When should a public good Be Provided? Payments must be individually rational ie UAWAOSUA(WA -8A, 1) an(2,0)≤UB(B-8B,1)
When Should a Public Good Be Provided? Payments must be individually rational; i.e. and UA(wA,0) UA(wA − gA,1) UB(wB,0) UB(wB − gB,1)
When should a public good Be Provided? Payments must be individually rational ie and AWA,O)SUAWA-8A, 1) UBWB, O)SUB(WB-8B, 1) Therefore, necessarily gA≤ ra and gB≤rB·
When Should a Public Good Be Provided? Payments must be individually rational; i.e. and Therefore, necessarily and UA(wA,0) UA(wA − gA,1) UB(wB,0) UB(wB − gB,1). gA rA gB rB
When should a public good Be Provided? And if UA(WA,O<UA(WA -8A, 1) and UBWB, 0<UB(WB-8B, 1) then it is Pareto-improving to supply the unit of good
When Should a Public Good Be Provided? And if and then it is Pareto-improving to supply the unit of good UA(wA,0) UA(wA − gA,1) UB(wB,0) UB(wB − gB,1)
When should a public good Be Provided? And if UA(WA,O<UA(WA -8A, 1) and UBWB, 0<UB(WB-8B, 1) then it is Pareto-improving to supply the unit of good, SO A+B>C is sufficient for it to be efficient to supply the good
When Should a Public Good Be Provided? And 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. UA(wA,0) UA(wA − gA,1) UB(wB,0) UB(wB − gB,1) rA + rB c
Private provision of a public Good? Suppose rA >c and rB<c Then a would supply the good even if B made no contribution B then enjoys the good for free; free riding(免费搭车)
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; freeriding (免费搭车). rA c rB c