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

1. This is a model of a Answerpositivenegative externality.
2. This is a model of an externality in Answerproductionconsumption.
3. What is the value of the market equilibrium quantity? Answer
4. What is the value of the socially optimal equilbrium quantity? Answer
5. What is the value of the market equilbrium price? $ Answer
6. What is the value of the socially optimal equilibrium price? $ Answer
7. What is the value of the total surplus for market equilibrium? $ Answer
8. What is the vlaue of the total surplus for the socially optimal equilibrium? $ Answer
9. What is the difference in total surplus between the market equilibrium and to socially optimal equilbrium? $ Answer
10. What is the vlaue of the externality at the market equilbrium? $ Answer
11. What is the vlaue of the deadweight loss? $ Answer

Answer 1

-This is a model of negative externality.

-This is a model of an externality in consumption

At Market Equilibrium QD = QS. This implies

30 - 2P = 2P - 2 which implies 4P = 32 which implies that P = 8

-Substituting the value of P in QD, the value of market equilibrium quantity will be 16 case of beer

- Socially optimal is where P = MC. This means P = $1.5. Plugging this in QD, we get socially optimal equilibrium quantity as 27 cases

-The value of market equilibrium price is $8.

- Socially optimal equilibrium price as shown above is $1.5.

-Total surplus at market equilibrium is = Consumer Surplus at market equilibrium(b) + Producer Surplus at market equilibrium(a)

Producer Surplus at Market Equilibrium = 1/2 *(Price at market equilibrium)*(Quantity/Demand at market equilibrium) = 1/2*8*16 = $64 ...(a)

Consumer Surplus at market equilibrium = 1/2*(Quantity/Demand at market Equilibrium)*((Price when Q=0) - Price at market Equilibrium))

= 1/2*16*(15-8) = 8*7 = $56.....(b)

So total surplus at market equilibrium = (a) + (b) = 64 + 56 = $120

- Similiarily for socially optimal equilibrium, P - $1.5, Corresponding quantity = 27, (P when Q=0) = $15

Plugging these values in equation for Consumer Surplus and Producer Surplus, we get,

Consumer Surplus = 1/2 *27*(15-1.5) = $182.25

Producer Surplus = 1/2*1.5*27 = $20.25

Total surplus at socially optimal equilibrium = $202.50

- Difference in total surplus at the 2 equilibriums = 202.5 - 120 = $82.5