Suppose the market for cigarettes is characterized by the following information:
ID: 1199387 • Letter: S
Question
Suppose the market for cigarettes is characterized by the following information:
Qd = 70 – 5P [Demand] Qs = 3P – 10 [Supply]
[Note: P = price per unit; Qd = thousands of units demanded; Qs = thousands of units supplied]
Suppose the government imposes a sales tax of $2 per unit.
Answer questions (i) through (v) below:
i) Calculate the magnitude of the consumer surplus and producer surplus in the pre-tax equilibrium.
ii) Calculate the tax revenue in the post-tax equilibrium.
iii) Calculate the change in consumer surplus due to the sales tax.
iv) Calculate the change in producer surplus due to the sales tax.
v) Calculate the Dead-Weight-Loss due to the sales tax.
Explanation / Answer
QS = 3P-10
IN EQ, 70-5P=3P-10 OR 8P=80
THUS, P=10
Q=70-50=20
QD = 70-5P
WHEN Q=0, P=14
THUS, CONSUMER SURPLUS = ½ * (14-10) * 20= 40
QS = 3P-10
WHEN Q=0, P=3.33
THUS, PRODUCER SURPLUS = ½ * (10-3.33) * 20= 6.67 *10 = 66.7
2. After imposing sales tax of $2, New supply eq , QS’ = 3(P-2)-10= 3P-16
IN EQ, 70-5P=3P-16 OR 8P=86
THUS, P=10.75
Q= 70-5(10.75) = 16.25
TAX REVENUE = Q*TAX = 16.25*2=32.5
3. WHEN Q=0, P=14
THUS, NEW CONSUMER SURPLUS = ½ * (14-10.75) * 20= 3.25*10 =32.5
Change = 40-32.5 = 7.5
4. QS’ = 3P-16
WHEN Q=0, P=5.33
THUS, NEW PRODUCER SURPLUS = ½ * (10.75-5.33) * 20= 5.42 *10 = 54.2
Change = 66.7-54.2 = 12.5
5. Deadweight loss = ½ * Change in Quantity after tax * Tax = ½ * 2* (20-16.25) = 3.75
QS = 3P-10
IN EQ, 70-5P=3P-10 OR 8P=80
THUS, P=10
Q=70-50=20
QD = 70-5P
WHEN Q=0, P=14
THUS, CONSUMER SURPLUS = ½ * (14-10) * 20= 40
QS = 3P-10
WHEN Q=0, P=3.33
THUS, PRODUCER SURPLUS = ½ * (10-3.33) * 20= 6.67 *10 = 66.7
IN EQ, 70-5P=3P-16 OR 8P=86
THUS, P=10.75
Q= 70-5(10.75) = 16.25
TAX REVENUE = Q*TAX = 16.25*2=32.5
THUS, NEW CONSUMER SURPLUS = ½ * (14-10.75) * 20= 3.25*10 =32.5
Change = 40-32.5 = 7.5
WHEN Q=0, P=5.33
THUS, NEW PRODUCER SURPLUS = ½ * (10.75-5.33) * 20= 5.42 *10 = 54.2
Change = 66.7-54.2 = 12.5
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