Question

3. Relationship between tax revenues, deadweight loss, and demandelasticity 

The government is considering levying a tax of $100 per unit on suppliers of either leather jackets or smartphones. The supply curve for each of these two goods is identical, as you can see on each of the following graphs. The demand for leather jackets is shown by DL (on the first graph), and the demand for smartphones is shown by Ds (on the second graph). 

Suppose the government taxes leather jackets. The following graph shows the annual supply and demand for this good. It also shows the supply curve (S + Tax) shifted up by the amount of the proposed tax ($100 per jacket). 

On the following graph, use the green rectangle (triangle symbols) to shade the area that represents tax revenue for leather jackets. Then use the black triangle (plus symbols) to shade the area that represents the deadweight loss associated with the tax.

Instead, suppose the government taxes smartphones. The following graph shows the annual supply and demand for this good, as well as the supply curve shifted up by the amount of the proposed tax ($100 per phone). 

On the following graph, do for smartphones the same thing you did previously on the graph for leather jackets. Use the green rectangle (triangle symbols) to shade the area that represents tax revenue for smartphones. Then, use the black triangle (plus symbols) to shade the area that represents the deadweight loss associated with the tax.

Complete the following table with the tax revenue collected and deadweight loss caused by each of the tax proposals. 

	Tax Revenue	Deadweight Loss
If the Government Taxes...	(Dollars)	(Dollars)
Leather jackets at $100 per jacket
Smartphones at $100 per phone

Suppose the government wants to tax the good that will generate more tax revenue at a lower welfare cost. In this case, it should tax _______  because, all else held constant, taxing a good with a relatively _______ elastic demand generates larger tax revenue and smaller deadweight loss.

Answer 1

S+ tax Price Supply DWL 160 Tax revenue DI il 60 150 350 Quantity

S+ tax Price Supply 220 DWL Tax revenue 120 Ds 300 350 Quantity

Tax revenue for Smartphone is Tax revenue Pricex Quantity ( 220-120) x 300 30,000 Hence, the tax revenue for Smartphone is S30,000 Dead weight loss The dead weight loss of the jacket is Dead weight loss -xbasex height -x (350-150) x (160-140)+-x(350-150)x(140-60) - 2,000 +8,000 -10,000 Hence, the dead weight loss is $10,000 Dead weight loss of the Smartphone Dead weight loss--х base x height -x (350-300)x(220-140)+-x(350-300)x(140-120) -2,000+500 -2,500 Hence, the dead weight loss is $2,500 Table: The table-1 shows the tax revenue and dead weight loss ах If the government taxes Leather jacket at $100 per iacket Smartphone at $100 per phone revenue Dead weight losses 15,000 30,000 10,000 2.500

Suppose the government wants to tax the good that will generate more tax revenue at the lower welfare cost. In this case, it should tax smart phone because all else held constant, taxing a goods with a relatively less elastic demand generate large tax revenue and smaller dead weight loss.

Answer 2

Leather Jacket Tan St 160 1806 --- 14 Tan Revenue Area Rect. ACFG 2 (160-60) A (150-0) 100 x 150 278 15,000 Deadweight loss Area AABC . ²x (350-180) (160-60) 2000 loo 819,000) O 150 350 Q Smart phones Tan S &

Smast phones. Star 112 1.o Tan Revenue Rect. ABDE 2(220-120) (300-0) 2100x300 2 $30,0 og Deadweight loss Area ABCD -Ź(350-300)(220 –120) 20.5x50x100 2142,500 300 350 teso

Answer 3

Leather Jacket Tan St 160 1806 --- 14 Tan Revenue Area Rect. ACFG 2 (160-60) A (150-0) 100 x 150 278 15,000 Deadweight loss Area AABC . ²x (350-180) (160-60) 2000 loo 819,000) O 150 350 Q Smart phones Tan S &

Smast phones. Star 112 1.o Tan Revenue Rect. ABDE 2(220-120) (300-0) 2100x300 2 $30,0 og Deadweight loss Area ABCD -Ź(350-300)(220 –120) 20.5x50x100 2142,500 300 350 teso

The government should tax more on smartphones as it is a good with relatively less elastic demand and can generate large tax revenue and smaller deadweight loss

Answer 4

Jackets market:

Smartphones market:

S+ tax Price Supply DWL 160 Tax revenue DI il 60 150 350 Quantity

S+ tax Price Supply 220 DWL Tax revenue 120 Ds 300 350 Quantity

If the Government taxes..	Tax revenue ($)	DWL ($)
Jackets	15000	10000
Smartphones	30000	2500

e.g. Smartphones:

Tax revenue = (220 - 120) x 300 = $ 30000

DWL = (220 - 120) x 0.5 x (350 - 300) = $ 2500

The government should tax smartphones because, all else held constant, taxing a good with a relatively less elastic demand generates larger tax revenue and smaller deadweight loss.

Answer 5

(1) Since I cannot access your graph tool, I am labelling the region you need to shade in.

In both graphs, tax revenue is the green rectangular area, and Deadweight loss is area of triangle ABC.

(2)

For Leather jackets, Pre-tax quantity = 350 and After-tax quantity = 150.

For Smartphones, Pre-tax quantity = 350 and After-tax quantity = 300.

Tax revenue = Unit Tax x Quantity after tax

Deadweight loss = (1/2) x Unit Tax x (Pre-tax quantity - After-tax quantity)

Tax @100	Tax revenue ($)	Deadweight loss ($)
Leather jackets	$100 x 150 = $15,000	(1/2) x $100 x (350 - 150) = $50 x 200 = $10,000
Smartphones	$100 x 300 = $30,000	(1/2) x $100 x (350 - 300) = $50 x 50 = $2,500

(3) In this case, government should tax Smartphones because, taxing a good with relatively less elastic demand generates larger tax revenue and smaller deadweight loss.

Answer 6

Ans.

1st Graph for laether jacket market -

Leather Jackets Market 240 220 Supply 200 S+Tax Tax Revenue 180 160 Deadweight Loss 140 PRICE (Dollars per jacket) 120 100 D 80 60 40 20 0 0 50 550 600 100 150 200 250 300 350 400 450 500 QUANTITY (Jackets)

Suppose when the gover taxes smartphones, Graph as follows -

Smartphones Market 240 220 Supply 200 Tax Revenue 180 160 Deadweight Loss 140 PRICE (Dollars per phone) 120 100 80 60 40 20 Ds 0 0 50 100 150 200 250 300 350 400 450 500 550 600 QUANTITY (Phones)

If govt. taxes	TR	D/W loss
Leather jacket at $100	$15000	$10000
Smartphones at $100	$30000	$2500

Working Note -

TR of Leather jacket = 100 x 150 = $15000

D/W loss of leather jacket = 0.5 x 100 x ( 350 - 150 )

                                          = 0.5 x 100 x 200 = $10000

TR of smartphones = 100 x 300 = $30000

D/W loss of smartphones = 0.5 x ( 350 - 300 ) x 100

                                         = 0.5 x 50 x 100 = $2500

Blank 1 = Tax smartphones

Blank 2 = less elastic

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