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 $2.50 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.

ii) [10 points] Calculate the tax revenue in the post-tax equilibrium.

iii) [10 points] Calculate the change in consumer surplus due to the sales tax.

iv) [10 points] Calculate the change in producer surplus due to the sales tax.

v) [10 points] Calculate the Dead-Weight-Loss due to the sales tax.

Be very complete in every answer with explaining Dead-Weight-Loss with steps with every question show the complete work and it should be perfect

Answer 1

Demand function is Qd = 70 – 5P and supply function is Qs = 3P – 10

Before tax, the market equilibrium has Qd = Qs

70 – 5P = 3P – 10

80 = 8P

P = 80/8 = $10

Qd = Qs = 70 – 10*5 = 3*10 – 10 = 20 units

Consumer surplus = 0.5*(max price – price consumers pay)*quantity purchased = 0.5*(70/5 – 10)*20 = $40

Producer surplus = 0.5*(price producers receive – minimum price)*quantity sold = 0.5*(10 – 10/3)*20 = 66.67.

After the tax is imposed, the supply is Qs* = 3(P – 2.50) – 10 or Qs* = 3P – 17.50

New equilibrium has Qd = Qs*

70 – 5P = 3P – 17.50

87.50 = 8P

P = 87.50/8 = $10.9375 (that buyers pay)

P* = 10.9375 – 2.50 = $8.4375 (that sellers receive)

Q* = 3*8.4375 – 10 = 15.3125 units

New consumer surplus = 0.5*(70/5 - 10.9375)*15.3125 = $23.44727

New producer surplus = 0.5*(8.4375 – 10/3)*15.3125 = $39.07878

Deadweight loss = 0.5*tax rate*reduction in quantity = 0.5*2.5*(20 - 15.3125) = 5.859375

Tax revenue = tax rate*quantity sold = 2.5*15.3125 = $38.28125

i) Consumer surplus and producer surplus in the pre-tax equilibrium

Consumer surplus = $40

Producer surplus = 66.67.

ii) Calculate the tax revenue in the post-tax equilibrium.

Tax revenue = $38.28125

iii) Calculate the change in consumer surplus due to the sales tax.

Change in CS = 40 - 23.44727 = $16.55273

iv) Calculate the change in producer surplus due to the sales tax.

Change in PS = 66.67 - 39.07878 = 27.59122

v) Calculate the Dead-Weight-Loss due to the sales tax.

Deadweight loss = $5.859375