3. A society consists of 3 identical individuals who derive utility from a publicgood. The public good can be provided at a constant marginal cost of 2. Letx, denote the level of public good provision by i, where i=1,2,3. Let X-x1 + x2 + x3 be the total provision. The net benefit enjoyed by individual i fromproviding x, units of the public good is given by4 In X-2x,U(x,x)where i=1,2. Is the total provision X under individual optimisation higheror lower than the socially optimal level of provision Xº? Explain the intuitionfor your result.4. If the price of a factor of production rises, a profit maximising firm might usemore of that factor. Is this true or false? Explain your answer by drawing com-parison for consumer choice for a Giffen good.

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3. A society consists of 3 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 2. Let x, denote the level of public good provision by i, where i 1,2,3. Let X- x1 + x2 + x3 be the total provision. The net benefit enjoyed by individual i from providing x, units of the public good is given by U(x,, X) -4 ln X-2x, where i=1,2. Is the total provision X under individual optimisation higher or lower than the socially optimal level of provision Xº? Explain the intuition for your result.

3. A society consists of 3 identical individuals who derive utility from a public good. The public good can be provided at a constant marginal cost of 2. Let x, denote the level of public good provision by i, where i 1,2,3. Let X- x1 + x2 + x3 be the total provision. The net benefit enjoyed by individual i from providing x, units of the public good is given by U(x,, X) -4 ln X-2x, where i=1,2. Is the total provision X under individual optimisation higher or lower than the socially optimal level of provision Xº? Explain the intuition for your result.

Principles of Microeconomics

7th Edition

ISBN:9781305156050

Author:N. Gregory Mankiw

Publisher:N. Gregory Mankiw

Chapter11: Public Goods And Common Resources

Section: Chapter Questions

Problem 2PA

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1. Suppose there is a society with two people who have the following valuations of level y of a public good: v1(y) = 1210√y and v2(y) = 410√y so their marginal benefits are given by 605/√y and 205/√y, respectively. The cost of providing the public good is given by c(y) = 10y. So we have MC(y) = 10. Suppose that their utility is given by u1 = x1 + v1(y) and u2 = x2 + v2(y) , where xi denotes person i’s money (that is not spent on the public good). Further, suppose their wealth/income levels are given by w1 = 500 and w2 = 800. (a) What is the socially optimal level of the public good?
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.
(a) Alpha, Beta and Gamma are consumers of a public good. The marginal benefit ($) of each unit of the public good is given by the following table. Public Good Alpha Beta Gamma 1st unit 8 10 12 2nd unit 4 8 3 3rd unit 2 5 0 4th unit 1 5 0 Suppose each unit of the public good costs $15. How many units of the public good would be optimal? Explain. (b) If the public good becomes a private good and the price drops to $8. The marginal benefits are the same as that given in (a). How many units of the private good would be purchased? Explain.
6. Consider the allocation of surface water between two types of users. The marginal net benefits are MNB, (q) =12-q, for one type and MNB, (q₂)=6-q, for the other type, where g, and q denote the quantity of water used by each type in suitable units and MNB denotes marginal net benefits in dollars per unit. a. Determine the aggregate marginal net benefit. b. Suppose there are q, 8 units of water available in a given year. Determine the efficient allocation of water to the two types. c. Suppose there are q, 4 units of water available in a given year. Determine the efficient allocation of water to the two types. d. Draw a clearly labeled graph illustrating the efficient allocation of water in parts b and c.
A strategy for consumer 1 in the private provision of public goods model is: A quantity of public good purchases that maximises 1’s utility for each level of public good purchases of consumer 2. A quantity of public good purchases. A quantity of public good purchases for each level of public good purchases of consumer 2. The total quantity of public goods consumed by consumer 1.
EXPLAIN THOROUGHLY 1) What are some of the problems that result when a government prints money rather than raises taxes to pay its expenses? 2) How should user charges for government-provided goods and services be set to achieve efficientoutputs and usage rates of such products? 3) Indicate whether you agree with the following statement, and give your reasons for doing so: “Ifthe highways crossing the City of Koronadal were a pure public good, efficiency would require that the price to use the road be zero. However, during rush hour congestion, the road cannot be regarded as a pure public good and a toll should be charged for its use.” If an automated vehicle identification system were established for residents of the City of Koronadal who use the highways, how would you set tolls to achieve efficient use of the road? The AVI system would allow you to send a bill to each user of the road each month based on miles traveled on the road and the price you charge which could vary by time of…
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(Negative Externalities) Suppose you wish to reduce a negative externality by imposing a tax on the activity that creates that externality. When the amount of the externality produced per unit of output increases as output increases, the correct tax can be determined by using a demand-supply diagram; show this. Assume that the marginal private cost curve slopes upward. Negative Externalities: The Market for Electricity in the Midwest:
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There three individuals each benefit from a public good. The marginal cost of the public good provision is fixed at $20 per unit: MC = $20Whereas each of the three individuals each receive a marginal benefit for each unit of the public good defined by: Person 1: MB1= 40 − 2Q Person 2: MB2= 30 − 2Q Person 3: MB3= 31 − Q They are non-rival, just like with public goods. Therefore, each person benefits from the overall quantity of Q purchased by everyone, not only from the value that they personally acquire.1. Draw a figure with all three MB curves, the MC curve, and the Social Marginal Benefit (SMB) Curve. Label all x-intercepts, y-intercepts, and kinks in the SMB curve.2. Given the above MB curves, write down the Social Marginal Benefit Curve as a function of Q. 3. What is the Socially Optimal Choice of Q and would any private individual purchase this on their own?
7-) We add the demands of private goods horizontally but add the demands of public goods vertically when determining the associated marginal benefit to society. Why do we do this and why are the procedures different for public and private goods?