ProblemSet2(DueDate:April9)1．Janeownsahousethatisworth$100,000.Shecaresonlyaboutherwealth,whichconsistsentirelyofthehouse.Inanygivenyear,thereisa20%chancethatthehousewillburndown.Ifitdoes,itsscrapvaluewillbe$22,500.Jane’sutilityfunctionofincomeis1/2()uWW.a)IsJaneriskaverse,riskneutralorarisklover?Explain.b)WhatistheexpectedmonetaryvalueofJane’suncertainty?c)WhatisthemaximumthatJaneiswillingtopaytocompletelyinsureherhouseagainstbeingdestroyedbythefire?d)SaythatHomeristhepresidentofaninsurancecompany.Heisriskneutralandhasanutilityfunctionofthefollowingtype()uWW,whereWishiswealth.Whatisthelowestpriceatwhichheiswillingtoprovideafairinsurancecontract(insurancepremiumequalsexpectedloss)tocompletelyinsureJane’srisk?2．SupposethattheprocessofproducinglightweightparkasbyPolly’sParkasisdescribedbythefunctionQ=10K0.8(L-40)0.2,whereQisthenumberofparkasproduced,Kisthenumberofmachinehours,andListhenumberofperson-hoursoflabors.1)Derivethecost-minimizingdemandsforKandLasafunctionofQ,wagerates(w),andrentalratesonmachines(r).Usethesetoderivethetotalcostfunction.2)Thisprocessrequiresskilledworkers,whoearn$32perhour.Therentalrateis$64perhour.Atthesefactorprices,whataretotalcostsasafunctionofQ?Doesthistechnologyexhibitdecreasing,constant,orincreasingreturnstoscale?3)Polly’sParkasplanstoproduce2000parkasperweek.Atthefactorpricesgivenabove,howmanyworkersshouldtheyhire(at40hoursperweek)andhowmanymachinesshouldtheyrent(at40machine-hoursperweek)?Whatarethemarginalandaveragecostsatthislevelofproduction?3．某个企业的生产函数如下：mimimizzzzQ....21211其中Q为产量，iz是第i个投入品，0i,i=1,2,…,m。1）请求出该企业的长期成本函数（假设iz的价格为iw）。2）企业平均成本的变化与企业规模报酬的性质是什么关系？请予以说明。4.Amanufacturerhastwoworkshops.Theproductionfunctionofoneworkshopis1/21/212xx,andtheproductionfunctionofotheris1/43/412xx.Pricesof1xand2xare2and5respectively.a)Whatisthecostfunctionoftwoworkshopsrespectively?b)Whatisthecostfunctionofthemanufacturer?5.Aschool...
