Rubinstein2005-page7 - nominal prices and wealth even if the budget set is unchanged Claim(Walras’s law If the preferences are monotonic then any

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October 21, 2005 12:18 master Sheet number 73 Page number 57 Demand: Consumer Choice 57 Claim: x ( p , w ) = x p , λ w ) (i.e., the demand function is homogeneous of de- gree zero ). Proof: This follows (with no assumptions about the preference relations) from the basic equality B p , λ w ) = B ( p , w ) and the assumption that the behavior of the consumer is “a choice from a set.” Note that this claim is sometimes interpreted as implying that “uniform inflation does not matter.” This is an incorrect interpre- tation. We assumed, rather than concluded, that choice is made from a set independently of the way that the choice set is framed. Inflation can affect choice since behavior may be sensitive to the
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Unformatted text preview: nominal prices and wealth even if the budget set is unchanged. Claim (Walras’s law): If the preferences are monotonic, then any solution x to the con-sumer’s problem B ( p , w ) is located on its budget curve (and thus, px ( p , w ) = w ). Proof: If not, then px < w . There is an ε > 0 such that p ( x 1 + ε , . . . , x K + ε) < w . By monotonicity, ( x 1 + ε , . . . , x K + ε) Â x , thus contradicting the assumption that x is optimal in B ( p , w ) . Claim: If % is a continuous preference, then the demand function is con-tinuous in prices (and also in w , see problem set)....
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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.

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