Question

Daisy Duck has a monopoly in oil refinement in the local market. The demand for Daisy’s oil is: P = 65 - q.The relevant marginal revenue function is MR(q) = 65 - 2 · q. Her marginal cost function is MC(q) = 8. In the refinement of oil, she emits pollution that has the marginal external cost function: MEC(q) = 2. What level of output will Daisy select to maximize profits? What is the marginal social cost of Daisy’s profit? What is the marginal social cost of Daisy's profit maximizing output? What do consumers pay for Daisy’s refined oil? Is this level of output efficient? If no, what is the efficient level of output? Should the local government charge her a pollution fee for each unit of oil she refines?

Answer 1

To get the profit maximizing level of output,

MR = MC

65-2Q = 8

Q = 57/2 = 28.5 units or 29 units

So, profit maximizing output level will be 28.5 or 29 units.

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Marginal social cost = Marginal private cost + marginal external cost = 8+2 = $10 per unit of output

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Price = 65-28.5 = $36.5

If Q = 29

Then,

Price = 65- 29 = $36

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It is market based efficient output 7 price level, but it is not a socially optimal level of output as only MPC Is considered to produce the profit maximizing output.

For socially optimal level of output,

MR = MSC

65-2Q = 10

55=2Q

Q = 27.5 units. It will give socially optimal equilibrium.

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Yes, she should be charged a pollution fee so that she will consider the MSC and reduce the output and increase the price to achieve the socially optimal outcome.