第12章講義 不確定性ppt課件

1、Chapter TwelveUncertaintyStructureuState contingent consumption (依情依情形而定的消費）形而定的消費）uState-contingent budget constraintuPreferences under uncertaintyuChoice under uncertaintyuRisk aversionuDiversification and risk spreadingUncertainty is PervasiveuWhat is uncertain in economic systems?utomorrows pric

2、esufuture wealthufuture availability of commoditiesupresent and future actions of other people.Uncertainty is PervasiveuWhat are rational responses to uncertainty?ubuying insurance (health, life, auto)ua portfolio of contingent consumption goods.States of NatureuPossible states of Nature:u“car accid

3、ent” (a)u“no car accident” (na).uAccident occurs with probability a, does not with probability na ; a + na = 1. uAccident causes a loss of $L.ContingenciesuA contract implemented only when a particular state of Nature occurs is state-contingent.uE.g. the insurer pays only if there is an accident.Con

4、tingenciesuA state-contingent consumption plan is implemented only when a particular state of Nature occurs.uE.g. take a vacation only if there is no accident.State-Contingent Budget ConstraintsuEach $1 of accident insurance costs .uConsumer has $m of wealth.uCna is consumption value in the no-accid

5、ent state.uCa is consumption value in the accident state.State-Contingent Budget ConstraintsCnaCaState-Contingent Budget ConstraintsCnaCa2017A state-contingent consumptionwith $17 consumption value in the accident state and $20 consumption value in the no-accident state.State-Contingent Budget Const

6、raintsuWithout insurance,uCa = m - LuCna = m.State-Contingent Budget ConstraintsCnaCamThe endowment bundle.m mL LState-Contingent Budget ConstraintsuBuy $K of accident insurance.uCna = m - K.uCa = m - L - K + K = m - L + (1- )K.State-Contingent Budget ConstraintsuBuy $K of accident insurance.uCna =

7、m - K.uCa = m - L - K + K = m - L + (1- )K.uSo K = (Ca - m + L)/(1- )State-Contingent Budget ConstraintsuBuy $K of accident insurance.uCna = m - K.uCa = m - L - K + K = m - L + (1- )K.uSo K = (Ca - m + L)/(1- )uAnd Cna = m - (Ca - m + L)/(1- )State-Contingent Budget ConstraintsuBuy $K of accident in

8、surance.uCna = m - K. （ K 為為premium(保保費費)）uCa = m - L - K + K = m - L + (1- )K.uSo K = (Ca - m + L)/(1- )uAnd Cna = m - (Ca - m + L)/(1- )uI.e.C Cm mL LC Cnanaa a1 11 1State-Contingent Budget ConstraintsCnaCamThe endowment bundle.m mL LC Cm mL LC Cnanaa a1 11 1m mL LState-Contingent Budget Constrain

9、tsCnaCamThe endowment bundle.sl opesl ope 1 1C Cm mL LC Cnanaa a1 11 1m mL Lm mL LState-Contingent Budget ConstraintsCnaCamThe endowment bundle.Where is themost preferredstate-contingentconsumption plan?C Cm mL LC Cnanaa a1 11 1sl opesl ope 1 1m mL Lm mL LPreferences Under Uncertaintyu2 states of na

10、ture:uAt probability a , consumption is cauAt probability na , consumption is cnaua + na = 1.uUtility is U(ca, cna, a, na).Preferences Under UncertaintyanaEUU(c )U(c )anaExpected utility functionVon-Neuman-Morgenstern utility functionPreferences Under UncertaintyuState-contingent consumption plans t

11、hat give equal expected utility are equally preferred.Preferences Under UncertaintyCnaCaEU1EU2EU3Indifference curvesEU1 EU2 EU3Preferences Under UncertaintyuWhat is the MRS of an indifference curve?uFor constant EU, dEU = 0.Preferences Under UncertaintyanaEUU(c )U(c )anaPreferences Under Uncertainty

12、aananadEUMU(c )dcMU(c )dcanaanaEUU(c )U(c )anaPreferences Under UncertaintyaananadEU0MU(c )dcMU(c )dc0anaanaEUU(c )U(c )anaaananadEUMU(c )dcMU(c )dcanaPreferences Under UncertaintyaananaMU(c )dcMU(c )dcana anaEUU(c )U(c )anaaananadEUMU(c )dcMU(c )dcanaaananadEU0MU(c )dcMU(c )dc0anaPreferences Under

13、UncertaintynaaanadcMU(c ).dcMU(c )ana anaEUU(c )U(c )anaaananadEUMU(c )dcMU(c )dcanaaananadEU0MU(c )dcMU(c )dc0anaaananaMU(c )dcMU(c )dcana Preferences Under UncertaintyCnaCaEU1EU2EU3Indifference curvesEU1 EU2 7 $45 for sure is preferred to the lottery risk-aversion (規(guī)避風(fēng)險）規(guī)避風(fēng)險）.uU($45) EU risk-avers

