Advanced microeconomics lecture 7: consumption theory IV
Advanced Microeconomics lecture 7:consumption theory IV
Aggregation and Welfare Content Consumer's surplus Aggregation Representation consumer
Aggregation and Welfare • Content: – Consumer’s surplus – Aggregation – Representation consumer
1. Consumer's surplus Money metric utility function e(p, u)measure the welfare of consumer in economy changing Definition: equivalent variation(En and compensating Variation( CV): see the fig Letu=v(p,w),u=v(p, w),e(po,u)=e(p, u)=w EV(p,p,w)=e(p,u-e(p,u=e(p, u)-w Cv(p,,p,w)=e(p,u-e(p, u)=w-e(p,u)
1.Consumer’s surplus • Money metric utility function measure the welfare of consumer in economy changing. • Definition: equivalent variation (EV) and compensating Variation (CV): see the fig. Let e u ( , ) p 0 1 0 1 0 0 0 1 EV w e u e u e u w ( , , ) ( , ) ( , ) ( , ) p p p p p = − = − 0 1 1 1 1 0 1 0 CV w e u e u w e u ( , , ) ( , ) ( , ) ( , ) p p p p p = − = − 0 0 1 1 0 0 1 1 u v w u v w e u e u w = = = = ( , ), ( , ), ( , ) ( , ) p p p p
1.Consumer's surplus Consider a changing only accurse in price of commodity 1 ev(p,p,w)=e(p,u)-w (p,)-e(p h,(pu, p_,u ) dp (p,p,w)=h,(pi AV(P,P,1)=x(2p1,)
1.Consumer’s surplus • Consider a changing only accurse in price of commodity 1. 0 1 1 1 0 1 0 1 0 1 1 1 1 1 1 1 1 ( , , ) ( , ) ( , ) ( , ) ( , , ) p p EV w e u w e u e u h p u dp − = − = − = p p p p p p 0 1 1 1 0 1 0 1 1 1 1 ( , , ) ( , , ) p p CV w h p u dp p p p = − 0 1 1 1 0 1 0 1 1 1 1 ( , , ) ( , , ) p p AV w x p u dp p p p = −
1.Consumer's surplus pI h2(P12P12°) h1(P1,p1,) EV P1 A x,(pi, p x(P,1)
EV AV 1.Consumer’s surplus p1 x1 0 1 1 1 h p u ( , , ) p− 1 1 1 x p w ( , , ) p− 1 1 1 1 h p u ( , , ) p− 1 1 x p w ( , ) 0 1 x p w ( , ) 1 1 p 0 1 p cV