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slide6-sept2 - ECON 401: Optimization Siyang Xiong Rice...

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ECON 401: Optimization Siyang Xiong Rice University August 31, 2011 Xiong (Rice University) ECON 401 August 31, 2011 1 / 15
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examples of optimization continued: consumption Vs leisure agents get utility from consumption goods x and leisure l : u . x , l / ; agents are endowed with H units of labor; agents can use labor to earn wage, with w being wage rate, i.e., if he worked for k units of labor, he earns a wage of w k ; p is the price for conumption goods, and agents can use his wage to buy consumption goods, Xiong (Rice University) ECON 401 August 31, 2011 2 / 15
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examples of optimization continued: consumption Vs leisure the consumption-leisure problem is: max u . x , l / s.t. . x , l / 2 . x , l / 2 R n C R C : p ± x ² w . H ³ l / and l ² H ± Xiong (Rice University) ECON 401 August 31, 2011 3 / 15
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examples of optimization continued: optimal commodity taxation problem the agent gets utility by consume x ; the agent use income I to buy x with the price p plus tax ; given . p , I , max u . x / s.t. x 2 x 2 R n C : . p
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slide6-sept2 - ECON 401: Optimization Siyang Xiong Rice...

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