of time available to her between labor (...

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ECON 401: Assignment 3 due date: October 3, 2011 1. Solve the following optimization problems: max (ln x + ln y ) s.t. x 2 + y 2 1 x ± 0 y ± 0 2. Consider the utility maximization problem with three goods. An agent tries to max- imize her utility u ( x 1 ; x 2 ; x 3 ) = x 1 x 2 x 3 , given his income I = 6 and prices p 1 = 1 ; p 2 = 2 ; p 3 = 3 for goods 1, 2, 3 respectively. Suppose the agent can only choose nonnegative units of each good, and further, he must consume at least two units of good 2. Solve the utility-maximizing bundle. 3. Consider the "consumption Vs leisure" problem. The agent allocates the
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Unformatted text preview: H = 16 hours of time available to her between labor ( l ) and leisure ( H ² l ) . Her only source of income is from the wages she obtains by working. She earns w = 3 dollors per hour; thus, if she works l 2 [0 ; H ] hours, her total income is wl dollors. She spends her income on food ( f ) and entertainment ( e ) which cost p = 1 dollar and q = 1 dollar respectively. Her utility function is given by u ( f; e; l ) = f 1 3 e 1 3 ² l 2 . Solve the optimal consumption-leisure plan. 1...
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## This note was uploaded on 02/09/2012 for the course ECON 401 taught by Professor Siyang during the Spring '11 term at Rice.

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