Question

A group of college students rent a house in a local neighborhood. They throw frequent rowdy beer-drinking parties and disturb the neighbors. The marginal external cost is a function of the number of cases of beer consumed at the party.

Model the market for beer based on the following supply and demand equations.

• Q_D = 30 - 2P
• Q_S = 2P - 2

Price = dollars per case
Quantity = cases of beer
MEC = $1.50/case

This is a model of a negative externality.

This is a model of an externality in consumption.

What is the value of the market equilibrium quantity? 14 units

What is the value of the socially optimal equilibrium quantity? 5.6 units

Please help with these others 1-7

1. What is the value of the market equilibrium price? $
2. What is the value of the socially optimal equilibrium price? $
3. What is the value of the total surplus for market equilibrium? $
4. What is the value of the total surplus for the socially optimal equilibrium? $
5. What is the difference in total surplus between the market equilibrium and to socially optimal equilibrium? $
6. What is the value of the externality at the market equilibrium? $
7. What is the value of the deadweight loss? $

Answer 1

market equilibrium price, demand = supply
30 - 2P = 2P -2
4P = 32
P = 8
Q = 14

socially optimal equilibrium price, MEC shall be incorporated in supply function
Supply: P = 0.5Qs + 1
Social Supply: P = (1.5+0.5)Qs + 1
30 - 2P = 0.5P - 0.5
2.5P = 30.5
P = 12.2
Q = 5.6

total surplus for market equilibrium
Consumer surplus = (15-8)*14
Producer surplus = (8-1)*14
Total surplus = (15-8)*14+ (8-1)*14 = 196

socially optimal equilibrium
Consumer surplus = (15-12.2)*5.6
Producer surplus = (12.2-1)*5.6
Total surplus = (15-12.2)*5.6+(12.2-1)*5.6 = 78.4

Difference = 196-78.4 = 117.6

Externality at the market equilibrium = 1.5*14 = 21

at Q=14, P = (1.5+0.5)*14 + 1 = 29
Deadweight loss = (29-12.2)*14*0.5 = 117.6

P Social Supply Deadweight loss Private Supply