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Chapter 7: Problem 5

In the United States, each state government can impose its own excise tax on the sale of cigarettes. Suppose that in the state of North Texarkana, the state government imposes a tax of \(\$ 2.00\) per pack sold within the state. In contrast, the neighboring state of South Texarkana imposes no excise tax on cigarettes. Assume that in both states the pre-tax price of a pack of cigarettes is \(\$ 1.00 .\) Assume that the total cost to a resident of North Texarkana to smuggle a pack of cigarettes from South Texarkana is \(\$ 1.85\) per pack. (This includes the cost of time, gasoline, and so on.) Assume that the supply curve for cigarettes is neither perfectly elastic nor perfectly inelastic.a. Draw a diagram of the supply and demand curves for cigarettes in North Texarkana showing a situation in which it makes economic sense for a North Texarkanan to smuggle a pack of cigarettes from South Texarkana to North Texarkana. Explain your diagram. b. Draw a corresponding diagram showing a situation in which it does not make economic sense for a North Texarkanan to smuggle a pack of cigarettes from South Texarkana to North Texarkana. Explain your diagram. c. Suppose the demand for cigarettes in North Texarkana is perfectly inelastic. How high could the cost of smuggling a pack of cigarettes go until a North Texarkanan no longer found it profitable to smuggle? d. Still assume that demand for cigarettes in North Texarkana is perfectly inelastic and that all smokers in North Texarkana are smuggling their cigarettes at a cost of \(\$ 1.85\) per pack, so no tax is paid. Is there any inefficiency in this situation? If so, how much per pack? Suppose chip- embedded cigarette packaging makes it impossible to smuggle cigarettes across the state border. Is there any inefficiency in this situation? If so, how much per pack?

Short Answer

Expert verified
Answer: In case of a perfectly inelastic demand, the maximum smuggling cost would be $2.00. Consumers can avoid the excise tax by smuggling cigarettes at a cost of $1.85 per pack which represents an additional cost that could have potentially been avoided in the absence of the excise tax.

Step by step solution

01

Draw Demand and Supply Curves

Start by drawing two coordinate axes, representing the quantity of cigarettes on the x-axis and the price on the y-axis. Draw the demand curve, which represents the consumers' willingness to pay for cigarettes, and a supply curve, which represents the producers' willingness to sell cigarettes.
02

Add Excise Tax

Now, add the excise tax of \(2.00 to the supply curve. This shifts the supply curve upwards by \)2.00, as producers will only be willing to supply cigarettes at a higher price due to the tax.
03

Determine Market Price

Find the intersection of the new supply curve with the demand curve. This is the new equilibrium price which includes the tax. Let's say this price is \(P_NT\).
04

Show Smuggling Price

Now, add the smuggling cost of \(1.85 to the original price of \)1.00. This gives us a total price of \(2.85. If this price is lower than the new equilibrium price (\)P_NT$), it represents a situation in which smuggling is economically profitable.
05

Explain the Diagram

The diagram shows that by smuggling cigarettes from South Texarkana, North Texarkana residents can acquire cigarettes at a lower price than by buying them in their own state, where the excise tax has raised the market price. This provides an incentive to smuggle cigarettes. #b. Diagram with unprofitable smuggling#
06

Draw Demand and Supply Curves

Similar to part a, draw two coordinate axes and the demand and supply curves for cigarettes.
07

Add Excise Tax

Add the excise tax of \(2.00 to the supply curve, shifting it upwards by \)2.00.
08

Determine Market Price

Find the intersection of the new supply curve with the demand curve. This is the new equilibrium price which includes the tax. Let's say this price is \(P_NT'\).
09

Show Smuggling Price

As before, add the smuggling cost of \(1.85 to the original price of \)1.00. This gives a total price of \(2.85. If this price is higher than the new equilibrium price (\)P_NT'$), it represents a situation in which smuggling is economically unprofitable.
10

Explain the Diagram

The diagram shows that by smuggling cigarettes from South Texarkana, North Texarkana residents would acquire cigarettes at a higher price than by buying them in their own state, where the excise tax has raised the market price. This provides no incentive to smuggle cigarettes. #c. Maximum smuggling cost#
11

Consider Perfectly Inelastic Demand

A perfectly inelastic demand curve is a vertical line. In this case, the quantity demanded does not change, regardless of the price.
12

Find the Maximum Smuggling Cost

The maximum smuggling cost occurs when the price of smuggled cigarettes is equal to the price of legally purchased cigarettes in North Texarkana, which includes the excise tax. Therefore, in this case, the maximum smuggling cost would be $2.00. #d. Inefficiency analysis#
13

Analyze Efficiency With Smuggling

When all consumers in North Texarkana smuggle cigarettes at a cost of \(1.85 per pack, they avoid the excise tax. However, there is still an inefficiency, as the cost of smuggling (\)1.85) per pack represents an additional cost which could have potentially been avoided in the absence of the excise tax.
14

