4-Utility and special indiff curvesm

4-Utility and special indiff curvesm - 4. Utility Varian,...

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1 4. Utility Varian, Chapter 4 Utility functions Continuity of the preference relation means that if X Y , and Z is sufficiently close to X , then Z Y as well • A preference relation that is complete, reflexive, transitive, continuous and monotonic can be represented by a continuous utility function
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2 Utility and Indifference Curves • Preferences can be described by a utility function with u ( X ) ≥ u ( Y ) if and only if X Y • An indifference curve (IC) is a level set of the utility function x 2 x 1 Indifference curve ( x 1 , x 2 ) ( y 1 , y 2 ) Utility and Indifference Curves
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3 Utility and Indifference Curves Utility and Indifference Curves
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4 Constructing a utility function x 2 x 1 Distance = u ( A ) A B C Reference ray Distance = u ( C ) Distance = u ( B ) Perfect substitutes u ( x 1 , x 2 ) = x 1 + x 2 • Indifference curve: x 1 +x 2 = u 0 x 2 = u 0 - x 1 u* ( x 1 , x 2 ) = x 1 + 5x 2 x 1 x 2
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5 Perfect complements u ( x 1 , x 2 ) = min{ x 1 ,x 2 } x 1 x 2 Perfect complements u* ( x 1 , x 2 ) = min{ x 1 ,2x 2 } x 1 x 2
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This note was uploaded on 01/29/2012 for the course ECONOMICS 101 taught by Professor Tikk during the Spring '11 term at University of Toronto- Toronto.

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4-Utility and special indiff curvesm - 4. Utility Varian,...

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