In: Economics
Let the market for cigarettes be characterized by the following information: Qd70-5P Demand] Qs= 3P-10 [Supply] Suppose the government imposes a sales tax of S1.50 per unit. Answer questions (i) through (v) below: i) [10 points] Calculate the magnitude of the consumer surplus and producer surplus in the pre-tax equilibrium Calculate the tax revenue in the post-tax equilibrium. Calculate the change in consumer surplus due to the sales tax. Calculate the change in producer surplus due to the sales tax. Calculate the Dead-Weight-Loss due to the sales tax. ii) [10 points) iii) [10 points] iv) [10 points] v) [10 points
Type the answers to be clear
Qd = 70 - 5P
Qs = 3P - 10
Qd = Qs
70 - 5P = 3P - 10
70 + 10 = 3P + 5P
80 = 8P
P = 10
Q = 70 - 5(10)
= 70 - 50
= 20
CS = 1/2(14 -10)(20)
= 1/2(4)(20)
= 40
PS = 1/2(10 - 10/3)20
= 1/2(20/3)(20)
= 200/3 = 66.67
AFTER TAX
Qd = 70 - 5(P +t)
= 70 - 5(P + 1.50)
= 70 - 5P - 7.5
= 62.5 - 5P
Qd = Qs
62.5 - 5P = 3P - 10
62.5 + 10 = 3P + 5P
72.5 = 8P
P = 72.5/8
= 9.06
So price received by seller Ps = 9.06
price paid by buyer Pb = Ps + t
= 9.06 + 1.5
= 10.56
Equilibrium quantity after tax Q = 3(9.06) - 10
= 27.18 - 10
= 17.18
TAX REVENUE(TR) = (10.65 - 9.06)17.18
= 25.77
CS = 1/2(14 - 10.56)17.18
= 29,54
PS = 1/2(9.06 - 10/3)17.18
= 49.19
Change in CS = 29.54 - 40 = - 10.46
So CS decreases by 10.46
Change in PS = 49.19 - 66.67 = - 17.48
so PS falls by 17.48
DWL = 1/2(10.56 - 9.06)(20 - 17.18)
= 1/2(1.5)(2.82)
= 2.11