Assume we have a nuclear power plant that discharges higher temperature water ou
ID: 1228243 • Letter: A
Question
Assume we have a nuclear power plant that discharges higher temperature water out of its cooling system into a river. Downstream the river is located a fishery that is negatively affected by the fact that the higher temperature water dumped into the water is affecting negatively aquatic life population, which translates into loss of revenues for the fishery. Note that this power plant is the only power plant in the region and provides electricity for the entire region, therefore, this power plant has a monopoly in producing power. Assume the Market Demand function or curve for power in the region is given by the following equation: Q_D = 60 - P Assume Supply function or Marginal Cost curve of power in the region is given by the following equation: Q_S = 2 P The Marginal Revenue for the power plant when it provides power is given by the following equation: MR = 60 - 2Q The Revenue Loss or (Marginal) External Cost (also called Negative Externality) incurred by the fishery when the power plant discharges higher temperature water out of its cooling system into a river is given by the following equation: MEC = 1/2 Q Answer the following questions: What is the free market equilibrium (that is what is the market equilibrium when the power plant is free to produce electricity regardless of how much pollution it generates)? What are the market equilibrium quantities? What is the market equilibrium price? At the free market equilibrium, how much pollution is being produced (how much revenues the fishery is losing)? When we account for the negative externality or revenue loss incurred by the fishery as a result of the power plant polluting the river, what are the efficient quantities? What is the efficient price of electricity? What is the efficient amount of pollution? How much more pollution is produced when the power plant is free to produce electricity? How much profits does the power plant make when it produces at the free market equilibrium?Explanation / Answer
1. Free market equilibrium is established where
Qd = Qs
60-P= 2P
3P = 60
P = 20
Q = 40 units
equilibrium price is $20 and equilibrium quantity is 40 units
2. 1/2 *40 = 20 units
3. Efficient price is determined where MR = MC
MR = 60-2Q
MC = 1/2Q
60-2Q = 1/2Q
120-4Q = Q
5Q = 120
Q = 24 units
P = $32
4. efficient amount of pollution is 1/2*24 = 12 units
5. 8 more units of polution is produced when power plant is free to produce electricity.