Question

4. The Laffer curve

Governments often place so-called sin taxes on goods or services such as cigarettes, alcohol, and pornography. 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 adult DVDs, 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.

012243648607284961081204036322824201612840PRICE (Dollars per DVD)QUANTITY (DVDs)Demand Supply

Graph Input Tool

Market for Adult DVDs
	Quantity (DVDs)
	Demand Price (Dollars per DVD)			Supply Price (Dollars per DVD)
	Tax Wedge (Dollars per DVD)

Suppose the government imposes an $8-per-DVD tax on suppliers.

At this tax amount, the equilibrium quantity of adult DVDs is

DVDs, and the government collects

in tax revenue.

Now calculate the government's tax revenue if it sets a tax of $0, $8, $16, $20, $24, $32, or $40 per DVD. (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.

Laffer Curve0481216202428323640960864768672576480384288192960TAX REVENUE (Dollars)TAX (Dollars per DVD)

Suppose the government is currently imposing a $24-per-DVD tax on adult DVDs.

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

True

False

Consider the deadweight loss generated in each of the following cases: no tax, a tax of $16 per DVD, and a tax of $32 per DVD.

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 12×Base×Height12×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.)

Deadweight Loss0481216202428323640960864768672576480384288192960DEADWEIGHT LOSS (Dollars)TAX (Dollars per DVD)

As the tax per DVD increases, deadweight loss   .

Answer 1

Suppose the government imposes $8 per DVD tax on suppliers.

As a result, the price buyers paid equals to $24 and price sellers reciever equals to $16, At this tax amount, the equilibrium quantity of adult DVDs is 48 DVDs and government collects ($8)(48)= $384 in revenue.

To plot the laffer curve, we have to calculate the tax revenue at different tax rates, this is shown in the following table:

Tax	Quantity after tax	Tax revenue
0	60	0
8	48	384
16	36	576
20	30	600
24	24	576
32	12	384
40	0	0

By plotting these points, we get the laffer curve as shown below:

Suppose the government is currently imposing a $24 per DVD tax on adult DVDs.

TRUE because the government can raise its tax revenue by decreasing  the per unit tax on adult DVDs . As we can see in the above table or graph ,that when tax is $24 per DVD ,then tax revenue =$576 and when tax is $20, ,then tax revenue is $600.

Deadweight loss is the area of the triangle = (0.5)(Reduction in quantity after tax)(Tax amount)

Tax	Reduction in quantity	Deadweight loss
0	0	0
16	(60-36)=24	(0.5)(24)(16)= 192
32	(60-12)=48	(0.5)(48)(32)=768

By plotting these points ,we get the deadweight loss curve as shown below:

As the tax per DVD increases,the deadweight loss increases by greater and greater amount as shown in the figure above.