d. Calculate the prices to be paid by individuals A (PA) and B (PB), respectively. PA = RM_ _; PB = RM_ e. Calculate the total quantity of public goods produced (G') assuming individual B is a free rider. G' = unit(s)
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- 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 two consumers with the following demand functions for a public good. P1 = 10 - 0.1G P2 = 20 - 0.1G where P1 is the price that person 1 is willing to pay for quantity G and P2 is the price that person 2 is willing to pay for quantity G What is the optimal level of the public good if the marginal cost of the public good is Ksh. 25. What is the total cost of producing the optimal quantity how much does each person contribute towards the costFirst consider a public good of value to Ann and Bob with the property that the value of the good can be expressed in monetary terms. In this case, the Samuelson condition states that the efficient level of the good is determined by MV +MVP where p is the per unit price of the good, and, for example, MV is Ann's marginal value of the good. Now consider a public good of value to Ann and Bob, the value of which CANNOT be expressed in monetary terms. In this case А a. We need more information before we can know how to modify the Samuelson condition. b. The Samuelson condition is of no use because we cannot compare Ann's utility to Bob's. Ⓒc. The price must be replaced with a relative price, and the marginal values must be replaced with the corresponding Marginal Rates of Substitution. d. The Samuleson condition continues to work as in the case where values CAN be expressed in monetary terms.
- 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 PA 60 - 2QA and agent B with inverse demand PB = 90 - 5QB, 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) State the condition for the Pareto optimal provision of a public good. Interpret the condition. B b) Consider agent A with (inverse) demand curve for the public good P₁ = 60 - 2Q and agent B with inverse demand PR = 90 - 5QB, 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.An economy consists of two individuals, A and B and two goods, a private good, which is called good 1, and a public good, which is called good 2. Each individual i = A, B is endowed with 24 units of time, which can be used to produce an amount of a private good at a labour cost of a units of time, and an amount of a public good at a labour cost of 2x units of time. Individual i's utility function is given by u(xi, x2) = (xi)¹/2 (g)¹/2, for both i = A, B and where g denotes the aggregate provision of the public good, i.e. g = x2 + x2. (a) Derive the allocation that maximises utilitarian welfare (i.e. the sum of both individ- ual's utility functions). 3 (b) Suppose both individuals decide on provision of feasible bundles (x,x) and (x,x) simultaneously and have full information about the other individual's utility function. Derive the Nash equilibrium of the noncooperative game. (c) Explain concisely (max three sentences) why there is usually under-provision of the public good (you can…
- Plants A and B emit 12 tons and 6 tons of carbon dioxide (CO2), respectively. MAC(marginal abatement costs) for a = 12 - Ea, MACb=12-2Eb MD(marginal damage) = 1/3*E (E indicates CO2 emission) Suppose the government decides to introduce a carbon tax on CO2 emissions. What is the tax amount (ie tax rate) per optimal ton of CO2 emissions? And what is the total revenue that would make the government sufficiently capable of introducing a carbon tax?Consider a municipality A and an irrigation district B with the following marginalnet benefit functions that describe net benefits from water consumption q.MNBA = 72-12qAMNBB = 30-qBRecall marginal net benefits (MNB) shows the difference between marginal benefits andmarginal costs. The quantity that maximizes net benefits is found where MNB=0.a.) Assume the municipality A and the irrigation district B have two different sources ofwater. Assume it has been a very snowy winter and there is plenty of water for everyone.How much water should be processed and consumed by each?b.)How much total surplus (net benefits) is enjoyed by each?c.) Now assume it has been a less snowy winter and water supplies are limited. Each lakecontains only 9 units of water for the season. What is the efficient water consumption foreach?d.) How much total surplus is enjoyed by each?e.) Now assume the municipality and the irrigation district have to share water from a singlelake. In the current year, only 9 total…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]
- There are three consumers of a public good. Their individual demands are as follows: P1 50 – G P2 110 – G P3 150 – G, where G measures the number of units of the good and p; is the price in dollars. MSC of the public good is $190 per unit. What is the optimal level of provision of the public good according to the Samuelson condition?There are 2 people in a community, A and B. The function of the demand for public goods from each of these individuals is: PA = 100 - G P3 = 140 - G where P is the maximum price level that each individual is willing to pay for each unit of public good G. Marginal costs for the production of each unit of public good are constant 120 Tokens. a. Illustrate in a graphical analysis the function of demand and supply (supply) of this public good. What is the efficient provision of public goods G? Describe the prerequisites for the efficient condition (supply) of public goods. b. Determine the Lindahl price for individual A and individual B. c. If later, individual C joins the community, with PC = 30 - G. Will Individual C contribute to the provision of the public goods? Explain.Suppose the demand for standard sized bottled water in the US is Qd=120-30.5P where Qd is monthly quantity demanded in millions and P is the price per bottle in dollars and cents. If the marginal private cost (MPC) of producing the bottled water is one dollar, calculate the market equilibrium quantity. Explain what a constant marginal cost implies. Does that mean the total opportunity cost of producing bottled water is unrelated to how many are produced? Let’s assume that the marginal private benefit (MPB) of bottled water equals the marginal social benefit (MSB). Explain what that means. At the equilibrium calculated in part A, what do you know about buyers’ willingness to pay in each transaction?