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Econ 337 TA #1 - Econ 337 TA Session 1 Jorge Catepillan 1...

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Econ 337 TA Session 1 Jorge Catepillan January 18, 2012 1 Utility Maximization Suppose we have two goods, lets say X and Y , and a consumer that values such goods according to a utility function U : R + × R + R this means that the consumer prefers the bundle ( x 1 , y 1 ) to ( x 2 , y 2 ) if and only if U ( x 1 , y 1 ) U ( x 2 , y 2 ) or that a bundle ( x, y ) gives her a level U ( x, y ) of utility. Examples of utility functions? Perfect complements (right and left shoe) U ( x, y ) = min { x, y } Perfect substitutes U ( x, y ) = x + y Cobb-Douglas, U ( x, y ) = x α y 1 - β etc. We will define the indifference curve or iso-utility curve of level α as the set IC α = { ( x, y ) s.t. U ( x, y ) = α } In words, is the set of point that gives the consumer the same level of utility. We want to study the decision of a consumer of buying a bundle given that she has wealth w and faces prices p x and p y per unit of X and Y respectively. The set of bundles that she can buy is going to be the budget set , i.e.: BS ( p, w ) = { ( x, y ) s.t. p x x + p y y w, x, y 0 }
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