Question

Exercise 2: Externality

Consider two oil refineries that both produce fuel, which has a market price of $3 per gallon. Assume that each refinery uses $1 in raw inputs (crude oil, electricity, labor) to produce 1 gallon of fuel. In addition, each plant produces smog, which creates $0.02 of environmental damage per cubic foot. The amount of smog per gallon of fuel produced differs at the two plants:

s1= 2y²₁ and s2=(1/4)y²₂

where y1 and y2 denote the number of gallons of fuel produced at each plant, and s1 and s2 denote the amount of smog generated. Plant 2 pollutes much less than plant 1 fora given production. Assume each plant can produce only up to 200 gallons.

(a)  Set up the problem for each plant, and determine production, pollution (smog) and damage when there is no policy.

(b)  Set up the problem for each plant, and determine production, pollution (smog) and damage that maximizes welfare.  (Hint: To solve it, imagine that each plant faces private costs plus the social costs of production).

(c)  Imagine that a Pigouvian tax (of $0.02 per unit of smog) is imposed on the plants. If you were to determine production, pollution (smog) and damage again, how does your answer compare to part (b)? Why?

Answer 1

Answer: According to (b) part both the plant faces private costs plus the social costs of production. So first we need to understand both the costs.

I) Private costs.

II) Social costs.

I) Private costs:- It means that costs which we have to spend on our personal use like petrol and buying car.

II) Social costs:- Social cost is the total cost to society it includes both private and external costs.

Note:- If social cost is greater than private cost so it is a negative externalities.

In general social costs is more than private costs. When it will happen that personal cost less than social costs. When a person have a luxurious life style.

At the end we can say that the oil refineries will maximize its profit but not maximize welfare. It means it is a negative externality.