Suppose the market for cigarettes is characterized by the following information:

Question

Suppose the market for cigarettes is characterized by the following information: Suppose the government imposes a sales tax of S2 per unit. Answer questions (i) through (v) below: 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. Suppose the government imposes a price ceiling of $50 on a market characterized by the following information: Calculate the magnitude of deadweight loss from the price ceiling. Find a price floor that will result in the same magnitude of deadweight loss.

Explanation / Answer

Equilibrium = Qd = Qs

70 – 5P = 3P – 10

2P = 80 or P = 40

Quantity = 120 -10 = 110

Consumer Surplus = 0.5* 110(70 – 200) = 0.5*110*130 = 7150

Producers Surplus = 0.5*110*(110)= 6050

Demand Function = 70 – 5P

The new supply function becomes = Qs – 2 = 3P -10 or Qs = 3P – 8

New equilibrium point

70 – 5P = 3P – 8

2P = 62 or P = 31

Quantity Supplied at the point of equilibrium = 3*31 – 8 = 85

Tax revenue = 2 *85 = 170

New consumer surplus = 0.5* 85 *(70 – 155) = 3612.5

New Producer Surplus = 0.5*85 *(85) = 3612.5

0.5* 2 * (85 – 110 ) = 25

2.

Qd = 700 – 2P and Qs = 100 +4P

At equilibrium

700 – 2P = 100 + 4P

= 2P = 600

P = 300

Quantity = 100 + 4 *300

= 100 + 1200 = 1300

At a price ceiling of $50, Quantity Demanded = 700 – 2*50

= 700 – 100

= 600

Magnitude of deadweight loss

0.5*50*(1300- 600)

17500

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