Let the market for cigarettes be characterized by the following information: Qd
ID: 1220570 • Letter: L
Question
Let the market for cigarettes be characterized by the following information: Qd = 70 - 5P [Demand] Qs = 3P - 10 [Supply] 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
(i) In pre-tax equilibrium, Qd = Qs
70 - 5P = 3P - 10
8P = 80
P = 10
Q = 70 - (5 x 10) = 70 - 50 = 20
From demand curve, when Q = 0, P = 70/5 = 14 (Reservation price)
Consumer surplus (CS) = Area between demand curve & price = (1/2) x (14 - 10) x 20 = (1/2) x 4 x 20 = 40
From supply curve, when Q = 0, P = 10/3 = 3.33
Producer surplus (PS) = Area between supply curve & price = (1/2) x (10 - 3.33) x 20 = (1/2) x 6.67 x 20 = 66.7
(ii) After tax, supply curve shifts left by $2 per unit. New supply curve is:
Qs = 3(P - 2) - 10 = 3P - 6 - 10 = 3P - 16
Equating with Qd,
3P - 16 = 70 - 5P
8P = 86
P = 10.75
Q = (3 x 10.75) - 16 = 32.25 - 16 = 16.25
Tax revenue = $2 x 16.25 = $32.5
(iii)
New CS = (1/2) x (14 - 10.75) x 16.25 = (1/2) x 3.25 x 16.25 = 26.41
Decrease in CS = 40 - 26.41 = 13.59
(iv)
For revised supply curve, when Q = 0, P = 16/3 = 5.33
New PS = (1/2) x (10.75 - 5.33) x 16.25 = (1/2) x 5.42 x 16.25 = 44.04
Decrease in PS = 66.7 - 44.04 = 22.66
(v)
Deadweight loss = (1/2) x Change in price x Change in quantity = (1/2) x (10.75 - 10) x (20 - 16.25)
= (1/2) x 0.75 x 3.75 = 1.41
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