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