Question

Question 2. Let the market for Wizzas be characterized by the following information:

Q = 70 – 5P [Demand]

Q = 3P – 10 [Supply]

where P is price per serving (Q) of Wizza.

Suppose the government imposes a sales tax of $2 per serving of Wizza. 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 deadweight loss due to the sales tax.

Answer 1

(i) Before tax, equilibrium is obtained byy equating demand and supply.

70 - 5P = 3P - 10

8P = 80

P = $10

Q = 70 - (5 x 10) = 70 - 50 = 20

From demand function, when Q = 0, P = 70/5 = $14 (Reservation price)

Consumer surplus (CS) = Area between demand curve & market price = (1/2) x $(14 - 10) x 20 = 10 x $4 = $40

From supply function, when Q = 0, P= $10/3 = $3.33 (Minimum price)

Producer surplus (PS) = Area between supply curve & market price = (1/2) x $(10 - 3.33) x 20 = 10 x $6.67 = $66.67

(ii) After tax, supply curve shifts leftward by $2 per unit and new supply function becomes

Q = 3(P - 2) - 10 = 3P - 6 - 10 = 3P - 16

Equating with demand,

70 - 5P = 3P - 16

8P = 86

P = $10.75 (Price paid by buyers)

Price received by sellers = $10.75 - $2 = $8.75

Q = 70 - (5 x 10.75) = 70 - 53.75 = 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) New PS = (1/2) x $(8.75 - 3.33) x 16.25 = (1/2) x $5.42 x 16.25 = $44.04

Decrease in PS ($) = 66.67 - 44.04 = 22.63

(v) Deadweight loss ($) = (1/2) x Unit tax x Change in quantity = (1/2) x $2 x (20 - 16.25) = $1 x 3.75 = $3.75