This question is in 11 parts. Assume we have a nuclear power plant that discharg
ID: 1228203 • Letter: T
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This question is in 11 parts. 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 = 2P 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 You are strongly encouraged to draw a graph to help you answer the 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?Explanation / Answer
1) Free market equilibrium for a monopoly is arrived when it produces profit maximizing level of output. This is done by equation MR and MC. MC is given as Q = 2P which implies P = Q/2
MR = MC
60 - 2Q = Q/2
60 = 5Q/2
Q* = 24 units
Profit maximizing price can be found by placing Q* = 24 in the demand function
24 = 60 - P
P = $36 per unit.
Free market equilibrium price is $36 per unit and quantity is 24 units.
2) Revenue loss function is given as MEC = 1/2Q = 12 units. The worth of this loss is 12*36 = $432
3) When the externality is ineternalized, the monopolist will produce an output level where MR will equal to Social Marginal cost SMC. SMC is the sum of private MC and External MC.
MR = (MC + MEC)
60 - 2Q = (Q/2 + Q/2)
60 = 3Q
Q = 20 units.
This is the efficient quantity after internalization of costs. To get the price, plug in this value in the demand function,
P = 60 - 20 = 40
Hence efficient price is $40 and quantity is 20 units.
4) Efficient amount of pollution is Q/2 or 10 units which is worth 10*40 = $400.
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