4. There are two individuals, and two goods: private X and public G. The prices of both goods are equal to one. Individual i has income 12 and contributes G; towards the public good, so the total amount of the public good is G = G1 +G2. The remaining money goes towards public good, so X; = 12 – Gj. The utility function of individual i is G * X;. || a) What is the contribution to a public good of each individual if they contribute indepedendly? What is the total amount of the public good? b) What is the efficient contribution to a public good?

4. There are two individuals, and two goods: private X and public G. The prices of both goods are equal to one. Individual i has income 12 and contributes G; towards the public good, so the total amount of the public good is G = G1 +G2. The remaining money goes towards public good, so X; = 12 – Gj. The utility function of individual i is G * X;. || a) What is the contribution to a public good of each individual if they contribute indepedendly? What is the total amount of the public good? b) What is the efficient contribution to a public good?

Principles of Economics, 7th Edition (MindTap Course List)

7th Edition

ISBN:9781285165875

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter22: Frontiers Of Microeconomics

Section: Chapter Questions

Problem 8PA

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10. A social indifference curve showsa . all allocations that yield the same total utility to individuals in the society.b. social attitudes toward equity.c. social attitudes toward efficiency.d. social utility possibilities as a function of resources.
Finn is in charge of decorations for an upcoming festival, and he is planning to decorate withclovers (C) and flags (F). Suppose his preferences over decorations can be represented by theutility function U(C, F) = C^(3/4)F^(1/4) For this problem, assume C and F are infinitely divisible so you don’t need to worry aboutrestricting to whole-number answers.(a) Write Finn’s budget constraint as a function of the prices PC, PF , and his budget I.(b) Write Finn’s constrained optimization problem in Lagrangian form and derive the threefirst order conditions.(c) Use two of the first order conditions to show that Finn’s marginal rate of substitution(MRS) equals the marginal rate of transformation (MRT) at the optimum. (Note: Youdo not need to solve the constrained optimization any more than this.)
Consider the model of a rational consumer that cares about consumption of private goods and consumption of broadcast public television (a public good). Suppose that the total level of broadcast public television provided through voluntary contributions is 10 hours of programming. Then the government decides to raise money through a tax and provide 10 hours of programming to the public. What would we predict about crowd-out of voluntary contributions to broadcast public television when government does this? How would the answer change if consumers get warm glow utility from donating to broadcast public television in addition to utility from the public television itself? (Be specific.)
9.Refer to Figure 2. Select the correct statement. A. Panel B is an example of a good, no- or low-cost public education program, and the social optimal ouput is Q5. B. Panel A is an example of a good, no- or low-cost public education program, and the social optimal ouput is Q3. C. Panel B is an example of a good, no- or low-cost public education program, and the social optimal ouput is Q4. D. Panel A is an example of a good, no- or low-cost public education program, and the social optimal ouput is Q2. E. None of the answers is correct.
7. a) State the condition for the Pareto optimal provision of a public good. Interpret the condition. b) Consider agent A with (inverse) demand curve for the public good and agent B with inverse demand , where prices are measured in £ per unit. The marginal cost of producing the public good is £10 per unit. What is the Pareto efficient level of the public good? Explain. Illustrate in a graph. [Hint: Compute the marginal social benefit of the public good by adding up the demand curves vertically, over the p’s] c) Describe the Vickrey-Clarke-Groves (VCG) Mechanism, provide examples and discuss problems with the VCG mechanism.
Consider an economy with n consumers, one privategood and one public good. We think of the private good as “all othergoods,” and measure it in terms of money. There are n individuals inthe economy with utility functions Ui(xi, y) = αi ln y + xi, where y is thepublic good, xi is the private good consumed by individual i = 1, . . . , n,and 0 < α1 < α2 < · · · < αn are parameters. Initial endowment of privategood of each consumer is given by wi. We donote the aggregate endowment 1of the private good by w =Pi wi. The cost of producing the public good is c(y) = cy for some c > 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.
1. A. State the condition for the Pareto optimal provision of a public good. Interpret the condition. B. Consider agent A with (inverse) demand curve for the public good and agent B with inverse demand , where prices are measured in £ per unit. The marginal cost of producing the public good is £10 per unit. What is the Pareto efficient level of the public good? Explain. Illustrate in a graph. [Hint: Compute the marginal social benefit of the public good by adding up the demand curves vertically, over the p’s]
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Consider 2 goods with prices p1 = 4 and p2 = 6, and a consumer with income m = 200. The government imposes a sales tax on good 1. Suppose the sales tax is (a) a quantity tax t = 2 (dollars per unit). (b) an ad valorem tax of 30 per cent (t = 0.3). Compute and graph the consumer’s budget line without a tax, and for the taxes in (a) and (b), respectively.
(4) The equilibrium quantity is _______the socially efficient quantity. greater than less than equal to (5) The private benefit curve is shifts outwards to the social benefit curve b.shifts inwards to the social benefit curve remains unchanged (6) The private cost curve is shifts outwards to the social cost curve b.shifts inwards to the social cost curve remains unchanged (7) The Efficient output is found where the → the socially efficient quantity. social cost and social benefit curve intersect private cost and social benefit curve intersect private cost and private benefit curve intersect social cost and private benefit curve intersect
Consider a two-good economy with one private and one public good. There are four consumers in this economy who contribute to public good provision. The price of the private good is $1 and the demand function of the public good for each consumer is as follows: p1 = 20 - 2G, p2 = 30-(5/10)G, p3 = 100-(G/2) and p4 = 60-G where G is the number of units of the public good and p^i is the price of each unit for consumer i in dollars. The cost of providing one extra unit of the public good is (alpha). (a) With 170 < alpha < 210, what is the optimal level of provision of the public good? Show the optimal point on a graph. (b) Is there a possibility that the public good is not supplied at all? Why? (c) If the public good is not supplied at all, what is the size of the deadweight loss due to this market failure? (d) If at least one person contributes, for what values of the public good will be supplied?