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Problem 3 Driving has some negative impacts such as pollution and traffic (we will see later in the course that these are examples of externalities). One approach to reducing these is to discourage driving by taxing gas. However, gas taxes tend to be unpopular with the public, as they hurt consumers financially. A policy that some economists have proposed to avoid this downside is ' For this question, you can make the (unrealistic!) assumption that books can be divided into any decimal amount. to impose a gas tax but then return the revenue collected to consumers in the form of a tax rebate. This problem asks you to use consumer theory to demonstrate the logic behind this proposal graphically. In particular, imagine that a consumer has Cobb Douglas preferences over gas consumption and consumption of a composite good (consisting of spending on all other goods). The consumer has a fixed budget, I > 0, and the price of gas is pg > 0, while the price of the

Problem 3 Driving has some negative impacts such as pollution and traffic (we will see later in the course that these are examples of externalities). One approach to reducing these is to discourage driving by taxing gas. However, gas taxes tend to be unpopular with the public, as they hurt consumers financially. A policy that some economists have proposed to avoid this downside is ' For this question, you can make the (unrealistic!) assumption that books can be divided into any decimal amount. to impose a gas tax but then return the revenue collected to consumers in the form of a tax rebate. This problem asks you to use consumer theory to demonstrate the logic behind this proposal graphically. In particular, imagine that a consumer has Cobb Douglas preferences over gas consumption and consumption of a composite good (consisting of spending on all other goods). The consumer has a fixed budget, I > 0, and the price of gas is pg > 0, while the price of the

ENGR.ECONOMIC ANALYSIS
ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN:9780190931919
Author:NEWNAN
Publisher:NEWNAN
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Problem 3 Driving has some negative impacts such as pollution and traffic (we will see later in the course that these are examples of externalities). One approach to reducing these is to discourage driving by taxing gas. However, gas taxes tend to be unpopular with the public, as they hurt consumers financialy. A policy that some economists have proposed to avoid this downside is ' For this question, you can make the (unrealistic!) assumption that books can be divided into any decimal amount. to impose a gas tax but then return the revenue collected to consumers in the form of a tax rebate. This problem asks you to use consumer theory to demonstrate the logic behind this proposal graphically. In particular, imagine that a consumer has Cobb Douglas preferences over gas consumption and consumption of a composite good (consisting of spending on all other goods). The consumer has a fixed budget, I > 0, and the price of gas is pg > 0, while the price of the composite good is $1.
Transcribed Image Text:Problem 3 Driving has some negative impacts such as pollution and traffic (we will see later in the course that these are examples of externalities). One approach to reducing these is to discourage driving by taxing gas. However, gas taxes tend to be unpopular with the public, as they hurt consumers financialy. A policy that some economists have proposed to avoid this downside is ' For this question, you can make the (unrealistic!) assumption that books can be divided into any decimal amount. to impose a gas tax but then return the revenue collected to consumers in the form of a tax rebate. This problem asks you to use consumer theory to demonstrate the logic behind this proposal graphically. In particular, imagine that a consumer has Cobb Douglas preferences over gas consumption and consumption of a composite good (consisting of spending on all other goods). The consumer has a fixed budget, I > 0, and the price of gas is pg > 0, while the price of the composite good is $1.
to impose a gas tax but then return the revenue collected to consumers in the form of a tax rebate. This problem asks you to use consumer theory to demonstrate the logic behind this proposal graphically. In particular, imagine that a consumer has Cobb Douglas preferences over gas consumption and consumption of a composite good (consisting of spending on all other goods). The consumer has a fixed budget, I > 0, and the price of gas is pg > 0, while the price of the composite good is $1. Suppose that the government imposes a tax of $t on gas and then gives a tax rebate of $R (which can be spent on either gas or other spending) just large enough that the consumer can afford the consumption bundle he/she chose without the tax (assume that this initial consumption bundle was optimal).? Show using a diagram that the consumer purchases less gas than before the tax and rebate, and is better off. To help you approach this problem, consider using the following steps (all on the same diagram): a) Draw a diagram with amount of gas on one axis and amount of the composite good on the other. Draw a budget line and indicate an optimal bundle by drawing an indifference curve tangent to the budget line. Hint: you have not been given any numbers, so the slopes of the lines and position of the optimal bundle are arbitrary. Remember that the indifference curves should correspond to Cobb Douglas preferences. b) The tax on gas is equivalent to increasing the price of gas to $pg + t. Change the budget line to reflect this. c) The tax rebate shifts the budget line out by $R, and should be just enough that the optimal bundle from part (a) is on the budget line. Change the budget line to reflect this and you have your new budget line. d) Indicate a new optimal consumption bundle and utility level by drawing an indifference curve of the same shape as in part (a) that is tangent to the new budget line. e) Interpret the diagram you have drawn.
Transcribed Image Text:to impose a gas tax but then return the revenue collected to consumers in the form of a tax rebate. This problem asks you to use consumer theory to demonstrate the logic behind this proposal graphically. In particular, imagine that a consumer has Cobb Douglas preferences over gas consumption and consumption of a composite good (consisting of spending on all other goods). The consumer has a fixed budget, I > 0, and the price of gas is pg > 0, while the price of the composite good is $1. Suppose that the government imposes a tax of $t on gas and then gives a tax rebate of $R (which can be spent on either gas or other spending) just large enough that the consumer can afford the consumption bundle he/she chose without the tax (assume that this initial consumption bundle was optimal).? Show using a diagram that the consumer purchases less gas than before the tax and rebate, and is better off. To help you approach this problem, consider using the following steps (all on the same diagram): a) Draw a diagram with amount of gas on one axis and amount of the composite good on the other. Draw a budget line and indicate an optimal bundle by drawing an indifference curve tangent to the budget line. Hint: you have not been given any numbers, so the slopes of the lines and position of the optimal bundle are arbitrary. Remember that the indifference curves should correspond to Cobb Douglas preferences. b) The tax on gas is equivalent to increasing the price of gas to $pg + t. Change the budget line to reflect this. c) The tax rebate shifts the budget line out by $R, and should be just enough that the optimal bundle from part (a) is on the budget line. Change the budget line to reflect this and you have your new budget line. d) Indicate a new optimal consumption bundle and utility level by drawing an indifference curve of the same shape as in part (a) that is tangent to the new budget line. e) Interpret the diagram you have drawn.
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