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 YBarzel(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 x;: private goods G: public goods 8i: is contribution to public goods u, (G,xi), utility function fg1+g2≥C G lo if 8+g2<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 l1(,w1-g1)>1(0,w1) l2(1,2-g2)>l2(O,2) r: the reservation price of i l4(1,2-7)=4(0,1)
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 十V>g1 ≥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: gi =c-8j u G,w-g=u (G,w-C+g) h>C-82 n>C f:81<C-,g1=0 Non cooperation equilibrium(0,O)
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(f(g1+g2),W-g) Social welfare function W=a1+(1-a)2
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 )
