北大微观经济学课件(英文版)Ch31 Welfare.ppt

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1、Chapter Thirty-OneWelfare2023/1/28中级微观经济学Social ChoiceuDifferent economic states will be preferred by different individuals.uHow can individual preferences be“aggregated”into a social preference over all possible economic states?2023/1/28中级微观经济学Aggregating Preferencesux,y,z denote different economic

2、 states.u3 agents;Bill,Bertha and Bob.uUse simple majority voting to decide a state?2023/1/28中级微观经济学Aggregating PreferencesMore preferredLess preferred2023/1/28中级微观经济学Aggregating PreferencesMajority Vote Resultsx beats y2023/1/28中级微观经济学Aggregating PreferencesMajority Vote Resultsx beats yy beats z20

3、23/1/28中级微观经济学Aggregating PreferencesMajority Vote Resultsx beats yy beats zz beats x2023/1/28中级微观经济学Aggregating PreferencesMajority Vote Resultsx beats yy beats zz beats xNosociallybestalternative!2023/1/28中级微观经济学Aggregating PreferencesMajority Vote Resultsx beats yy beats zz beats xMajority voting

4、 doesnot always aggregatetransitive individualpreferences into atransitive socialpreference.Nosociallybestalternative!2023/1/28中级微观经济学Aggregating Preferences2023/1/28中级微观经济学Aggregating PreferencesRank-order vote results(low score wins).2023/1/28中级微观经济学Aggregating PreferencesRank-order vote results(l

5、ow score wins).x-score=62023/1/28中级微观经济学Aggregating Preferencesx-score=6y-score=6Rank-order vote results(low score wins).2023/1/28中级微观经济学Aggregating Preferencesx-score=6y-score=6z-score=6Rank-order vote results(low score wins).2023/1/28中级微观经济学Aggregating Preferencesx-score=6y-score=6z-score=6Nostate

6、 isselected!Rank-order vote results(low score wins).2023/1/28中级微观经济学Aggregating Preferencesx-score=6y-score=6z-score=6Nostate isselected!Rank-order votingis indecisive in thiscase.Rank-order vote results(low score wins).2023/1/28中级微观经济学Manipulating PreferencesuAs well,most voting schemes are manipul

7、able.uI.e.one individual can cast an“untruthful”vote to improve the social outcome for himself.uAgain consider rank-order voting.2023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.2023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introduces anew alternative

8、2023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introduces anew alternative2023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introduces anew alternative andthen lies.2023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introduces

9、 anew alternative andthen lies.Rank-order voteresults.x-score=82023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introduces anew alternative andthen lies.Rank-order voteresults.x-score=8y-score=72023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introdu

10、ces anew alternative andthen lies.Rank-order voteresults.x-score=8y-score=7z-score=62023/1/28中级微观经济学Manipulating PreferencesThese are truthfulpreferences.Bob introduces anew alternative andthen lies.Rank-order voteresults.x-score=8y-score=7z-score=6-score=9z wins!2023/1/28中级微观经济学Desirable Voting Rul

11、e Propertiesu1.If all individuals preferences are complete,reflexive and transitive,then so should be the social preference created by the voting rule.u2.If all individuals rank x before y then so should the voting rule.u3.Social preference between x and y should depend on individuals preferences be

12、tween x and y only.2023/1/28中级微观经济学Desirable Voting Rule PropertiesuKenneth Arrows Impossibility Theorem:The only voting rule with all of properties 1,2 and 3 is dictatorial.2023/1/28中级微观经济学Desirable Voting Rule PropertiesuKenneth Arrows Impossibility Theorem:The only voting rule with all of propert

13、ies 1,2 and 3 is dictatorial.uImplication is that a nondictatorial voting rule requires giving up at least one of properties 1,2 or 3.2023/1/28中级微观经济学Social Welfare Functionsu1.If all individuals preferences are complete,reflexive and transitive,then so should be the social preference created by the

14、 voting rule.u2.If all individuals rank x before y then so should the voting rule.u3.Social preference between x and y should depend on individuals preferences between x and y only.2023/1/28中级微观经济学Social Welfare Functionsu1.If all individuals preferences are complete,reflexive and transitive,then so

15、 should be the social preference created by the voting rule.u2.If all individuals rank x before y then so should the voting rule.u3.Social preference between x and y should depend on individuals preferences between x and y only.Give up which one of these?2023/1/28中级微观经济学Social Welfare Functionsu1.If

16、 all individuals preferences are complete,reflexive and transitive,then so should be the social preference created by the voting rule.u2.If all individuals rank x before y then so should the voting rule.u3.Social preference between x and y should depend on individuals preferences between x and y onl

17、y.Give up which one of these?2023/1/28中级微观经济学Social Welfare Functionsu1.If all individuals preferences are complete,reflexive and transitive,then so should be the social preference created by the voting rule.u2.If all individuals rank x before y then so should the voting rule.There is a variety of v

18、oting procedureswith both properties 1 and 2.2023/1/28中级微观经济学Social Welfare Functionsuui(x)is individual is utility from overall allocation x.2023/1/28中级微观经济学Social Welfare Functionsuui(x)is individual is utility from overall allocation x.uUtilitarian:2023/1/28中级微观经济学Social Welfare Functionsuui(x)is

