Question

The supply curve in the market for vodka is Q = 0 if P < 4, Q = any value if P = 4, and Q =∞ if P > 4. The demand curve is Q = 12 - P if P≤12 and 0 otherwise. Answer the following

questions, showing your work. Illustrate using diagrams.

(a) What are the equilibrium consumer surplus and producer surplus?

(b) Now change the situation by supposing that each unit of vodka sold inflicts an average

negative externality of 2 on people who have to deal with vodka drinkers. What is the total

social surplus? What is the surplus-maximizing quantity? What is the DWL at the equilibrium

quantity?

(c) Suppose next that there is an externality of 2, but the government also imposes a price floor

of 5. What is the total surplus? Is it higher than in (b)?

(d) Finally, suppose that there is an externality of 2, but the government can impose a tax on

sellers of vodka. What is the optimal amount of tax? What are the consumer surplus and

producer surplus? What is the total surplus? Is it higher than in (c)?

Answer 1

The supply curve is horizontally straight line at=4,

The property of perfect elastic supply curve; as we decrease price from p=4 leads to QUANTITY supplied to zero. And Increase leads to QUANTITY supplied infinite.

You can think as , producer have a constant 4 $ Marginal cost.so Marginal cost curve and supply curve will be horizontal at p/MC=4

So equilibrium will be at p*=4

Equilibrium quantity=12-4=8

CONSUMER surplus=1/2*8*(12-4)=64/2=32

Producer surplus=1/2*8*(4-4)=0

B) negitive externalities cost=2*unit sold=2*8=16

Social surplus=32-16=16

Social marginal cost=private marginal cost+external cost=4+2=6

EQUILIBRIUM ,

P*=6

Q*=12-6=6

CONSUMER surplus/social surplus=1/2*6*(12-6)=36/2=18

Deadweight loss =social surplus at social optimal Quantity- social surplus at private optimal QUANTITY=18-16=2

C)at p=5, QUANTITY demanded=12-5=7

CONSUMER surplus/private surplus=1/2*7*(12-5)=49/2=24.5

Total surplus/ social surplus=private surplus- external cost=24.5-2*7=24 .5-14=10.5

Total surplus without price floor=16

So total surplus is lower with government price floor at p=5.

D) the optimal tax per vodka should equal to external cost of vodka=2

With 2$ tax new Marginal cost to seller is 6$

So equilibrium price=6

Equilibrium quantity=12-6=6

CONSUMER surplus=1/2*6*(12-6)=36)2=18

Producer surplus=1/2*6*(6-6)=0

Total surplus=18+0=18

Total surplus with price floor at p=5 was 10.5

So it is higher than c).