Question

Suppose that a market is described by the following supply and demaod equations: QD 240-P Suppose that a tax of T is placed o
Use the green points (triangle symbol) to graph tax revenue for the following tax (T) values: 0, 30, 90, 120, 150, 210, and 2
The followinig graph shows the old and new equilibrium information and how the deadweight loss of a tax is the area of the tr
Recall that the area of a triangle is x Base x Height. According to this graph, the base of the deadweight loss triangle is ,
2 Deadweight Loss (Thousands of dollars)
The government now levies a tax on this good of $140 per unit. Which of the following statements are true? Check all that app
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Answer #1

The after-tax quantity is given to be Q = 160-2T/3 . For the given values of taxes, we have the table as below.

T Q 160-27/3 TR = QT
0 160 0
30 140 4200
90 100 9000
120 80 9600
150 60 9000
210 20 4200
240 0 0

The graph would be as below.

TR 10000 5000 100 200

According to the graph, the base of the DWL triangle is T, and the height is 2T/3.

The reason being that, the base of the triangle is the difference between the price charged to customers and the price received by the producers, which is T. Also, the height of the triangle would be 160-(160-2T/3) = 2T/3 .

The DWL would be \frac{1}{2}*T*2T/3 = T^2/3 . The table would be as below.

T DWL
0 0
60 1200
120 4800
180 10800
240 19200

The graph would be as below.

20000 15000 10000 5000 50 100 150 200

The correct options would be

  • The government could decrease the dead-weight loss by reducing the tax.
  • The government could increase tax revenue by reducing the tax to $120.

As can be seen in the second graph, the DWL increases as T increases, and reducing the tax T would reduce the DWL. Also, in the first graph, the curve is maximum at T=$120, and reducing tax to that would definitely increase tax-revenue in compare to T=$140. After $120, for each next tax, the tax revenue decreases. Hence, tax revenue at T=$140 would be definitely more than tax revenue at T=$240.

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