Question

The market for vodka is described as the following: Supply: P = 5 + QS 10 Demand: P = 20− QD 5

However, drinking vodka causes $3 worth of harm per bottle to the rest of society, through health care costs, reduced productivity, and drunken mistakes.

(a) Sketch a graph of this market. Calculate the private equilibrium price, quantity, producer surplus, consumer surplus, total external costs, and total surplus. (Be careful about fractions.) Label the area of deadweight loss on your graph.

(b) Now suppose the government puts in a Pigouvian tax of $3 per bottle onto suppliers to cancel out the harms, so the new supply curve is:

Supply: P = 8 + QS 10

Show this supply shift on your previous graph of the market. Calculate the new social equilibrium, CS and PS (using the new supply curve), external costs and tax revenue, and total surplus. How much did total surplus change?

(c) Tax revenue from Pigouvian tax in theory should be targeted at solving the problems that the externality creates. What can the government spend the tax revenue on to best balance the externality?

Answer 1

a. Private Equilibrium Price and quantity-

5+10Q=20-5Q

15/15=Q

Q*=1

P*= 5+10*1=$15

Consumer surplus=0.5(20-15)(1)= $2.5

Producer surplus=0.5(15-5)(1)=$7.5

Total external cost=0.5(3)(1-0.8)= $0.3

Total surplus=$7.5+$2.5-$0.3= $9.7

b.

New social equilibrium-

8+10Q=20-5Q

12/15=Q

Q**=0.8

P**=8+10*0.8=16

CS=0.5(20-16)(0.8)= $1.6

PS= 0.5(13-5)(0.8)= $3.2

External cost=0 as externality is taken into account.

Government revenue=3*0.8= $2.4

Total surplus= $7.2

Total surplus change= $9.3-$7.2=$2.1

c. Government can spend the tax revenue on awareness campaign to educate people about negative effects of drinking, increase expenditure on health care etc.