TsinghuaMicroCh35PublicGood(清华李稻葵).ppt

Chapter Thirty-Five Public Goods Main Issues uReservation Price uNecessary and Sufficient conditions for providing public good to be Pareto Improvement uFree Riding Problem uLindahl Equilibrium uDemand Revelation Public Goods - Definition uA 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 uBroadcast radio and TV programs. uNational defense. uPublic highways. uReductions in air pollution. uNational parks. Reservation Prices uA consumers reservation price for a unit of a good is his maximum willingness-to-pay for it. uConsumers wealth is uUtility of not having the good is Reservation Prices uA consumers reservation price for a unit of a good is his maximum willingness-to-pay for it. uConsumers wealth is uUtility of not having the good is uUtility of paying p for the good is Reservation Prices uA consumers reservation price for a unit of a good is his maximum willingness-to-pay for it. uConsumers wealth is uUtility of not having the good is uUtility of paying p for the good is uReservation price r is defined by Reservation Prices; An Example Consumers utility is Utility of not buying a unit of good 2 is Utility of buying one unit of good 2 at price p is Reservation Prices; An Example Reservation price r is defined by I.e. by When Should a Public Good Be Provided? uOne unit of the good costs c. uTwo consumers, A and B. uIndividual payments for providing the public good are gA and gB. ugA + gB c if the good is to be provided. When Should a Public Good Be Provided? uPayments must be individually rational; i.e. and When Should a Public Good Be Provided? uPayments must be individually rational; i.e. and uTherefore, necessarily and When Should a Public Good Be Provided? uAnd if and then it is Pareto-improving to supply the unit of good When Should a Public Good Be Provided? uAnd if and then it is Pareto-improving to supply the unit of good, so is sufficient for it to be efficient to supply the good. Private Provision of a Public Good? uSuppose and . uThen A would supply the good even if B made no contribution. uB then enjoys the good for free; free- riding. Private Provision of a Public Good? uSuppose and . uThen neither A nor B will supply the good alone. Private Provision of a Public Good? uSuppose and . uThen neither A nor B will supply the good alone. uYet, if also, then it is Pareto -improving for the good to be supplied. Private Provision of a Public Good? uSuppose and . uThen neither A nor B will supply the good alone. uYet, if also, then it is Pareto -improving for the good to be supplied. uA and B may try to free-ride on each other, causing no good to be supplied. Free-Riding uSuppose A and B each have just two actions - individually supply a public good, or not. uCost of supply c = $100. uPayoff to A from the good = $80. uPayoff to B from the good = $65. Free-Riding uSuppose A and B each have just two actions - individually supply a public good, or not. uCost of supply c = $100. uPayoff to A from the good = $80. uPayoff to B from the good = $65. u$80 + $65 $100, so supplying the good is Pareto-improving. Free-Riding Buy Dont Buy Buy Dont Buy Player A Player B Free-Riding Buy Dont Buy Buy Dont Buy Player A Player B (Dont Buy, Dont Buy) is the unique NE. Free-Riding Buy Dont Buy Buy Dont Buy Player A Player B But (Dont Buy, Dont Buy) is inefficient. Free-Riding uNow allow A and B to make contributions to supplying the good. uE.g. A contributes $60 and B contributes $40. uPayoff to A from the good = $40 $0. uPayoff to B from the good = $25 $0. Free-Riding Contribute Dont Contribute Contribute Dont Contribute Player A Player B Free-Riding Contribute Dont Contribute Contribute Dont Contribute Player A Player B Two NE: (Contribute, Contribute) and (Dont Contribute, Dont Contribute). Free-Riding uSo allowing contributions makes possible supply of a public good when no individual will supply the good alone. uBut what contribution scheme is best? uAnd free-riding can persist even with contributions. Variable Public Good Quantities uE.g. how many broadcast TV programs, or