191T4 - ECON191(Spring 2009 2-3.3.2009(Tutorial 4 Chapter 2...

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1 ECON191 (Spring 2009) 2-3.3.2009 (Tutorial 4) Chapter 2 Consumer Theory (Chapter 3 & 4 of textbook) Revealed preference (i) Revealed preference Bundle X that the consumer chooses is revealed preferred to bundle Y, a bundle that he could have chosen. (ii) Weak axiom of revealed preference (WARP) If X is revealed preferred to Y, then Y will not be revealed preferred to X. (The diagram shows the violation of WARP) (iii) Strong axiom of revealed preference (SARP) If X is revealed preferred to Y, and Y is revealed preferred to Z, then Z will not be revealed preferred to X. If we know the choices a consumer has made, we can determine what their preferences are if we have information about a sufficient number of choices that are made when prices and incomes vary. The indifference curve must lie within the unshaded area A B X Y A B X Y (i) (ii) (iii) A B X Y Z
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2 Expenditure function It identifies the minimum amount of income that allows a consumer to achieve a predetermined level of utility at given prices. Ö Expenditure function: ) , , ( 2 1 u p p e E = Utility maximization : Suppose prices are p 1 and p 2 , and income = W (within the economically feasible set), which bundle would we choose to maximize our utility? Ö The utility maximization: Max ) , ( 2 1 x x u s . t . 2 2 1 1 x p x p W + = ) , , ( 2 1 1 * 1 p p W x x = Æ Demand function ) , , ( 2 1 2 * 2 p p W x x = Æ Demand function Income (cost) minimization : Suppose prices are p 1 and p 2 , what is the minimum amount of income that allows us to reach u* ?
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