An oil refinery operating on the bank of a river releases pollutants into the ri
ID: 1189298 • Letter: A
Question
An oil refinery operating on the bank of a river releases pollutants into the river which contaminates the water downstream and, as a consequence, the residents of a community located downstream have to purify the water to serve their daily needs. For every litre of oil refined the cost of decontamination goes up by $12 for the community. Suppose that the supply curve of the refinery is given by the formula Q = 2P (or, equivalently, P = 12 Q) and the demand curve for the oil refinery’s product is given by the formula Q = 1200 – 10P (or, equivalently, P = 120 – (1/10) Q), and assume that both producer and consumers are competitive price takers.
a) In equilibrium, how much would be produced and at what price?
b) At the social optimum, where the social supply curve is Q = -24 + 2P (or equivalently, P = (1/2) Q +12), what would be the quantity produced and price?
c) In a diagram, show what would be the efficiency loss to society as a whole at the equilibrium compared to the social optimum and explain why.
Explanation / Answer
a.
Calculate equilibrium price and quantity-
Given that Qs = 2P and Qd = 1200-10P
At equilibrium conditions,
Qs = Qd
2P = 1200 -10P
P= 100
Q= 2*100 = 200
Hence, equilibrium price = $100 and equilibrium quantity = 200 units.
b.
Qs = Qd
-24 +2p = 1200-10P
P= 1224/12
P = $102
And Q = -24 + 2*100 = 176 units
c.
Efficiency loss = 0.5*( price difference)(quantity difference)
= 0.5(102-100)(200-176) =24