how much land to include into a national park. Variable Public Good Quantities uE.g. how many broadcast TV programs, or how much land to include into a national park. uc(G) is the production cost of G units of public good. uTwo individuals, A and B. uPrivate consumptions are xA, xB. Variable Public Good Quantities uBudget allocations must satisfy Variable Public Good Quantities uBudget allocations must satisfy uMRSA i = 1,n. Then efficient public good production requires Efficient Public Good Supply - the Quasilinear Preferences Case uTwo consumers, A and B. u Efficient Public Good Supply - the Quasilinear Preferences Case uTwo consumers, A and B. u u uUtility-maximization requires Efficient Public Good Supply - the Quasilinear Preferences Case uTwo consumers, A and B. u u uUtility-maximization requires u is is public good demand/marg. utility curve; i = A,B. Efficient Public Good Supply - the Quasilinear Preferences Case MUA MUB pG G Efficient Public Good Supply - the Quasilinear Preferences Case MUA MUB MUA+MUB pG G Efficient Public Good Supply - the Quasilinear Preferences Case pG MUA MUB MUA+MUB MC(G) G Efficient Public Good Supply - the Quasilinear Preferences Case G pG MUA MUB MUA+MUB MC(G) G* Efficient Public Good Supply - the Quasilinear Preferences Case G pG MUA MUB MUA+MUB MC(G) G* pG* Efficient Public Good Supply - the Quasilinear Preferences Case G pG MUA MUB MUA+MUB MC(G) G* pG* Efficient Public Good Supply - the Quasilinear Preferences Case G pG MUA MUB MUA+MUB MC(G) G* pG* Efficient public good supply requires A nobody can lower the supply level. Free-Riding Revisited uWhen is free-riding individually rational? uIndividuals can contribute only positively to public good supply; nobody can lower the supply level. uIndividual utility-maximization may require a lower public good level. uFree-riding is rational in such cases. Free-Riding Revisited uGiven A contributes gA units of public good, Bs problem is subject to Free-Riding Revisited G xB gA Bs budget constraint; slope = -1 Free-Riding Revisited G xB gA Bs budget constraint; slope = -1 is not allowed Free-Riding Revisited G xB gA Bs budget constraint; slope = -1 is not allowed Free-Riding Revisited G xB gA Bs budget constraint; slope = -1 is not allowed Free-Riding Revisited G xB gA Bs budget constraint; slope = -1 is not allowed (i.e. free-riding) is best for B Demand Revelation uA scheme that makes it rational for individuals to reveal truthfully their private valuations of a public good is a revelation mechanism. uE.g. the Groves-Clarke taxation scheme. uHow does it work? Demand Revelation uN individuals; i = 1,N. uAll have quasi-linear preferences. uvi is individual is true (private) valuation of the public good. uIndividual i must provide ci private good units if the public good is supplied. Demand Revelation uni = vi - ci is net value, for i = 1,N. uPareto-improving to supply the public good if Demand Revelation uni = vi - ci is net value, for i = 1,N. uPareto-improving to supply the public good if Demand Revelation uIf and or and then individual j is pivotal; i.e. changes the supply decision. Demand Revelation uWhat loss does a pivotal individual j inflict on others? Demand Revelation uWhat loss does a pivotal individual j inflict on others? uIf then is the loss. Demand Revelation uWhat loss does a pivotal individual j inflict on others? uIf then is the loss. uIf then is the loss. Demand Revelation uFor efficiency, a pivotal agent must face the full cost or benefit of her action. uThe GC tax scheme makes pivotal agents face the full stated costs or benefits of their actions in a way that makes these statements truthful. Demand Revelation uThe GC tax scheme: uAssign a cost ci to each individual. uEach agent states a public good net valuation, si. uPublic good is supplied if otherwise not. Demand Revelation uA pivotal person j who changes the outcome from supply to not supply pays a tax of Demand Revelation uA pivotal person j who changes the outcome from supply to not supply pays a tax of uA pivotal person j who changes the outco