Suppose the market for cigarettes is characterized by the following information:
ID: 1199492 • 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.
B. [25 points] Suppose the government imposes a price ceiling of $50 on a market characterized
by the following information:
Qd = 700 - 2P Qs = 100 + 4P
[Note: P = price per unit; Qd = hundreds of units demanded; Qs = hundreds of units supplied]
Calculate the magnitude of deadweight loss from the price ceiling. Find a price floor that will
result in the same magnitude of deadweight loss.
Explanation / Answer
The reference figure is given at the end of this solution.
(i) Calculate the price level at which the quantity supplied equals the quantity demanded as follows:
Quantity demanded = quantity supplied
70 – 5P = 3P – 10
8P = 80
P = 10
So the equilibrium price is 10, at this price quantity (supplied and demanded) is
Q = 70 – 5(10)
= 20
Consumer surplus = area enclosed in the region BCE
= ½ (14 – 10) (20 – 0)
= $40
Producer surplus = area enclosed in the region ACE
= ½ (10 – 10/3) (20 – 0)
= $66.67
(ii)
In the United States, sales tax is generally imposed on sellers. When a per-unit tax is imposed on sellers, then the supply curve shifts upwards by the per-unit tax amount. So the new supply curve is
Q = 3(P – 2) – 10
Q = 3P – 6 – 10
Q = 3P – 16
Calculate the price level now at which the quantity supplied equals the quantity demanded as follows:
Quantity demanded = quantity supplied
70 – 5P = 3P – 16
8P = 86
P = 10.75
So the new equilibrium price is 10, at this price quantity (supplied and demanded) is
Q = 70 – 5(10.75)
= 16.25
The price paid by sellers is $10.75, and the price received after deduction of $2 tax is $8.75.
Tax revenue = $2 × Quantity sold = $2(16.25) = $32.50
(iii)
New consumer surplus = area enclosed in the region BHG
= ½ (14 – 10.75) (16.25 – 0)
= $26.41
Change in consumer surplus = $40 - $26.41= $13.59
(iv)
New producer surplus = area enclosed in the region AIF
= ½ (8.75 – 3.33) (16.25 – 0)
= $44.01
Change in consumer surplus = $66.67 - $44.01= $22.66
(v)
Change in total surplus = New CS + New PS + Tax revenue – (Old CS + Old PS)
= $26.41 + $44.01 + $32.50 – ($40 + $66.67)
= – $3.75
So the deadweight loss is $3.75.
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