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# lecture2full - Monotonic Transformations 2 f ( u ( x 1 , x...

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Preferences Consider two goods, 1 and 2, where x 1 indicates the amount of good 1. Consider two baskets of these goods, A and B . { x A 1 , x A 2 } ± { x B 1 , x B 2 } implies A is at least as good as B { x A 1 , x A 2 } ² { x B 1 , x B 2 } implies A is strictly better than B { x A 1 , x A 2 } ∼ { x B 1 , x B 2 } is indifferent between A and B Assumption 1: Preferences are complete

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More assumptions Assumption 2: Preferences are transitive Assumption 3: Preferences are monotonic Assumption 4: Preferences are convex
Convex preferences and Marginal Rates of Substitution (MRS)

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Utility functions and Indifference Curves Utility function maps preferences into numbers
Marginal Utilities and MRS More generally, we can think about how utility changes as we move x 1 and x 2 du ( x 1 , x 2 ) = u ( x 1 , x 2 ) x 1 dx 1 + u ( x 1 , x 2 ) x 2 dx 2

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Monotonic Transformations

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Unformatted text preview: Monotonic Transformations 2 f ( u ( x 1 , x 2 )) is a monotonic transformation of u ( x 1 , x 2 ) if, for all baskets A and B where u ( x A 1 , x A 2 ) > u ( x B 1 , x B 2 ) , f ( u ( x A 1 , x A 2 )) > f ( u ( x B 1 , x B 2 )) Monotonic Transformations 3 Elasticity of Substitution σ = ± ± ± ± %Δ( x 2 / x 1 ) %Δ MRS ± ± ± ± = ± ± ± ± MRSd ( x 2 / x 1 ) ( x 2 / x 1 ) dMRS ± ± ± ± = d ln ( x 2 / x 1 ) d ln | MRS | Elasticity of Substitution 2 u ( x 1 , x 2 ) = ( α x-ρ 1 + ( 1-α ) x-ρ 2 )-1 /ρ Homothetic Tastes Tastes are homothetic when MRS only depends upon the ratio x 2 / x 1...
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## This note was uploaded on 05/13/2010 for the course ECON 105D taught by Professor Cur during the Fall '09 term at Duke.

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lecture2full - Monotonic Transformations 2 f ( u ( x 1 , x...

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