19、 individual is utility from overall allocation x.uUtilitarian:uWeighted-sum:2023/1/28中级微观经济学Social Welfare Functionsuui(x)is individual is utility from overall allocation x.uUtilitarian:uWeighted-sum:uMinimax:2023/1/28中级微观经济学Social Welfare FunctionsuSuppose social welfare depends only on individuals

20、 own allocations,instead of overall allocations.uI.e.individual utility is ui(xi),rather than ui(x).uThen social welfare iswhere is an increasing function.2023/1/28中级微观经济学Social Optima&EfficiencyuAny social optimal allocation must be Pareto optimal.uWhy?2023/1/28中级微观经济学Social Optima&EfficiencyuAny s

21、ocial optimal allocation must be Pareto optimal.uWhy?uIf not,then somebodys utility can be increased without reducing anyone elses utility;i.e.social suboptimality inefficiency.2023/1/28中级微观经济学Utility PossibilitiesOBOA002023/1/28中级微观经济学Utility PossibilitiesOBOA002023/1/28中级微观经济学Utility Possibilities

22、OBOA002023/1/28中级微观经济学Utility PossibilitiesOBOA002023/1/28中级微观经济学Utility PossibilitiesOBOA002023/1/28中级微观经济学Utility PossibilitiesOBOA002023/1/28中级微观经济学Utility PossibilitiesOBOA00Utility possibilityfrontier(upf)2023/1/28中级微观经济学Utility PossibilitiesOBOA00Utility possibilityfrontier(upf)Utility possibi

23、lity set2023/1/28中级微观经济学Social Optima&EfficiencyUpf is the set of efficient utility pairs.2023/1/28中级微观经济学Social Optima&EfficiencyUpf is the set of efficient utility pairs.Socialindifferencecurves2023/1/28中级微观经济学Social Optima&EfficiencyUpf is the set of efficient utility pairs.Socialindifferencecurv

24、esHigher social welfare2023/1/28中级微观经济学Social Optima&EfficiencyUpf is the set of efficient utility pairs.SocialindifferencecurvesHigher social welfare2023/1/28中级微观经济学Social Optima&EfficiencyUpf is the set of efficient utility pairs.SocialindifferencecurvesSocial optimum2023/1/28中级微观经济学Social Optima&

25、EfficiencyUpf is the set of efficient utility pairs.SocialindifferencecurvesSocial optimum is efficient.2023/1/28中级微观经济学Fair AllocationsuSome Pareto efficient allocations are“unfair”.uE.g.one consumer eats everything is efficient,but“unfair”.uCan competitive markets guarantee that a“fair”allocation

26、can be achieved?2023/1/28中级微观经济学Fair AllocationsuIf agent A prefers agent Bs allocation to his own,then agent A envies agent B.uAn allocation is fair if it isPareto efficientenvy free(equitable).2023/1/28中级微观经济学Fair AllocationsuMust equal endowments create fair allocations?2023/1/28中级微观经济学Fair Alloc

27、ationsuMust equal endowments create fair allocations?uNo.Why not?2023/1/28中级微观经济学Fair Allocationsu3 agents,same endowments.uAgents A and B have the same preferences.Agent C does not.uAgents B and C trade agent B achieves a more preferred bundle.uTherefore agent A must envy agent B unfair allocation.

28、2023/1/28中级微观经济学Fair Allocationsu2 agents,same endowments.uNow trade is conducted in competitive markets.uMust the post-trade allocation be fair?2023/1/28中级微观经济学Fair Allocationsu2 agents,same endowments.uNow trade is conducted in competitive markets.uMust the post-trade allocation be fair?uYes.Why?2

29、023/1/28中级微观经济学Fair AllocationsuEndowment of each is uPost-trade bundles are and2023/1/28中级微观经济学Fair AllocationsuEndowment of each is uPost-trade bundles are anduThenand2023/1/28中级微观经济学Fair AllocationsuSuppose agent A envies agent B.uI.e.2023/1/28中级微观经济学Fair AllocationsuSuppose agent A envies agent

30、B.uI.e.uThen,for agent A,2023/1/28中级微观经济学Fair AllocationsuSuppose agent A envies agent B.uI.e.uThen,for agent A,uContradiction.is not affordable for agent A.2023/1/28中级微观经济学Fair AllocationsuThis proves:If every agents endowment is identical,then trading in competitive markets results in a fair alloc

31、ation.2023/1/28中级微观经济学Fair AllocationsOAOBEqual endowments.2023/1/28中级微观经济学Fair AllocationsOAOBGiven pricesp1 and p2.Slope=-p1/p22023/1/28中级微观经济学Fair AllocationsOAOBGiven pricesp1 and p2.Slope=-p1/p22023/1/28中级微观经济学Fair AllocationsOAOBGiven pricesp1 and p2.Slope=-p1/p22023/1/28中级微观经济学Fair Allocation

32、sOAOBPost-tradeallocation-is it fair?2023/1/28中级微观经济学Fair AllocationsOAOBPost-tradeallocation-is it fair?Swap As andBs post-tradeallocations2023/1/28中级微观经济学Fair AllocationsOAOBPost-tradeallocation-is it fair?Swap As andBs post-tradeallocationsA does not envy Bs post-trade allocation.B does not envy As post-trade allocation.2023/1/28中级微观经济学Fair AllocationsOAOBPost-tradeallocation-is it fair?Swap As andBs post-tradeallocationsPost-trade allocation is Pareto-efficient andenvy-free;hence it is fair.2023/1/28中级微观经济学