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Rubinstein2005-page65

# Rubinstein2005-page65 - I is an indifference curve then the...

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October 21, 2005 12:18 master Sheet number 63 Page number 47 Consumer Preferences 47 Figure 4.4 Quasi-linear (in good 1) preferences. the preferences are homothetic, α x t ( x ) , ... , α t ( x )) and thus u x ) = α t ( x ) = α u ( x ) . Let us now consider an additional class of consumer preferences. Quasi-Linear Preferences: A preference is quasi-linear in commodity 1 (referred to as the “nu- meraire”) if x % y implies ( x + ε e 1 ) % ( y + ε e 1 ) (where e 1 = ( 1, 0, ... , 0 ) and ε> 0). (See Fg. 4.4.) The indifference curves of preferences that are quasi-linear in com- modity 1 are parallel to each other (relative to the Frst commodity axis). That is, if
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Unformatted text preview: I is an indifference curve, then the set I ε = { x | there exists y ∈ I such that x = y + (ε , 0, . . . , 0 ) } is an indifference curve. Any preference relation represented by x 1 + v ( x 2 , . . . , x K ) for some function v is quasi-linear in commodity 1. ±urthermore: Claim: Any continuous preference relation satisfying strong monotonicity (at least in commodity 1) and quasi-linearity in commodity 1 can be represented by a utility function of the form x 1 + v ( x 2 , . . . , x K ) ....
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