Question

You are an industry analyst that specializes in an industry where the market inverse demand is P = 300 - 5Q. The external marginal cost of producing the product is MC_External = 8Q, and the internal cost is MC_Internal = 14Q.

Instructions: Enter your responses rounded to the nearest two decimal places.

a. What is the socially efficient level of output?

units


b. Given these costs and market demand, how much output would a competitive industry produce?

units


c. Given these costs and market demand, how much output would a monopolist produce?

units


d. Which of the following are actions the government could take to induce firms in this industry to produce the socially efficient level of output.

Instructions:  In order to receive full credit, you must make a selection for each option. For correct answer(s), click the box once to place a check mark. For incorrect answer(s), click twice to empty the box.

• Pollution permits unanswered (leave checked or unchecked)
• Non-rival consumption unanswered (leave checked or unchecked)
• Pollution taxes unanswered (leave checked or unchecked)

Answer 1

a. Socially efficient level of output is where the marginal social benefit is equal to the marginal social cost. The marginal social benefit is nothing but the demand, while the marginal social cost is the summation of the marginal private cost and marginal external cost. Thus the marginal social cost= 8Q+14Q=22Q

Setting it equal to demand gives us: 22Q=300-5Q

27Q=300

Q=11.1 or 11

b. A competitive firm sets its price equal to its marginal cost. Hence we have 300-5Q=14Q

19Q=300 which gives Q=15.7

c. A monopolist sets its price where the marginal revenue is equal to the marginal cost of production. The marginal revenue is the derivative of total revenue with respect to its quantity.

Total revenue= Price * quantity= (300-5Q)Q=300Q-5Q^2

Marginal revenue= 300-10Q

Setting it equal to the marginal cost gives: 300-10Q=14Q

24Q=300

Q=12.5

d. Note that since the firms are only considering their private cost, hence they are producing more than the socially efficient level, hence the government must incentivize these producers to produce less. Pollution permits work when the pollution units are set. Non-rival consumption does not affect production. it is the pollution tax which the government can levy on the units the firms are producing and hence their private cost will increase which will cause them to reduce their production level. Hence pollution tax is the correct answer.