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- image attached that has the inverse demand function b) Consider agent A with (inverse) demand curve for the public good P₁ = 60 - 2QA and agentB with inverse demand PÅ = 90 — 5QB, where prices are measured in £ per unit. The marginalcost of producing the public good is £10 per unit. What is the Pareto efficient level of the publicgood? Explain. Illustrate in a graph. [Hint: Compute the marginal social benefit of the publicgood by adding up the demand curves vertically, over the p's]

The condition for the Pareto optimal provision of a public good is that the sum of individual…

b) Consider agent A with (inverse) demand curve for the public good PA = 60 - 2Q₁ and agent B with inverse demand PB = 90 - 50B, 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]

b) Consider agent A with (inverse) demand curve for the public good PA = 60 - 2Q₁ and agent B with inverse demand PB = 90 - 50B, 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]

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter19: Externalities And Public Goods

Section: Chapter Questions

Problem 19.7P

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(Optimal Provision of Public Goods) Using at least two individual consumers, show how the market demand curve is derived from individual demand curves (a) for a private good and (b) for a public good. Once you have derived the market demand curve in each case, introduce a market supply curve and then show the optimal level of production.
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.
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]
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]
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?
Suppose there are two residents in a neighborhood, and you know both of their demand curves for a public good. What would you have to do in order to figure out what the social demand curve? a-Subtract the demand of the person with the higher valuation of the public good from the demand of the person with the lower valuation of the public good b-Add their demand curves together c-Multiply the two demand curves together d-Subtract the demand of the person with the lower valuation of the public good from the demand of the person with the higher valuation of the public good
Scenario 3 Suppose there are one hundred residents in a neighborhood, and each resident has an identical demand for a public good. The demand for each resident is given by P = 2 - .01Q. If your answer is not a whole number, please make sure to round to the nearest hundredth. Refer to Scenario 3. Find the social demand curve for the public good in this neighborhood. What is the y-intercept of the social demand curve?
Consider the production and sale of Good B. Suppose that the “Social Value” of each unit of Good B is greater than the “Willingness to Pay” of the individual who consumes that unit. There are NO externalities associated with the production or consumption of Good B, and Good B is sold in a competitive market. Suppose that the “Efficient” level of output for Good B is 400,000 units. Is the market equilibrium level of output greater than 400,000, less than 400,000, or equal to 400,000 ( just circle your answer; you don’t have to explain)?
Consider a product market with three consumers X, Y and Z with demand function PX = 6 - QX, PY = 12 - QY and PZ = 18 - QZ respectively, where P is the price in dollars and QX, QY and QZ are the quantities demanded by Consumer X, Y and Z respectively. If the product is public good, obtain the marginal social benefit function and draw the diagram. Determine the optimal quantity of the product in the market if the marginal cost of the product is constant at (a) $3, (b) $9 and (c) $21.
Suppose there are three consumers of a public good with the following marginal benefits of consumption related to the quantity of the public good provided: Consumer 1: MB1 = 5 – 2Q Consumer 2: MB2 = 4 – Q Consumer 3: MB3 = 3 – Q Calculate and draw the total marginal benefit function of the public good in a fully labelled diagram. If the marginal cost of producing the public good is MC = 2Q, what is the efficient quantity and how much should each consumer contribute to its provision if it were to provided at the efficient level (assuming the non-rival and non-excludable problems could be resolved)?
Scenario 3 Suppose there are one hundred residents in a neighborhood, and each resident has an identical demand for a public good. The demand for each resident is given by P = 2 - .01Q. If your answer is not a whole number, please make sure to round to the nearest hundredth. Refer to Scenario 3. Find the social demand curve for the public good in this neighborhood. What is the slope of the social demand curve?
Suppose there are two residents in a neighborhood, and you know both of their demand curves for a public good. What would you have to do in order to figure out what the social demand curve? A.Multiply the two demand curves together B.Add their demand curves together C.Subtract the demand of the person with the lower valuation of the public good from the demand of the person with the higher valuation of the public good D.Subtract the demand of the person with the higher valuation of the public good from the demand of the person with the lower valuation of the public good