Varian_Chapter36_Public_Goods

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1、Chapter36PublicGoodsPublicGoods--Definition?Agoodispurelypublicifitisbothnonexcludableandnonrivalinconsumption.–Nonexcludable--allconsumerscanconsumethegood.–Nonrival--eachconsumercanconsumeallofthegood.PublicGoods--Examples?BroadcastradioandTVprograms.?Nationaldefense.?Publichighways.?Reductionsin

2、airpollution.?Nationalparks.ReservationPrices?Aconsumer’sreservationpriceforaunitofagoodishismaximumwillingness-to-payforit.?Consumer’swealthisw.?UtilityofnothavingthegoodisU(w,0).?UtilityofpayingpforthegoodisU(w?p,1).?ReservationpricerisdefinedbyU(w,0)=U(w?r,1).ReservationPrices;AnExampleConsumer’

3、sutilityisU(x1,x2)=x1(x2+1).Utilityofnotbuyingaunitofgood2iswwV(w,0)=(0+1)=.p1p1Utilityofbuyingoneunitofgood2atpricepisw?p2(w?p)V(w?p,1)=(1+1)=.p1p1ReservationPrices;AnExampleReservationpricerisdefinedbyV(w,0)=V(w?r,1)I.e.byw2(w?r)w=?r=.p1p12WhenShouldaPublicGoodBeProvided??Oneunitofthegoodcostsc.?

4、Twoconsumers,AandB.?Individualpaymentsforprovidingthepublicgoodaregandg.AB?g+g≥cifthegoodistobeprovided.ABWhenShouldaPublicGoodBeProvided??Paymentsmustbeindividuallyrational;i.e.UA(wA,0)≤UA(wA?gA,1)andUB(wB,0)≤UB(wB?gB,1).?Therefore,necessarilygA≤rAandgB≤rB.WhenShouldaPublicGoodBeProvided??AndifUA(

5、wA,0)cissufficientforittobeefficienttosupplythegood.PrivateProvisionofaPublicGood??Supposeand.rA>crB

6、PublicGood??SupposerAcalso,thenitisPareto-improvingforthegoodtobesupplied.?AandBmaytrytofree-rideoneachother,causingnogoodtobesupplied.Free-Riding?SupposeAandBeachhavejusttwoactions--individuallysupplyapublicgood,ornot.?Costofsupplyc=$1

7、00.?PayofftoAfromthegood=$80.?PayofftoBfromthegood=$65.?$80+$65>$100,sosupplyingthegoodisPareto-improving.Free-RidingPlayerBDon’tBuyBuyBuy-$20,-$35-$20,$65PlayerADon’tBuy$80,-$35$0,$0(Don’t’Buy,Don’tBuy)ist