1. Suppose there are 2 firms with the following marginal abatement costs:
MCA = 50 + 2A and MCB = 150 + 2A, where A is units of pollution abated. Assume both
firms are given some number of tradable permits where each permit allows firms to abate 1
less unit of pollution. Suppose the regulator sets each firm’s pollution abatement at 50 units.
Suppose firm A sells 25 permits to firm B at a price of $200 per permit. What is the net gain
to firm A? What is the net gain to firm B?
2. There are two firms that emit pollutant SO2. Currently each emits 150 tons of SO2 per
month. Assume the pollution abatement technology of the two firms can be represented by
MC functions: MCA = 30 + 2QA, MCB = 50 + 4QB (MC is in terms of dollars and Q in terms
of tons of SO2 abated). Suppose the government issues to each firm 100 pollution permits
which allow the firm to emit 100 tons of SO2, and the permits can be traded by these two
firms.
a) Which firm will want to sell permits and which will buy?
b) Eventually how many permits will be traded?
c) What will be the price for the last permit?
d) Eventually how many tons of SO2 will firm A emit? How many tons of SO2 will
firm B emit?
e) How much is the net gain firm A obtains from permit trade? What about firm B?
3. An industry that is characterized by a decreasing cost structure has a demand curve given
by P = 100−Q and the marginal revenue curve by MR = 100−2Q. The marginal cost is MC
= 4, and average cost is AC = 4+188/Q.
(a) Graph this cost and demand structure.
(b) Calculate the efficient output and the monopoly output for the industry.
(c) What price would the monopolist charge if he were unregulated, and what would be his
profit per unit?
(d) What price and output would emerge if the supplier were regulated so that his allowable
price equalled average cost? Compute the value of the deadweight loss associated with
having an unregulated monopoly relative to having a regulated monopoly where a price is
permitted that covers ATC.
(e) As an alternative to regulating the supplier such that price covers average total cost,
suppose that a two-part tariff were used to generate revenue. This scheme involves charging
the MC for each unit that is purchased and in addition charging each buyer in the market a
fixed cost that is independent of the amount he purchases. If an efficient output is supplied
in the market, estimate the total revenue to be obtained from the component covering a
price per unit of the good supplied, and the component covering fixed cost.
4. An economy is composed of two individuals, whose demands for a public good –
street lighting – are given by P = 12−(1/2)Q and P = 8−(1/3)Q.
(a) Graph these demands on a diagram.
(b) Derive the total demand for this public good by summing the demands vertically, and
write down a resulting equation for this demand curve.
(c) Let the marginal cost of providing the good be $5 per unit. Find the efficient supply of
the public good in this economy – where the marginal cost equals the total value of a
marginal unit.
5. Tracey and Justin are the two residents of an island. They use the surrounding waters to
fish. Because the waters are sometimes rough and they often return to the island after dark,
they desire to build a lighthouse to light their way home at night. The two persons have
different demands for lighthouse and their demands are given by the following:
Tracey: Qd = 20 – P
Justin: Qd = 20 – 2P
The marginal cost of providing the lighthouse is MC = Q, where Q represents the intensity
of the lighthouse beacon.
a) What is the optimal amount of lighthouse to be provided?
b) What is the total price paid to provide this lighthouse?
c) Of this price, how much will be paid by Tracey?
d) Will this optimal amount of the public good necessarily be provided by the residents of
the island? Explain your reasoning.
6. “Everybody’s business is nobody’s business.” How is this proverb related to economics
that you have learned from this course? Briefly explain.
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