Take an economy with 2 consumers, 1 private good, and 1 public good. Let each consumer have an income of M. The prices of public and private good are both 1. Let the consumers have utility functions a. Assume that the public good is privately provided, so G = gA + gB. Eliminating xA from the utility function using the budget constraint, show that along an indifference curve Solve the last equation to find the locus of points along which the indifference curve of A is horizontal and use this to sketch the indifference curves of A. b. Consider A choosing gA to maximize utility. Show that the optimal choice satisfies c. Repeat part b for B, and calculate the level of private provision of the public good. d. Calculate the optimal level of provision for the welfare function Contrast this with the private provision level.
Take an economy with 2 consumers, 1 private good, and 1 public good. Let each consumer have an income of M. The prices of public and private good are both 1. Let the consumers have utility functions a. Assume that the public good is privately provided, so G = gA + gB. Eliminating xA from the utility function using the budget constraint, show that along an indifference curve Solve the last equation to find the locus of points along which the indifference curve of A is horizontal and use this to sketch the indifference curves of A. b. Consider A choosing gA to maximize utility. Show that the optimal choice satisfies c. Repeat part b for B, and calculate the level of private provision of the public good. d. Calculate the optimal level of provision for the welfare function Contrast this with the private provision level.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Take an economy with 2 consumers, 1 private good, and 1 public good. Let each consumer have an income of M. The prices of public and private good are both 1. Let the consumers have utility functions
a. Assume that the public good is privately provided, so G = gA + gB. Eliminating xA from the utility function using the budget constraint, show that along an indifference curve
Solve the last equation to find the locus of points along which the indifference curve of A is horizontal and use this to sketch the indifference curves of A.
b. Consider A choosing gA to maximize utility. Show that the optimal choice satisfies
c. Repeat part b for B, and calculate the level of private provision of the public good.
d. Calculate the optimal level of provision for the welfare function
Contrast this with the private provision level.
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