Chapter Thirty-FivePublic Goods -- DefinitionPublic Goods -- ExamplesReservation PricesSlide 5Slide 6Reservation Prices; An ExampleSlide 8When Should a Public Good Be Provided?Slide 10Slide 11Slide 12Slide 13Private Provision of a Public Good?Slide 15Slide 16Slide 17Free-RidingSlide 19Slide 20Slide 21Slide 22Slide 23Slide 24Slide 25Slide 26Variable Public Good QuantitiesSlide 28Slide 29Slide 30Slide 31Slide 32Slide 33Slide 34Slide 35Slide 36Slide 37Slide 38Slide 39Slide 40Efficient Public Good Supply -- the Quasilinear Preferences CaseSlide 42Slide 43Slide 44Slide 45Slide 46Slide 47Slide 48Slide 49Slide 50Free-Riding RevisitedSlide 52Slide 53Slide 54Slide 55Slide 56Slide 57Slide 58Slide 59Demand RevelationSlide 61Slide 62Slide 63Slide 64Slide 65Slide 66Slide 67Slide 68Slide 69Slide 70Slide 71Slide 72Slide 73Slide 74Slide 75Slide 76Slide 77Slide 78Slide 79Slide 80Slide 81Slide 82Slide 83Slide 84Slide 85Slide 86Slide 87Slide 88Slide 89Slide 90Slide 91Slide 92Slide 93Slide 94Slide 95Slide 96Slide 97Slide 98Slide 99Chapter Thirty-FivePublic GoodsPublic Goods -- DefinitionA good is purely public if it is both nonexcludable and nonrival in consumption.–Nonexcludable -- all consumers can consume the good.–Nonrival -- each consumer can consume all of the good.Public Goods -- ExamplesBroadcast radio and TV programs.National defense.Public highways.Reductions in air pollution.National parks.Reservation PricesA consumer’s reservation price for a unit of a good is his maximum willingness-to-pay for it.Consumer’s wealth is Utility of not having the good isU w( , ).0w.Reservation PricesA consumer’s reservation price for a unit of a good is his maximum willingness-to-pay for it.Consumer’s wealth is Utility of not having the good isUtility of paying p for the good isU w( , ).0w.U w p( , ). 1Reservation PricesA consumer’s reservation price for a unit of a good is his maximum willingness-to-pay for it.Consumer’s wealth is Utility of not having the good isUtility of paying p for the good isReservation price r is defined byU w( , ).0w.U w p( , ). 1U w U w r( , ) ( , ).0 1 Reservation Prices; An ExampleConsumer’s utility isU x x x x( , ) ( ).1 2 1 21 Utility of not buying a unit of good 2 isV wwpwp( , ) ( ) .0 0 11 1  Utility of buying one unit of good 2 atprice p isV w pw ppw pp( , ) ( )( ).  1 1 121 1Reservation Prices; An ExampleReservation price r is defined byV w V w r( , ) ( , )0 1 I.e. bywpw rprw1 122 ( ).When Should a Public Good Be Provided?One unit of the good costs c.Two consumers, A and B.Individual payments for providing the public good are gA and gB.gA + gB  c if the good is to be provided.When Should a Public Good Be Provided?Payments must be individually rational; i.e.andU w U w gA A A A A( , ) ( , )0 1 U w U w gB B B B B( , ) ( , ).0 1 When Should a Public Good Be Provided?Payments must be individually rational; i.e.andTherefore, necessarily andU w U w gA A A A A( , ) ( , )0 1 U w U w gB B B B B( , ) ( , ).0 1 g rA Ag rB B .When Should a Public Good Be Provided?And ifandthen it is Pareto-improving to supply the unit of goodU w U w gA A A A A( , ) ( , )0 1 U w U w gB B B B B( , ) ( , )0 1 When Should a Public Good Be Provided?And ifandthen it is Pareto-improving to supply the unit of good, so is sufficient for it to be efficient to supply the good.U w U w gA A A A A( , ) ( , )0 1 U w U w gB B B B B( , ) ( , )0 1 r r cA B Private Provision of a Public Good?Suppose and .Then A would supply the good even if B made no contribution.B then enjoys the good for free; free-riding.r cAr cBPrivate Provision of a Public Good?Suppose and .Then neither A nor B will supply the good alone.r cAr cBPrivate Provision of a Public Good?Suppose and .Then neither A nor B will supply the good alone.Yet, if also, then it is Pareto-improving for the good to be supplied.r cAr cBr r cA B Private Provision of a Public Good?Suppose and .Then neither A nor B will supply the good alone.Yet, if also, then it is Pareto-improving for the good to be supplied.A and B may try to free-ride on each other, causing no good to be supplied.r cAr cBr r cA B Free-RidingSuppose A and B each have just two actions -- individually supply a public good, or not.Cost of supply c = $100.Payoff to A from the good = $80.Payoff to B from the good = $65.Free-RidingSuppose A and B each have just two actions -- individually supply a public good, or not.Cost of supply c = $100.Payoff to A from the good = $80.Payoff to B from the good = $65.$80 + $65 > $100, so supplying the good is Pareto-improving.Free-Riding-$20, -$35 -$20, $65$100, -$35 $0, $0BuyDon’tBuyBuyDon’tBuyPlayer APlayer BFree-Riding-$20, -$35 -$20, $65$100, -$35$0, $0BuyDon’tBuyBuyDon’tBuyPlayer APlayer B(Don’t’ Buy, Don’t Buy) is the unique NE.Free-Riding-$20, -$35 -$20, $65$100, -$35 $0, $0BuyDon’tBuyBuyDon’tBuyPlayer APlayer BBut (Don’t’ Buy, Don’t Buy) is inefficient.Free-RidingNow allow A and B to make contributions to supplying the good.E.g. A contributes $60 and B contributes $40.Payoff to A from the good = $40 > $0.Payoff to B from the good = $25 > $0.Free-Riding$20, $25 -$60, $0$0, -$40 $0, $0ContributeDon’tContributeContributeDon’tContributePlayer APlayer BFree-Riding$20, $25 -$60, $0$0, -$40 $0, $0ContributeDon’tContributeContributeDon’tContributePlayer APlayer BTwo NE: (Contribute, Contribute) and (Don’t Contribute, Don’t Contribute).Free-RidingSo allowing contributions makes possible supply of a public good when no individual will supply the good alone.But what contribution scheme is best?And free-riding can persist even with contributions.Variable Public Good QuantitiesE.g. how many broadcast TV programs, or how much land to include into a national park.Variable Public Good QuantitiesE.g. how many broadcast TV programs, or how much land to include into a national park.c(G) is the production cost of G units of public good.Two individuals, A and B.Private consumptions are xA, xB.Variable Public Good QuantitiesBudget allocations must satisfyx x c G w wA B A