Substituting into the budget constraint yields the

Info icon This preview shows pages 6–9. Sign up to view the full content.

View Full Document Right Arrow Icon
Substituting into the budget constraint yields the following modified reaction function C F = 55 - C M 2 Similarly, we have for Mozart: C M = 55 - C F 2 Solving for an interior solution, the system of two equations in two unknowns, yields: C F = C M = 55 / 3 = 18 . 334 , The total number of concerts that each would enjoy would be 46.667 ( C F + C M + 10), and they would enjoy X = 46 . 667. So, the government solution does not improve on the competitive equilibrium (same private savings, same number of concerts). (c) To find the social optimum is to use the Samuelson condition together with the aggregate resource (budget) constraint. The marginal cost of providing one more concert is equal to 1 (this is stated in the problem). Using our utility function,
Image of page 6

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

View Full Document Right Arrow Icon
the Samuelson condition is: ∂U F /∂C ∂U F /∂X F + ∂U M /∂C ∂U M /∂X M = MC X M C + X F C = 1 X F + X M = C The aggregate resource constraint is: X F + X M + C = 140 Solving the system of equations for C yields: C = 70 which implies that X M = 35 = X F . We conclude that the competitive equilib- rium is inefficient since it does not provide enough public goods. (d) If a benefactor pays for 10 concerts, Falco chooses C F and X F by solving the following problem: max X F ,C F U = log X F + log( C M + C F + 10) subject to 70 = X F + C F solving this optimization problem yields the following reaction function: C F = 60 - C M 2 Since Falco’s and Mozart’s utility functions are the same, we have: C M = 60 - C F 2 which implies the following equilibrium: C M = C F = 20 Thus, the total number of concerts enjoyed is 40, with Falco and Mozart each retaining 50 units of income for private consumption. The provision is not socially optimal because this provision provides less than the socially optimal number of concerts (70). However individuals are better of in (c) than in (a) or (b).
Image of page 7
4. Efficiency of Public Good Provision: (a) For each i = 1 , 2 , 3, we can compute the marginal rate of substitution as follows: ∂U i ∂G / ∂U i ∂X i = X i G .
Image of page 8

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

View Full Document Right Arrow Icon
Image of page 9
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