清华大学中级微观经济学讲义清华李稻葵

ChapterSeventeen,Auctions,Whereareweinthecourse,WeareworkingonafewimportantadditionstoourmicroeconomicsframeworkWearediscussingaimportantcaseofnon-competitivemarket,WhoUsesAuctions?,Ownersofart,cars,stamps,machines,mineralrightsetc.Q:Whyauction?A:Becausemanymarketsareimperfectanditishardtodiscoverpotentialbuyerstruevaluationsofyourasset.Auctionshelptodiscoverthisinformation.,TypesofAuctions,Englishauction:bidsarepublicannouncementsbidpricerisesuntiltherearenofurtherbidshighestbidwinswinnerpayshisbid.,TypesofAuctions,Sealed-bidfirst-priceauction:bidsareprivateinformationbidsaremadesimultaneouslyhighestbidwinswinnerpayshisbid.,TypesofAuctions,Sealed-bidsecond-priceauction:bidsareprivateinformationbidsaremadesimultaneouslyhighestbidderwinswinnerpayssecond-highestbidalsoknownasaVickreyauction.,TypesofAuctions,Dutchauction:auctioneerannouncesahighbidandthengraduallylowersthebidfirstbuyertoacceptwinsandpaysthatprice.,ReservePrice,Asellerspecifiedbidlevelbelowwhichnosaleismade.,EconomistsClassificationofAuctions,Private-valueauctions:everypotentialbuyerknowsforsureherownvaluationoftheitemforsalealltheseindividualvaluationsareindependentofeachother.,EconomistsClassificationofAuctions,Common-valueauctions:itemforsalehasthesamevaluetoeverypotentialbuyerpotentialbuyersdifferintheirownestimatesofthiscommonvalue.,AuctionDesign,Goals:Paretoefficiencymaximizationofthesellersprofit.,AuctionDesign,Paretoefficiency:theitemmustselltothebuyerwiththehighestvaluationoftheitem.WhichauctionsareParetoefficient?,AuctionsandEfficiency,Englishauctionwithnoreservepricemustbeefficientsince,ifabuyerwithalowvaluationwasabouttobuy,thehighestvaluationbuyerwouldbidhigher.,AuctionsandEfficiency,Englishauctionwithareservepriceneednotbeefficientsinceifthereservepriceissetabovethe(unknowntotheseller)highestbuyervaluation,thentherewillbenosaleandsonogains-to-trade.,AuctionsandEfficiency,Dutchauctionneednotbeefficient.Nobuyerknowsotherbuyersvaluations,sothehighestvaluationbuyermaydelaytoolongandlosetoanotherbidder.,AuctionsandEfficiency,Sealed-bidfirst-priceauctionneednotbeefficient.Nobuyerknowsotherbuyersvaluations,sothehighestvaluationbuyermaybidtoolowandlosetoanotherbidder.,AuctionsandEfficiency,Sealed-bidsecond-priceauctionisParetoefficienteventhoughnobuyerknowstheotherbuyersvaluations(moreonthislater).,WhyUseaReservePrice?,Supposethereare2buyers.Thesellerbelieveseachbuyersvaluationis$20withchance1/2and$50withchance1/2.I.e.withchance1/4each,thesellerbelievesshefacesbuyervaluations($20,$20),($20,$50),($50,$20)and($50,$50).,WhyUseaReservePrice?,I.e.withchance1/4each,thesellerbelievesshefacesbuyervaluations($20,$20),($20,$50),($50,$20)and($50,$50).UseanEnglishauction.Bidsmustberaisedbyatleast$1.Withchance1/4each,winningbidswillbe$20,$21,$21and$50ifthereisnoreserveprice.,WhyUseaReservePrice?,Withchance1/4each,winningbidswillbe$20,$21,$21and$50ifthereisnoreserveprice.Sellersexpectedrevenueis($20+$21+$21+$50)/4=$28withnoreserveprice.,WhyUseaReservePrice?,Withchance1/4each,thesellerbelievesshefacesbuyervaluations($20,$20),($20,$50),($50,$20)and($50,$50).Setareservepriceof$50.Withchance1/4therewillbenosale.Withchance3/4thewinningbidwillbe$50.,WhyUseaReservePrice?,Setareservepriceof$50.Withchance1/4therewillbenosale.Withchance3/4thewinningbidwillbe$50.Sellersexpectedrevenueis,ReservePriceandEfficiency,Thereservepricecausesanefficiencylosssince,withchance1/4,thereisnotrade.,Second-Price,Sealed-BidAuction,bidsareprivateinformationbidsaremadesimultaneouslyhighestbidderwinswinnerpayssecond-highestbidalsoknownasaVickreyauction.,Second-Price,Sealed-BidAuction,Nobidderknowsanyotherbidderstruevaluationoftheitemforsale.Yet,itisindividuallyrationalforeachbiddertostatetruthfullyhisownvaluation.Why?E.g.twobidderswithtruevaluationsv1andv2.,Second-Price,Sealed-BidAuction,E.g.twobidderswithtruevaluationsv1andv2.Bidsareb1andb2.Expectedgaintobidder1is,Second-Price,Sealed-BidAuction,Expectedgaintobidder1isHowisthismaximized?Ifv1b2,thenmaximizetheprob.ofwinning;i.e.setb1=v1.Ifv1b2,thenminimizetheprob.ofwinning;i.e.setb1=v1.Eitherway,tellingthetruthisbest!,Second-Price,Sealed-BidAuction,Sincetruth-tellingisbestforeverybidder,thehighestvaluationbidderwillwin.Hencethesecond-price,sealed-bidauctionisPareto-efficient.,Common-ValueAuctions,Theitemforsalehasthesamevaluetoeverypotentialbuyer.Potentialbuyersdifferintheirownestimatesofthiscommonvalue.Bidderisestimateiswhereisthecommonvalueandisbidderisestimationerror.,Common-ValueAuctions,Bidderisestimateiswhereisthecommonvalueandisbidderisestimationerro