Lecture 15: public goods and externality
Lecture 15: public goods and externality
Content Public goods Subscription Efficient provision of public goods Public choice EXternality What's externality? How to solute it? What's the efficient condition with externality
Content • Public goods – Subscription – Efficient provision of public goods – Public choice • Externality – What’s externality? – How to solute it? – What’s the efficient condition with externality
Public goods Subscription Excludable Non-excludable Rival Private goods/ Regulated goods Non-rival Club goods Public goods
Public goods • Subscription Excludable Non-excludable Rival Private goods Regulated goods(?) Non-rival Club goods Public goods
Public goods Subscription Excludability is the property problem Rivality is the physical problem Y Barzel(1989), Public domain Price determined by the property
Public goods • Subscription – Excludability is the property problem – Rivality is the physical problem. – Y.Barzel(1989), Public domain – Price determined by the property
Public goods Efficient provision of public goods Discrete case xi: private goods G: public goods gi: is contribution to public goods u, (G, x; ) utility function lifg1+g2≥c G 0 if g,+g<c
Public goods • Efficient provision of public goods • Discrete case: – xi : private goods – G: public goods – gi : i’s contribution to public goods – ui (G,xi ), utility function 1 2 1 2 1 if 0 if g g c G g g c + = +
Public goods Discrete case: benchmark If providing the public goods will Pareto dominate non So l4(1,w1-g1)>1(0,w1) l2(,12-82)>l2(0,02) r; the reservation price of i l(12,-r)=l1(0,)
Public goods • Discrete case: benchmark • If providing the public goods will Pareto dominate non. So • ri : the reservation price of i. 1 1 1 1 1 2 2 2 2 2 (1, ) (0, ) (1, ) (0, ) u w g u w u w g u w − − (1, ) (0, ) i i i i i u w r u w − =
Public goods Then will get +12>g1+g2≥C The sum of reservation price exceeds the cost of public goods, it's efficient to provide the public goods
Public goods • Then will get: • The sum of reservation price exceeds the cost of public goods, it’s efficient to provide the public goods. 1 2 1 2 r r g g c + +
Public goods But, can private provide it? Reflection function: 8 =c-g l1(G,w2-g)=l(G,-c+g) 1>C-82 2>C-81 f:81<C-r28=0 Non cooperation equilibrium(0,0
Public goods • But, can private provide it? • Reflection function: • If: • Non cooperation equilibrium (0,0) i j g c g = − ( , ) ( , ) i i i i i j u G w g u G w c g − = − + 1 2 2 1 r c g r c g − − , 0 i j j g c r g − =
Public goods Voting
Public goods • Voting:
Public goods Continuous case G=f(81+g2) l1((g1+g2),w-g) Social welfare function W=a1+(1-al2
Public goods • Continuous case: • Social welfare function: 1 2 G f g g = + ( ) 1 2 ( ( ), ) i i i u f g g w g + − 1 2 W au a u = + − (1 )
