B now we know that the marginal cost of the public

Info icon This preview shows pages 8–11. Sign up to view the full content.

View Full Document Right Arrow Icon
(b) Now, we know that the marginal cost of the public good is 10. Thus, the Samuel- son condition will be 3 X i =1 X i G = 10 , or X 1 + X 2 + X 3 = 10 G . (c) The aggregate resource constraint is X 1 + X 2 + X 3 +10 G = w 1 + w 2 + w 3 (= 100). Thus, substituting the Samuelson condition into the resource constraint, we have 10 G + 10 G = 100 , which implies G * = 5.
Image of page 8

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

View Full Document Right Arrow Icon
5. Majority Rule: The resource constraint is given by: G = N X i =1 T i = t N X i =1 Y i = tN Y Therefore, we can rewrite the proportional income tax in terms of G T i = G N Y Y i The preferred level of public good provision for a voter with income level Y i can be calculated by solving the following individual optimization problem: max G U i = Y i - G N Y Y i 1 - α G α = Y 1 - α i 1 - G N Y 1 - α G α The first order condition of this problem is: ∂U i ∂G = Y 1 - α i 1 - G N Y 1 - α G α ( (1 - α ) 1 - G N Y - 1 - 1 N Y + αG - 1 ) = Y 1 - α i 1 - G N Y 1 - α G α (1 - α ) - 1 N Y - G + α 1 G = 0 You can find the solution by making the terms inside the bracket to be zero: (1 - α ) 1 N Y - G = α 1 G The individual preferred level is given by: G = αN Y which is the same for all the members of society, and hence it is the outcome of majority rule voting.
Image of page 9
6. Congestion Costs: Figure 1: Commuting Time (a) Proportion of Car Users Commuting Time 0 1 80 70 Bus Car (b) A bus trip and a car trip take the same amount of time if 70 = 20 + 60 x o , or, x o = 5 6 . Suppose x e is the true equilibrium. If x e < x o , then a car trip would be shorter than a bus trip; if this is the case, some bus riders will stop riding the bus and start driving instead, so x e would not really ”stable” (and hence, not an equilibrium). Similarly, if x e > x o , then a bus trip would be shorter than a car trip; if this is the case, some car drivers will stop driving and start taking the bus instead, so x e would not really be ”stable” (and hence, not an equilibrium). (c) To minimize total travel time, we want to find a proportion of drivers, x * , that minimizes the total, or, average, traveling time: min x * x * (20 + 60 x * ) + (1 - x * )70 THE FOC is given by: 20 + 120 x * - 70 = 0 which implies that: x * = 5 12
Image of page 10

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

View Full Document Right Arrow Icon
(d) x * < x o because nobody in the competitive outcome ( x o ) wants to waste his
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    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.

    Student Picture

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

  • Left Quote Icon

    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.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    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.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern