Question

Suppose the market for cigarettes is characterized by the following information: Qd = 70 – 5P [Demand] Qs = 3P – 10 [Supply]

Suppose the government imposes a sales tax of $2 per unit. Calculate the Dead-Weight- Loss due to the sales tax.

[Note: P = price per unit; Qd = thousands of units demanded; Qs = thousands of units supplied]

Answer 1

Qd = 70 -5P

Qs = 3P- 10

At equilibrium : Qd = Qs , we get :

70-5P = 3P- 10

8P= 80

P= 10 (Equilibrium price)

Q = 70-5(10)= 20 (Equilibrium quantity)

When government imposes a sales tax of $2 . Then , Qs = 3(P-2)-10 = 3P- 16

Equate Qd and new Qs, we get:

3P-16= 70-5P

8P= 86

P= 10.75 (Equilibrium price after tax)

Q = 70- 5(10.75)= 16.25 (Equilibrium quantity after tax)

Price sellers receive = (10.75-2) = 8.75

Deadweight loss = (0.5)(10.75-10)(20-16.25) + (0.5)(10-8.75)(20-16.25)

= (0.5)(0.75)(3.75) + (0.5)(1.25)(3.75)

= 1.40625 + 2.34375

= $3.75 (Deadweight loss due to the sales tax)