Question

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

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

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.

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.

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 \(P_NT\).

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.

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#

Draw Demand and Supply Curves

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

Add Excise Tax

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

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 \(P_NT'\).

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.

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#

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.

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#

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.

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.

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.

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$.