《高级微观经济学Advanced Microeconomics》PPT课件：lecture7 consumption theory IV

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

1.Consumer's surplus Commodity taxation: P!=pi +t, T=tx,(p, w) The loss of the taxation 1.=-EV(p,p,)-T=e(p,l)-e(p,l)-T Pi+t Th, (pu,p_i,u)-h,(pi+t, p-i, u)]dpy 2.=-CW(p,p,w)-T=e(p,l)-e(p,l)-7 =(p2)(+p2

1.Consumer’s surplus • Commodity taxation: • The loss of the taxation: 1. 2. 1 0 1 1 1 1 p p t T t x p w = + =  , ( , ) 0 1 0 1 1 0 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1 ( , , ) ( , ) ( , ) [ ( , , ) ( , , )] p t p L EV w T e u e u T h p u h p t u dp + − − = − − = − − = − +  p p p p p p 0 1 0 1 2 0 1 1 0 0 0 0 0 0 1 1 1 1 1 1 1 ( , , ) ( , ) ( , ) [ ( , , ) ( , , )] p t p L CV w T e u e u T h p u h p t u dp + − − = − − = − − = − +  p p p p p p

1.Consumers surplus P(,F1,n) h(P1,p1,) pi+t PI x(D12p12w) h, (pi+t,p_, u) h,(pr+t, p_,u xI

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− 0 1 p 0 1 p t + 0 1 1 1 1 h p t u ( , , ) + p− 0 0 1 1 1 h p t u ( , , ) + p−

1.Consumer's surplus

1.Consumer’s surplus x2 x(p 1 ,w) x(p 0 ,w) u 1 u 0 L 1 x1 L 2

2. Aggregation across consumers Can a society behave like a ration man? If a society behave like a ration man, can the utility of this"man" represented the Welfare of society? Aggregate demand:xpw…v)=∑x(p1) Wealth distribution w=(w,w,) And total wealth w=∑w

2.Aggregation across consumers • Can a society behave like a ration man? • If a society behave like a ration man, can the utility of this “man” represented the welfare of society? • Aggregate demand: • Wealth distribution • And total wealth 1 1 ( , ) ( , ) I I i i i w w x w = x p p =  1 ( ) w = w wI 1 I i i w w = = 

2. Aggregation across consumers Step1: x(p, w,w)=x(p, w), that means aggregate demand are independent on the distribution of the wealth Proposition 1: f and only if each consumer has a indirect utility function of Gormans 7(p,w)=a1(P)+b(p) aggregate demands are independent on the distribution of the wealth

2.Aggregation across consumers • Step1: , that means aggregate demand are independent on the distribution of the wealth. • Proposition1:if and only if each consumer has a indirect utility function of Gorman’s aggregate demands are independent on the distribution of the wealth. 1 ( , ) ( , ) x p x p w w w I = ( , ) ( ) ( ) i i i v w a p b p w p = +