Advanced microeconomics lecture 7: consumption theory V
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.Consumers 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. Let u=v(po,w),u'=v(p,w),el(p,u=elp,u)=w Ev(p,p, w)=e(po, u)-e(po,u)=e(, u)-w C(p,p,1)=e(p,l)-e(p,l)=1-e(p,l)
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,u/)-e(p h,(p, p_, u )dp, C(P,p2,)=k(P1p1,地如 A(p,p,w)=x(p1,p1°p
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.Consumers surplus P h1(D1,p12) h(p1,p1,) P1 22 x(12p1) x1(p,) x(p,)
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