Question

In: Economics

Let the market for cigarettes be characterized by the following information: Qd70-5P Demand] Qs= 3P-10 [Supply]...

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

Solutions

Expert Solution

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


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