This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: N (13) The inequality follows from the fact that c 2 b &lt; c b (14) Welfare is also higher in (b) W E = a 2 c 2 b &gt; a 2 c b + a 2 b ( c b ) 2 = W N (15) In the decentralized case, individual city does not value the positive spillover effect it brings to the other city. However, in the centralized provision, the social benefits from spillover effects are internalized, and hence more public goods are provided. d) Consider the following subsidies, s 1 = s 2 = b (16) Taking city 2s contribution as given, city 1 chooses its public good provision level g 1 to maximize the following welfare function: W 1 ( g 1 ,g 2 ) = 2 [ a g 1 + b g 1 g 2 ] cg 1 + bg 1 (17) The firstorder condition resulting from this maximization problem is given below: a 1 g 1 + b g 2 g 1 = c b (18) Solving for g 1 gives us the reaction function: g 1 ( g 2 ) = a + b g 2 c b ! 2 (19) City 2s reaction function is similar: g 2 ( g 1 ) = a + b g 1 c b ! 2 (20) From symmetry of the problem we can calculate the equilibrium provision level with subsidy g NS by solving the following equation: g NS = a + b q g NS c b 2 (21) which is the same as the provision level in (b): g NS = a c 2 b 2 (22) Problem 3: Tiebout Sorting and Segregation a) Roys identity implies that the demand for housing can be expressed as: h ( p,y ) = V p V y = Bpy p B 1 py  1 p B = By p (23) The price and income elasticity of housing demand is given by: e p = h ( p,y ) p y h ( p,y ) = By p 2 p By p = 1 (24) e y = h ( p,y ) y y h ( p,y ) = B p y By p = 1 (25) b) There will exist a household with income y that is exactly indifferent between living in j or j + 1 . This household is characterized by the following indifference condition: V ( g j ,p j ,y ) = V ( g j +1 ,p j +1 ,y ) (26) Specifically,...
View
Full Document
 Fall '12
 Sieg
 Fiscal Policy, Public Good, G1 G2, provision level

Click to edit the document details