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Unformatted text preview: October 21, 2005 12:18 master Sheet number 64 Page number 48 48 Lecture Four Proof: In the problem set you will prove that every preference relation that is monotonic, continuous, and quasi-linear in commodity 1 sat- isfies that for every ( x 2 , . . . , x K ) there is some number v ( x 2 , . . . , x K ) so that ( v ( x 2 , . . . , x K ) , 0, . . . , 0 ) ( 0, x 2 , . . . , x K ) . Then, from quasi- linearity in commodity 1, for every bundle x , ( x 1 + v ( x 2 , . . . , x K ) , 0, . . . , 0 ) ( x 1 , x 2 , . . . , x K ) , and thus by strong monotonicity in the first commodity, the function x 1 + v ( x 2 , . . . , x K ) represents . Differentiable Preferences (and the Use of Derivatives in Economic Theory) We often assume in microeconomics that utility functions are dif- ferentiable and thus use standard calculus to analyze the consumer. In this course I (almost) avoid calculus. This is part of a deliberate attempt to steer you away from a mechanistic approach to eco- nomic theory.nomic theory....
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This note was uploaded on 12/29/2011 for the course ECO 443 taught by Professor Aswa during the Fall '10 term at SUNY Stony Brook.
- Fall '10