review2_sol

# 2 b c b 2 w n 15 in the decentralized case individual

• Notes
• 10
• 100% (2) 2 out of 2 people found this document helpful

This preview shows pages 3–6. Sign up to view the full content.

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 2’s 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)

This preview has intentionally blurred sections. Sign up to view the full version.

Solving for g 1 gives us the reaction function: g 1 ( g 2 ) = a + b g 2 c - b ! 2 (19) City 2’s 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) Roy’s identity implies that the demand for housing can be expressed as: h ( p, y ) = - ∂V ∂p ∂V ∂y = - Bpy ρ p - - 1 py ρ - 1 p - = 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, - n αg ρ j +1 + h yp - B j +1 i ρ o = - n αg ρ j + h yp - B j i ρ o (27) Collect terms containing y on the left-hand side: y ρ h p - j +1 - p - j i = α h g ρ j - g ρ j +1 i (28) Solve for y y = α h g ρ j - g ρ j +1 i h p - j +1 - p - j i 1 ρ (29) c) Households that indifferent between both communities are still characterized by the indifference condition as above. Since households also differ in

This preview has intentionally blurred sections. Sign up to view the full version.

This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern