review2_sol

N(13 the inequality follows from the fact that c 2

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Unformatted text preview: N (13) The inequality follows from the fact that c- 2 b < c- b (14) Welfare is also higher in (b) W E = a 2 c- 2 b > a 2 c- b + a 2 b ( c- b ) 2 = W N (15) In the decentralized case, individual city does not value the positive spill-over effect it brings to the other city. However, in the centralized provision, the social benefits from spill-over 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 first-order 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,...
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N(13 The inequality follows from the fact that c 2...

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