You are an industry analyst that specializes in an industry where the market inverse demand is P = 150 - 4Q. The external marginal cost of producing the product is MCExternal = 6Q, and the internal cost is MCInternal = 10Q. 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.
Market demand curve is as follows -
P = 150 - 4Q
Derive the total revenue curve -
TR = P * Q = (150 - 4Q) * Q = 150Q - 4Q2
Derive the marginal revenue curve -
MR = dTR/dQ = d(150Q - 4Q2)/dQ = 150 - 8Q
MCsocialcost = MCinternal + MCexternal
MCsocialcost = 10Q + 6Q = 16Q
At socially efficient output level,
MR = MCsocialcost
150 - 8Q = 16Q
24Q = 150
Q = 150/24
Q = 6.25
The socially efficient level of output is 6.25 units.
A competitive industry output is that corresponding to which price equals the marginal cost (internal)
P = MCinternal
150 - 4Q = 10Q
14Q = 150
Q = 150/14
Q = 10.71
The competitive industry produce 10.71 units.
A monopolist produce that level of output corresponding to which marginal revenue equals the marginal cost(internal).
MR = MCinternal
150 - 8Q = 10Q
18Q = 150
Q = 150/18
Q = 8.33 units
A monopolist can produce 8.33 units
The industry is imposing an external cost on society and thus is creating a negative externality.
Negative externality is combated by tax.
Government should impose pollution taxes.
Hence, the correct answer is the option (2) [Pollution taxes].
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