Question 4. (Adapted from Gruber textbook, Ch.5 Q18) Suppose that the (private)
ID: 1142254 • Letter: Q
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Question 4. (Adapted from Gruber textbook, Ch.5 Q18) Suppose that the (private) cost and benefit of aluminum production is given by MC 100+2Q and MB 900-2Q. Also suppose that aluminum production emits pollution and the marginal damage this pollution causes to the society is MD = 300 + 5Q (hence the social marginal cost is the private marginal cost plus the marginal damage of pollution) (1) What is the socially efficient quantity? (2) Suppose the (private) benefit of aluminum production, MB 900-2Q, is private information to the factory, and the best information the government has is that MBG 1000-2Q. If the government imposes a (per-unit) tax St based on this wrong information, what would t be? What quantity would such a tax actually induce? (3) Again assume the government believes that MBG 1000-2Q. If the government sets a limit in quantity directly by regulation, what would be the quantity? (4) Which gives better results, taxation or regulation? What would your answer be if the marginal damage of pollution were 300 +3Q (instead of 300+ 5Q), everything else the same?Explanation / Answer
1) Socially efficient quantity is one where marginal social cost (MSC) = marginal social benefit (MSB)
MSC = MC + MD
MSC = 100 + 2Q + 300 +5Q
MSC = 400 + 7Q
Let Q* be the socially efficient quantity. Then, MSC = MB
400 + 7Q* = 900 - 2Q*
9Q* = 500
Q* = 55.5 units
2) The tax to be levied is equal to the differenct between marginal private cost and marginal social cost at the effiecient level of output. However, since government considers the marginal benefit to be different from that considered by the firm, the efficient level of output for the government will be:
400 + 7Q = 1000 - 2Q
9Q = 600
Q = 66.6
The tax will be equal to the marginal damage at 66.6 units of output i.e.
MD (Q = 55.5) = 300 + 5 (66.6) = 633.3
Therefore. the tax will be $ 633.3 per unit
3) As calculated in part 2), if government sets regulation on quantity it will set the maximum production quantity to be 66.6 units
4) Both taxation and regulation provides similar results. If marginal damage is 300 + 3Q, the socially optimal quantity will be
100 + 2Q +300 + 3Q = 1000 - 2Q
7Q = 600
Q = 85.7
Tax will be, 300 + 3 (85.7) = $557.14
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