Please show steps with work! Mr. Barnes has a monopoly in the production of powe
ID: 1206172 • Letter: P
Question
Please show steps with work!
Mr. Barnes has a monopoly in the production of power in the local market. The demand for Mr. Barnes power is: P = 100 - 0.25q MR(q) = 100 - 0.5q. Mr. Barnes marginal costs are constant at 5. In the generation of power, Mr. Barnes plant emits pollution that causes marginal external damages according to: MEC(q) = 0.05q. If the local government does nothing, how much will Mr. Barnes produce to maximize profits? What is the marginal social cost of his level of output? What price do consumers pay for each unit of Mr. Barnes' output? Is this level of production optimal? Should the local government institute a pollution fee? If so, what is the optimal fee?
Explanation / Answer
(1) If government does nothing, equilibrium is obtained by equating MR with MC:
100 - 0.5q = 5
0.5q = 95
q = 190
(2) When q = 190, MEC = 0.05q = 0.05 x 190 = 9.5
So, marginal social cost (MSC) = MC + MEC = 5 + 9.5 = 14.5
(3) When q = 190,
P = 100 - 0.25q = 100 - (0.25 x 190) = 100 - 47.5 = 52.5
(4) This production level is not optimal because external cost is ignored in absence of government intervention.
(5) A pollution fee will lower quantity produced and reduce inefficiency. It should be equal to the price under private equilibrium and price under social equilibrium.
Social equilibrium is achieved by equating MR with MSC:
100 - 0.5q = 5 + 0.05q
0.55q = 95
q = 172.73
P = 100 - (0.25 x 172.73) = 100 - 43.18 = 56.82
So, optimal fee = 56.82 - 52.5 = 4.32