14、ion.2EU=7$45UtilityPreferences Under UncertaintyWealth$0$9012U($45)U($45) EU risk-aversion.2EU=7$45MU declines as wealthrises.U”0.UtilityPreferences Under UncertaintyWealth$0$90122EU=7$45UtilityPreferences Under UncertaintyWealth$0$9012U($45) EU risk-loving.2EU=7$45U($45)UtilityPreferences Under Unc

15、ertaintyWealth$0$9012U($45) 0.U($45)UtilityPreferences Under UncertaintyWealth$0$90122EU=7$45UtilityPreferences Under UncertaintyWealth$0$9012U($45) = EU risk-neutrality.2U($45)=EU=7$45UtilityPreferences Under UncertaintyWealth$0$9012U($45) = EU risk-neutrality.2$45MU constant as wealthrises.U”=0.U(

16、$45)=EU=7UtilityExample: Competitive InsuranceuSuppose entry to the insurance industry is free.uExpected economic profit = 0.uI.e. K - aK - (1 - a)0 = ( - a)K = 0.uI.e. free entry = a.uIf price of $1 insurance = accident probability, then insurance is fair.Competitive InsuranceuWhen insurance is fai

17、r, rational insurance choices satisfy1 11 1aaanaM U (cM U (c ) )M U (cM U (c) )a ananaCompetitive InsuranceuWhen insurance is fair, rational insurance choices satisfyuI.e.M U (cM U (c ) )M U (cM U (c) )a anana1 11 1aaanaM U (cM U (c ) )M U (cM U (c) )a ananaCompetitive InsuranceuWhen insurance is fa

18、ir, rational insurance choices satisfyuI.e.uMarginal utility of income must be the same in both states.1 11 1aaanaM U (cM U (c ) )M U (cM U (c) )a ananaM U (cM U (c ) )M U (cM U (c) )a ananaCompetitive InsuranceuHow much fair insurance does a risk-averse consumer buy?M U (cM U (c ) )M U (cM U (c) )a

19、 ananaCompetitive InsuranceuHow much fair insurance does a risk-averse consumer buy?uRisk-aversion MU(c) as c .M U (cM U (c ) )M U (cM U (c) )a ananaCompetitive InsuranceuHow much fair insurance does a risk-averse consumer buy?uRisk-aversion MU(c) as c .uHence M U (cM U (c ) )M U (cM U (c) )a ananac

20、 cc c. .a ananaCompetitive InsuranceuHow much fair insurance does a risk-averse consumer buy?uRisk-aversion MU(c) as c .uHence uI.e. full-insurance.M U (cM U (c ) )M U (cM U (c) )a ananac cc c. .a anana“Unfair” InsuranceuSuppose insurers make positive expected economic profit.uI.e. K - aK - (1 - a)0

21、 = ( - a)K 0.“Unfair” InsuranceuSuppose insurers make positive expected economic profit.uI.e. K - aK - (1 - a)0 = ( - a)K 0.uThen a 1 11 1aa.“Unfair” InsuranceuRational choice requires1 1anaM U (cM U (c ) )M U (cM U (c) )a anana“Unfair” InsuranceuRational choice requiresuSince1 1anaM U (cM U (c ) )M

22、 U (cM U (c) )a anana1 11 1aa, M U (cM U (c ) ) M U (cM U (c) )a anana“Unfair” InsuranceuRational choice requiresuSinceuHence for a risk-averter.1 1anaM U (cM U (c ) )M U (cM U (c) )a anana1 11 1aa, M U (cM U (c ) ) M U (cM U (c) )a ananac c M U (cM U (c) )a ananac c c ca ananaUncertainty is Pervasi

23、veuWhat are rational responses to uncertainty?ubuying insurance (health, life, auto)ua portfolio of contingent consumption goods.Uncertainty is PervasiveuWhat are rational responses to uncertainty?ubuying insurance (health, life, auto)ua portfolio of contingent consumption goods. Uncertainty is Perv

24、asiveuWhat are rational responses to uncertainty?ubuying insurance (health, life, auto)ua portfolio of contingent consumption goods. ?Diversification (多樣化）uTwo firms, A and B. Shares cost $10.uWith prob. 1/2 As profit is $100 and Bs profit is $20.uWith prob. 1/2 As profit is $20 and Bs profit is $10

25、0.uYou have $100 to invest. How?DiversificationuBuy only firm As stock?u$100/10 = 10 shares.uYou earn $1000 with prob. 1/2 and $200 with prob. 1/2.uExpected earning: $500 + $100 = $600DiversificationuBuy only firm Bs stock?u$100/10 = 10 shares.uYou earn $1000 with prob. 1/2 and $200 with prob. 1/2.uExpected earning: $500 + $100 = $600Diversificatio