Advanced Microeconomics lecture 7:consumption theory IV,Aggregation and Welfare,Content: Consumers surplus Aggregation Representation consumer.,1.Consumers 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,1.Consumers surplus,Consider a changing only accurse in price of commodity 1.,1.Consumers surplus,p1,x1,1.Consumers surplus,Commodity taxation: The loss of the taxation: 1.2.,1.Consumers surplus,1.Consumers surplus,x2,x(p1,w),x(p0,w),u1,u0,L1,x1,L2,2.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,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 Gormansaggregate demands are independent on the distribution of the wealth.,2.Aggregation across consumers,Step2: how can the AD satisfied WA? Definition: ULD (un-compensation law of demand), Proposition2: satisfied ULD, then AD satisfied WA. Proposition3: consumers have the same preference, and their wealth non-increasing distribution on ,then AD satisfied ULD.,3.Representation consumer,We can regard AD as a rational consumer. When can we measure welfare of society by the preference of this consumer? Definition: PRC (positive representative consumer) , there is a rational educing AD, then exist a PRC.,3.Representation consumer,Definition: Bergson-Samuelson social welfare function: A merciful government distribute the wealth to maximize W.(*),3.Representation consumer,Porposition4: if w is the solution of (*), then the value function of (*) is the indirect utility function of PRC for AD. Definition: NRC (normative ) , if w is the solution of (*), and the value function of (*) is the indirect utility function of . The PRC of W(.) is NRC for AD, which,3.Representation consumer,The existence of PRC does not necessary means existing NRC. A “as good at least set” of RC:And Scitovsky counter set:,Representation consumer,Assignment,Text boook:ex.10.2 PPT: Proposition2.,EV & CV,x1,x2,x(p1,w),x(p0,w),u1,u0,EV,CV,3.Aggregation across consumers,