Question

4. The Laffer curve

Governments often place so-called sin taxes on goods or services such as cigarettes and alcohol. These kinds of taxes are popular with politicians because they are usually more palatable to voters than income taxes.

To understand the effect of such a tax, consider the monthly market for cigarettes, which is shown on the following graph.

Use the graph input tool to help you answer the following questions. You will not be graded on any changes you make to this graph.

Note: Once you enter a value in a white field, the graph and any corresponding amounts in each grey field will change accordingly.

Suppose the government imposes a $4-per-pack tax on suppliers.

At this tax amount, the equilibrium quantity of cigarettes is _______ packs, and the government collects $_______ in tax revenue.

Now calculate the government's tax revenue if it sets a tax of $0, $4, $8, $10, $12, $16, or $20 per pack. (Hint: To find the equilibrium quantity after the tax, adjust the "Quantity" field until the Tax Wedge equals the value of the per-unit tax.) Using the data you generate, plot a Laffer curve by using the green points (triangle symbol) to plot total tax revenue at each of those tax levels.

Note: Plot your points in the order in which you would like them connected. Line segments will connect the points automatically.

Suppose the government is currently imposing a $12-per-pack tax on cigarettes.

True or False: The government can raise its tax revenue by decreasing the per-unit tax on cigarettes.

True

False

Consider the deadweight loss generated in each of the following cases: no tax, a tax of $8 per pack, and a tax of $16 per pack.

On the following graph, use the black curve (plus symbols) to illustrate the deadweight loss in these cases. (Hint: Remember that the area of a triangle is equal to 1/2 × Base × Height. In the case of a deadweight loss triangle found on the graph input tool, the base is the amount of the tax and the height is the reduction in quantity caused by the tax.)

As the tax per pack increases, deadweight loss _______ .

Answer 1

A tax amount of $4 is shown in the diagram as the vertical green line. The quantity is 48 packs and therefore, the government will collect $192 (= $4x 48). Thus, at this tax amount, the equilibrium quantity of cigarettes is 48 packs, and the government collects $192 in tax revenue. Similarly, at different tax amounts, the quantity and revenue generated by the government are scheduled below: 60 48 Tax Amount Quantity Tax Revenue 0 0 192 288 300 288 192 0 Thus, it is plotted as follows:

Tax Revenue 5 10 15 20 25 Tax -Laffer Curve As seen above, at $12 of tax amount, $288 is collected as tax revenue. If it reduces its tax amount to $10, a higher tax revenue of $300 is generated. Thus, reducing tax amount is increasing the tax revenue. Therefore, the given statement is true.

At a tax amount of $0, there is no deadweight loss and the equilibrium is at the intersection of demand and supply curves. At a tax of $8 per pack, calculate deadweight loss as follows: DWL.: = 5*(14-6) (60 -36) = 5x8x24 = 96 At a tax of $16 per pack, calculate deadweight loss as follows: DWLss = x(18–2)x(60–12) 4x16x48 = 384 Plot it on the graph as follows:

Deadweight loss Deadweight Loss DEADWEIGHT LOSS (Dollars) 0 2 4 16 18 20 6 8 10 12 14 TAX (Dollars per pack) As seen above, deadweight loss option B: increases by a greater and greater amount.