In a country there are 4 types of individuals The utility function of the ith type is given by: U, (x,,G) = x₁ + i*InG; i = 1,2,3,4 where, x, denotes the private good consumed by each citizen and G denotes the public good. The first type has 2 individuals, the second type has 3 individuals, the third and the fourth type have 2 individuals each. The marginal cost of providing the public good is 9/-. a. Compute the efficient level of provision of the public good. b. Assume that the local government asks the voters to directly decide about level of G

Microeconomic Theory
12th Edition
ISBN:9781337517942
Author:NICHOLSON
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Chapter19: Externalities And Public Goods
Section: Chapter Questions
Problem 19.7P
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In a country there are 4 types of individuals The utility function of the ith type is given by:
U, (x,₁,G) = x₁ + i*InG; i = 1, 2, 3, 4
where, x, denotes the private good consumed by each citizen and G denotes the public good.
The first type has 2 individuals, the second type has 3 individuals, the third and the fourth type have
2 individuals each. The marginal cost of providing the public good is 9/-.
a.
Compute the efficient level of provision of the public good.
b. Assume that the local government asks the voters to directly decide about level of G
informing them that for each unit of the public good, each of them will be asked to pay a
contribution equal to 1. What would be the preferred level of G by each of the four
subgroups be? Which G would come out of the voting process?
Page 2 of 3
Transcribed Image Text:In a country there are 4 types of individuals The utility function of the ith type is given by: U, (x,₁,G) = x₁ + i*InG; i = 1, 2, 3, 4 where, x, denotes the private good consumed by each citizen and G denotes the public good. The first type has 2 individuals, the second type has 3 individuals, the third and the fourth type have 2 individuals each. The marginal cost of providing the public good is 9/-. a. Compute the efficient level of provision of the public good. b. Assume that the local government asks the voters to directly decide about level of G informing them that for each unit of the public good, each of them will be asked to pay a contribution equal to 1. What would be the preferred level of G by each of the four subgroups be? Which G would come out of the voting process? Page 2 of 3
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