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AnswerTu11

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School
University of Technology Sydney**We aren't endorsed by this school
Course
BUSINESS 23567
Subject
Economics
Date
Dec 19, 2024
Pages
9
Uploaded by DoctorGerbilPerson99
Tutorial11Q1.·Thebank'soffer:$81withcertainty·Tennisplayer:$25withprob=08$400withprob=0.2·Utilityfunction:Et24()/2-ERiskAversion>(a)E(X)=0.2x400+0.8x25=80+20=100(b)·Bank'soffer:n(81)==9·Tennisplayer:E(u)=Pr(success)·UC400+Pr(failure)-U(25)=0.2xNo+0.8 xNes=4+4=8
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·LisawillchooseBank'soffer.U(XcE)==(1)CCertaintyEquivalent:Itisthamountofmoneywhoselevelofutilityisexactlyequaltotheexpected&N(400)+(1-2)·U(25)=0.2x20+0.8x5=8xSit.u(x)=Err)=$·M=8#x=64=1008=64(d)RiskPremium:theexpectedvalueofthegamble-thecertaintyequivalent=100-64=36
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(2)MethodI:Theriskpremiumispositive->RiskAversion.Theriskpremiumisnegative=>shloring.UN↑utilityofTriskpremiumtheexpectedI>=c-d=0thegamble"d!x-theexpectedvaluethecertaintyequivalent.ofthegamble·Riskpremium=36 70)Riskaversion,Method1:*comparingtheexpectedutilityofthegambleECU)withtheutilityoftheexpectedvalueofthegambleH(E(x)18Fin<U(E)->riskaverseUm-②EIU)<UK)=riskloving⑤ECM=UCEN)=>riskneutrial
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·Em)<UCEN)ERiskLoving·(u)<u(E()=>Riskaversion-⑭··Ecu)=8<UCEN)=100)=Noo-10Lisaisriskaversion.
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(f)(i)P=$90,b=$100E(XMurance)=Presuccess)x(400-4)+Pr(failure)x(25+b-4)=0.2x1400-90)+0.8x125+100-90)=90(ii)F(x/insuranceprobofbadthiny=8.(Xg+d-p)+(1-5).(Xy-4)-=(1-3)-xG+Sxs-p+8./um-mIfTheexpectedvalueofthegamblewithoutinsurance·Actuariallyfair:Aninsurancecontractinsurances=doesnotchangetheexpectedvalueofthegamble.MethodI.-p+s-b=0=b=YE(x)=100from(a.)b=100,p:90.S=0.8=(X/insurance)=gofrom(f) (i):No,itisnotactuariallyfair.-Y=%.8=11.5>100=6·inotactuariallyfair,
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(iii)·Theexpectedutilityofgamblewithinsurance:0.2 x Mogo+0.8x1500-go=8.25Theexpectedutilitywithoutinsuranceis8from(b).i.shebuystheinsurance.(iv).·LisacanchooseanyPandb,suchthatb="Yo.8.·Thebestinsurancecontractamongalltheactuariallyfaircontractsisthecontractthatguaranteesthetheindividualisfullyinsured.·Thevaluewhenbadthinghappendwithinsurance=Thevaluewhengoodthing-=Theexpectedvalueofthegamble
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&25+b-p=1400-4=100P=0.8- B·p=400-100=300&25+b-D=400-4=100·b=0=3%0=375Q2.$100Ifinvest:(I+0.1)X100=110withprob.=0.5100withprob=0311-0.1)x100=90withprob=0.2(a)E(x)=0.5x/10+0.3x100+0.2x90=103(b)Wecannottell.weneedtoknowherutilityfunctionorherattitudetowardsrisk.z(n)U(100)EA(C)Yes,shewillinvest.RiskNeutral#ComparingtheexpectedvaluesU(x)↑Kisequivalenttocomparingtheexpectedutility.>XE(x)=103>(05
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WewanttocompareUCEC)WithElu)·RiskNeutral:UW)=AXIfinvest:·E(u)=0.5-U(110)+0.3.UC100)+0.2:4190=0.5./10·9+p.3x100.a+0.2-90a=(55+30+18)a=103aIfnotinvest:·Ul100)=100d.E(U)=103>M/100)=loodiinvest,a)Yes,shewillinvest.gEcrsofinvestmentRiskLoving:Usiod>UIEN)<U(E=103)=U(03)<Ecu)<UCc00)mir
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(e)No,wecannottellacce!RiskAversion:A)>Ems↑OUCE(X)=103)=U(103)>Ecu)OMclos)>Uccool
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