Suppose the following model of government efficiency. Utility function over consumption of private goods (C) and public goods (G) is such that this country desires to have 3 units of consumption good per each unit of public good. Exogenous Income: Y = 18 Lump-sum tax: T Government efficiency: q = 0.2 (This measures the number of public goods that can be produced from one unit of private consumption good) If we want to maximize the representative consumer's utility and balance the government budget, what is the optimal lump-sum tax? O A. 3.375 O B. 2.25 OC. 16.875 O D. 11.25 O E. none of the above

Suppose the following model of government efficiency. Utility function over consumption of private goods (C) and public goods (G) is such that this country desires to have 3 units of consumption good per each unit of public good. Exogenous Income: Y = 18 Lump-sum tax: T Government efficiency: q = 0.2 (This measures the number of public goods that can be produced from one unit of private consumption good) If we want to maximize the representative consumer's utility and balance the government budget, what is the optimal lump-sum tax? O A. 3.375 O B. 2.25 OC. 16.875 O D. 11.25 O E. none of the above

Economics For Today

10th Edition

ISBN:9781337613040

Author:Tucker

Publisher:Tucker

Chapter14: Environmental Economics

Section: Chapter Questions

Problem 15SQ

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In a Lindahl equilibrium, which of the following is true: All individuals pay the same tax shares. Individuals who have a higher demand for public goods consume more public goods. The quantity of public goods consumed is more than the quantity of private goods. The quantity of public goods provided satisfies the Samuelson rule.
In the context of public finance and taxation, which scenario best illustrates the concept of a "Pigovian tax"? a) A government introduces a tax on carbon emissions from industries to correct for environmental externalities. b) The state increases income tax rates across the board to fund a new public healthcare system. c) A local government implements a sales tax on all retail goods to raise general revenue. d) A country imposes high tariffs on imported luxury goods to protect its domestic industries.
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?
Consider an economy with 1,000 people and two goods, one private and one public. The people all have the same utility function Ui(Xi, G) = Xi – 100/G, where Xi is the quantity of the private good consumed by person i and G is the quantity of the public good. The price of the private good is 1 and the price of the public good is 10. Each person has a total income of 1,000O. Find the Pareto efficient amount of G in this economy.
In many models, the amount of government offered services that is socially and economically efficient tends to be much smaller than that is actually produced and given to the people. Discuss why this appears to be the case, and show with a graph where the efficient level of government output would lie with respect to actual output. Do you understand why historically, the level of government services provided tends to rise irrespective of what the efficient level ought to be? Why would this be?
Consider the model of public goods in the last section of this chapter. (a) Suppose that preferences over private consumption C and public goods G are such that these two goods are perfect substitutes; that is, the marginal rate of substitution of public goods for private goods is a constant b > 0 . Determine the optimal quantity of public goods that the government should provide, and interpret your results. Make sure you show all of the relevant cases. What happens when b changes, or when q changes? (b) Repeat part (a), except with perfect complements preferences; that is, for the case where the representative consumer always wishes to consume private consumption goods and public goods in fixed proportions, or C = aG, with a > 0.
QUESTION 24 Consider the following provision of public good problem: Citizen 1 initial budget: w1 = 80,000 $ Citizen 2 initial budget: w2= 60,000 $ Cost of public good: C = 40,000 Citizen 1 Utility Function: U1(x1 g) = 3(x1) + 90,000g Citizen 2 Utility Function: U2(x2, g) = 2(x2) + 60,000g Notation: xi is the budget that citizen i spends on goods other than the public good; g is a public good indicator variable which takes on the value 1 when the public good is provided and zero otherwise. Given this information, the level of utility of citizen 1 when 1 pays and 2 free-rides will be (type it using two decimal places and no thousand separator, e.g. 200000.00):
2. Consider a simple public good economy with two people and two goods: one public (x) and one private (y). Assume that one unit of public good can be produced with two units of private good. Person 1's utility function is u₁(x,y) = 2x¹2 + y₁ and Person 2's utility function is u2(x,y) = x¹2 + y₂. Consider the private good provision mechanism where Person 1 makes a contribution for the public good first, then Person 2 follows. a. Find the optimal output of the public good by using Samuelson condition. b. Show that in the private good provision mechanism Person 2 rides free. C. Is the private good provision mechanism efficient? Explain. N
Consider an economy consisting of three people – A, B, and C. Person i (where i is A, B, or C) has the utility function where z is the quantity of public good provided and ci is person i’s consumption of private goods. Person i’s income yi is divided between consumption of the private good and his contribution to the financing of the public good. Person i’s contribution is the product of his “tax price” ti and the quantity of the public good, so Person A’s income is 90, person B’s income is 120 and person C’s income is 150. Twenty units of private good must be given up to produce each unit of public good. Find the Lindahl equilibrium
This problem uses the 'wedge' approach in a supply and demand diagram to show the effect of a tax. The government is considering levying a tax of €20 per unit on either carbon emissions or car batteries. The supply curve for each of these goods is identical and is shown by S. The demand for carbon emissions is shown by D1, and the demand for car batteries is shown by D2. Assume the government were to tax carbon emissions. The following graph shows the supply and demand for this good. The graph also shows a wedge representing the tax. Use the tan triangle (dash symbols) to shade the area that represents the deadweight loss associated with the tax.
In a Lindahl equilibrium, which of the following is true: A) All individuals pay the same tax shares. B) The quantity of public goods consumed is more than the quantity of private goods. C) The quantity of public goods provided satisfies the Samuelson rule. D) Individuals who have a higher demand for public goods consume more public goods.
Consider an economy with n consumers, one private good and one public good. We think of the private good as "all other goods," and measure it in terms of money. There are n individuals in the economy with utility functions U₁(x,y) = α₁ = a.lny + x, where y is the public good, x, is the private good consumed by individual i 1,..., n i 1 2 n and 0 0. Find the optimal provision of the public good as well as how much is provided under voluntary contributions.