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slide4-aug29 - ECON 401: Utility function Siyang Xiong Rice...

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ECON 401: Utility function Siyang Xiong Rice University August 29, 2011 Xiong (Rice University) ECON 401 August 29, 2011 1 / 12
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A classic optimization problem in Economics There are n goods; income: I 2 R C ; consumption: x D . x 1 , x 2 , ..., x n / 2 R n C ; utility: u : R n C ! R ; by consuming x D . x 1 , x 2 , ..., x n / , you get a utility of u . x / ; for example: two goods and u . x 1 , x 2 / D x 1 C x 2 ; price: p D . p 1 , p 2 , ..., p n / 2 R n C ; a unit of good k costs p k ; cost of consumption: p x D . p 1 , p 2 , ..., p n / . x 1 , x 2 , ..., x n / D p 1 x 1 C p 2 x 2 C ... C p n x n budget constraint: p x ± I . Xiong (Rice University) ECON 401 August 29, 2011 2 / 12
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A classic optimization problem in Economics Utility maximization problem: max u . x / s.t. p x ± I interpretation: given the income I and the price p of n goods, the agent choosees the optimal consumption x of the n goods within his budget constraints (i.e., he can use the income I to buy the n goods). Xiong (Rice University) ECON 401 August 29, 2011 3 / 12
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More on the utility function u : R n C ! R Econ 101 example: I want to pay $5 to buy the &rst apple; I want to pay $3 to buy the second apple;
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slide4-aug29 - ECON 401: Utility function Siyang Xiong Rice...

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