Problem 3Driving has some negative impacts such as pollution and traffic (we will see later in the coursethat these are examples of externalities). One approach to reducing these is to discouragedriving by taxing gas. However, gas taxes tend to be unpopular with the public, as they hurtconsumers 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 taxrebate.This problem asks you to use consumer theory to demonstrate the logic behind this proposalgraphically. In particular, imagine that a consumer has Cobb Douglas preferences over gasconsumption 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 thecomposite good is $1. to impose a gas tax but then return the revenue collected to consumers in the form of a taxrebate.This problem asks you to use consumer theory to demonstrate the logic behind this proposalgraphically. In particular, imagine that a consumer has Cobb Douglas preferences over gasconsumption 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 thecomposite 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 canafford the consumption bundle he/she chose without the tax (assume that this initialconsumption bundle was optimal).? Show using a diagram that the consumer purchases less gasthan before the tax and rebate, and is better off.To help you approach this problem, consider using the following steps (all on the samediagram):a) Draw a diagram with amount of gas on one axis and amount of the composite good onthe other. Draw a budget line and indicate an optimal bundle by drawing an indifferencecurve tangent to the budget line. Hint: you have not been given any numbers, so theslopes of the lines and position of the optimal bundle are arbitrary. Remember that theindifference 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 budgetline to reflect this.c) The tax rebate shifts the budget line out by $R, and should be just enough that theoptimal bundle from part (a) is on the budget line. Change the budget line to reflect thisand you have your new budget line.d) Indicate a new optimal consumption bundle and utility level by drawing an indifferencecurve of the same shape as in part (a) that is tangent to the new budget line.e) Interpret the diagram you have drawn.

Question

Problem 3Driving has some negative impacts such as pollution and traffic (we will see later in the coursethat these are examples of externalities). One approach to reducing these is to discouragedriving by taxing gas. However, gas taxes tend to be unpopular with the public, as they hurtconsumers 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 taxrebate.This problem asks you to use consumer theory to demonstrate the logic behind this proposalgraphically. In particular, imagine that a consumer has Cobb Douglas preferences over gasconsumption 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 thecomposite good is $1. to impose a gas tax but then return the revenue collected to consumers in the form of a taxrebate.This problem asks you to use consumer theory to demonstrate the logic behind this proposalgraphically. In particular, imagine that a consumer has Cobb Douglas preferences over gasconsumption 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 thecomposite 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 canafford the consumption bundle he/she chose without the tax (assume that this initialconsumption bundle was optimal).? Show using a diagram that the consumer purchases less gasthan before the tax and rebate, and is better off.To help you approach this problem, consider using the following steps (all on the samediagram):a) Draw a diagram with amount of gas on one axis and amount of the composite good onthe other. Draw a budget line and indicate an optimal bundle by drawing an indifferencecurve tangent to the budget line. Hint: you have not been given any numbers, so theslopes of the lines and position of the optimal bundle are arbitrary. Remember that theindifference 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 budgetline to reflect this.c) The tax rebate shifts the budget line out by $R, and should be just enough that theoptimal bundle from part (a) is on the budget line. Change the budget line to reflect thisand you have your new budget line.d) Indicate a new optimal consumption bundle and utility level by drawing an indifferencecurve of the same shape as in part (a) that is tangent to the new budget line.e) Interpret the diagram you have drawn.

Accepted Answer

X axis denotes the Consumption goods 
Y axis denotes the Gas expense . 
Price of consumption goods…