Advanced microeconomics lecture 7: consumption theory IV
Advanced Microeconomics lecture 7:consumption theory IV
Aggregation and Welfare · Content Consumers surplus gregation 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(po, w), u'=vp, w),e(po,u)=e(p, u)=w E(p",p,w)=e(p,l)-e(p,u)=e(p,)- 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 E(p,p,w)=e(p,)- e(p,u-elp h(P1,p1,u地d CV(p,P, w)=h(P, P-, u) Av(P, P, w)=x(Pi, P-1, u dp
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 h1(P12p1,2 h1(P1,p1) E∨ PI CV PI x, (p, p. x(p,) x(p,)
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