Calculate Inefficiency With Smuggling

The inefficiency per pack is equal to the smuggling cost (\(1.85) minus the original price without the tax (\)1.00), which is $0.85 per pack.
15

Analyze Efficiency Without Smuggling

In the case where smuggling is not possible due to chip-embedded packaging, all consumers in North Texarkana will have to buy cigarettes at the higher price due to the excise tax.
16

Calculate Inefficiency Without Smuggling

The inefficiency per pack in this case is equal to the difference between the post-tax price and the original price without the tax (\(1.00). Let's say the post-tax price is \)P_T\(. Then the inefficiency per pack is \)P_T - 1.00$.

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Most popular questions from this chapter

Assess the following four tax policies in terms of the benefits principle versus the ability-to-pay principle. a. A tax on gasoline that finances maintenance of state roads b. An \(8 \%\) tax on imported goods valued in excess of \(\$ 800\) per household brought in on passenger flights c. Airline-flight landing fees that pay for air traffic control d. A reduction in the amount of income tax paid based on the number of dependent children in the household.

The state needs to raise money, and the governor has a choice of imposing an excise tax of the same amount on one of two previously untaxed goods: the state can tax sales of either restaurant meals or gasoline. Both the demand for and the supply of restaurant meals are more elastic than the demand for and the supply of gasoline. If the governor wants to minimize the deadweight loss caused by the tax, which good should be taxed? For each good, draw a diagram that illustrates the deadweight loss from taxation.

In each of the following cases involving taxes, explain: (i) whether the incidence of the tax falls more heavily on consumers or producers, (ii) why government revenue raised from the tax is not a good indicator of the true cost of the tax, and (iii) how deadweight loss arises as a result of the tax. a. The government imposes an excise tax on the sale of all college textbooks. Before the tax was imposed, 1 million textbooks were sold every year at a price of \$50. After the tax is imposed, 600,000 books are sold yearly; students pay \(\$ 55\) per book, \(\$ 30\) of which publishers receive. b. The government imposes an excise tax on the sale of all airline tickets. Before the tax was imposed, 3 million airline tickets were sold every year at a price of \(\$ 500\). After the tax is imposed, 1.5 million tickets are sold yearly; travelers pay \(\$ 550\) per ticket, \(\$ 450\) of which the airlines receive. c. The government imposes an excise tax on the sale of all toothbrushes. Before the tax, 2 million toothbrushes were sold every year at a price of $\$ 1.50$. After the tax is imposed, 800,000 toothbrushes are sold every year; consumers pay \(\$ 2\) per toothbrush, \(\$ 1.25\) of which producers receive.

Each of the following tax proposals has income as the tax base. In each case, calculate the marginal tax rate for each level of income. Then calculate the percentage of income paid in taxes for an individual with a pre-tax income of \(\$ 5,000\) and for an individual with a pre-tax income of \(\$ 40,000 .\) Classify the tax as being proportional, progressive, or regressive. (Hint: You can calculate the marginal tax rate as the percentage of an additional \(\$ 1\) in income that is taxed away.)a. All income is taxed at \(20 \%\). b. All income up to \(\$ 10,000\) is tax-free. All income above \(\$ 10,000\) is taxed at a constant rate of \(20 \%\). c. All income between \(\$ 0\) and \(\$ 10,000\) is taxed at \(10 \%\). All income between \(\$ 10,000\) and \(\$ 20,000\) is taxed at \(20 \%\). All income higher than \(\$ 20,000\) is taxed at \(30 \%\). d. Each individual who earns more than \(\$ 10,000\) pays a lump-sum tax of $\$ 10,000\(. If the individual's income is less than \)\$ 10,000$, that individual pays in taxes exactly what his or her income is. e. Of the four tax policies, which is likely to cause the worst incentive problems? Explain.

You work for the Council of Economic Advisers, providing economic advice to the White House. The president wants to overhaul the income tax system and asks your advice. Suppose that the current income tax system consists of a proportional tax of \(10 \%\) on all income and that there is one person in the country who earns \(\$ 110\) million; everyone else earns less than \(\$ 100\) million. The president proposes a tax cut targeted at the very rich so that the new tax system would consist of a proportional tax of \(10 \%\) on all income up to \(\$ 100\) million and a marginal tax rate of \(0 \%\) (no tax) on income above \(\$ 100\) million. You are asked to evaluate this tax proposal. a. For incomes of \(\$ 100\) million or less, is this proposed tax system progressive, regressive, or proportional? For incomes of more than \(\$ 100\) million? Explain. b. Would this tax system create more or less tax revenue, other things equal? Is this tax system more or less efficient than the current tax system? Explain.
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