9.29 Aggregation - Lecture 12 - Aggregation (Part 2)...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare Aggregation (Part 2) September 29, 2011 Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare What is it? I consumers with preferences & i Choice set X R L + Price vector p 2 R L + Can we generate a "representative consumer" as a concise description of markets for ... Predicting market outcomes (Positive Representative Agent) Evaluating Welfare (Normative Representative Agent) Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare Basic Ideas Let us just aggregate together demand by x ( p , w 1 , ..., w I ) = x ( p , w ) = I i = 1 x i ( p , w i ) w = I i = 1 w i tracks wealth distribution for us Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare Basic Ideas De&nition x ( p , w ) satis&es the Weak Axiom if p & x ( p , w ) w and x ( p , w ) 6 = x ( p , w ) implies p & x ( p , w ) > w for any ( p , w ) and ( p , w ) So for any ( w 1 , ..., w I ) and ( w 1 , ..., w I ) such that I i = 1 w i = w and I i = 1 w i = w we have p & x ( p , w ) = I i = 1 p & x i ( p , w i ) I i = 1 w i = w p & x ( p , w ) = I i = 1 p & x i ( p , w i ) > I i = 1 w i = w Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare Basic Ideas De&nition x ( p , w ) satis&es the Weak Axiom if p & x ( p , w ) w and x ( p , w ) 6 = x ( p , w ) implies p & x ( p , w ) > w for any ( p , w ) and ( p , w ) The problem is that some agents might have p & x ( p , w i ) w i and others might have p & x ( p , w i ) w i and so naively adding up doesnt work Another way of putting it: As we go from ( p , w ) to ( p , w ) , we know WA , Compensated law of demand. Consumers "disagree" about this ... [Picture 4.C.1 p. 110] Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare Uncompensated Law of Demand De&nition x i ( p , w i ) satis&es the Uncompensated Law of Demand (ULD) if ( p & p ) ( x i ( p , w i ) & x i ( p , w i )) for any p , p and &xed w i Basically, wealth e/ects are not too extreme We think of "most preferences" as satisfying ULD Alternate: D p x i is negative semide&nite, then x i satis&es ULD Aggregation (Part 2) Aggregation Why we care Properties of Aggregate Demand Social Welfare...
View Full Document

Page1 / 23

9.29 Aggregation - Lecture 12 - Aggregation (Part 2)...

This preview shows document pages 1 - 8. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online