ECN 345 SPRING 2012
PROBLEM SET 4
Due by end of class on March 15, 2012
1. Missioni sweaters are greatly admired by their aficionados. The demand for these sweaters is given by Q = 13 - 0.02 P, where Q is the quantity of sweaters purchased per person per year, and P is the price of a sweater. These sweaters typically sell at the Missioni store for $500 per sweater. However, in a special promotion, Target decides to offer Missioni sweaters at a price of $50, while limiting purchases to 2 sweaters per person. What is the gain in consumer’s surplus for a Missioni fan who can get these sweaters at Target instead of at the Missioni? Draw the appropriate diagram to illustrate this gain, and also do the numerical calculation.
2. Profits associated with polluting for Friedman Inc. are ? = 40Q - 2Q2, where Q = pollution emitted (in tons), and profits are measured in dollars. Marginal benefits (Marginal profit) from polluting, derived from this function, are M? = 40 - 4Q.
(a) How much pollution do you expect Friedman to produce in the absence of pollution regulation?
(b) The damages (costs) associated with pollution from Friedman are estimated as Damages = D = 3Q2, where damages are measured in dollars. What are the damages (costs) associated with Friedman’s unregulated level of pollution? What are the net benefits at this point?
(c) The marginal damages (costs) associated with that function are MD = 6Q. What is the efficient level of pollution? What are total benefits and costs at the efficient level of pollution? What is the level of net benefits at this point?
(d) What are the marginal benefits and costs at the efficient level of pollution?
(e) Suppose that the damages affect only one person, Samuelson, and Friedman has a clear right to emit as much as it likes. Samuelson and Friedman can negotiate at no cost. With no government regulatory programs, how much do you expect the firm to pollute? Why?
(f) Now suppose the damages affect only Samuelson, who has a clear right to be free of harm from pollution. Samuelson and Friedman can negotiate at no cost. With no government regulatory programs, how much do you expect the firm to pollute? Why?
(g) Suppose the damages affect only Samuelson, who has a clear right to be free of harm from pollution. Now, though, enforcing that right will require Samuelson to spend $500 in legal fees. With no government regulatory programs, how much do you expect Friedman to pollute, and why?
3. A builder proposes a skyscraper that would block sunlight to the neighboring houses. The building would have net benefits to the builder of $100,000. The neighbors, who use some solar heating, would face reduced property values and increased heating costs totaling $80,000.
(a) The law clearly stipulates that the neighbors have the right to solar access. Is a Pareto-improving exchange possible? What do you expect the outcome to be?
(b) How, if at all, would the outcome be different if the builder had the right to construct the skyscraper, even if it blocked solar access?
(c) Suppose again that the neighbors have the rights. Because there is a large number of neighbors, hiring an attorney to negotiate with all of them will be expensive, perhaps as much as $25,000. Is a Pareto-improving exchange possible? What do you expect the outcome to be?
(d) Now suppose that the builder has the rights, and the costs of the lawyer (still $25,000) belong to the neighbors. Is a Pareto-improving exchange possible? What do you expect the outcome to be? Compare this scenario with those of the other parts of this problem. What has led to these different outcomes?
4. About 45 million tons of NOz, a pollutant, are emitted annually in the US by automobiles and electric power plants. The marginal costs of abatement are 0.5Qe for powerplants, where Qe is the amount of NOz in millions of tons abated by powerplants; and 4.5 + 0.1Qa , where Qa is the amount of NOz in millions of tons abated by automobiles.
(a) What are the formulas for the total cost of abatement by powerplants and by automobiles? (Hint: see the formulas given on page 37 of the lecture on Cost Minimization and Conditional Input Demand Functions)
(b) Congress passes legislation requiring that annual emissions of NOz from power plants and automobiles be reduced by a total of 15 million tons. If the goal is to minimize the cost of meeting this target, how much abatement should be undertaken by power plants and how much by automobiles? Explain the rule that generates this answer.
(c) What is the annual total cost of the emission abatement in part (b)?
(d) Following lobbying by the automobile companies, Congress instead decides only to regulate NOz from power plants, and not from automobiles. It requires power plants to reduce their emissions NOz by 15 million tons annually. What is the total cost of emission abatement in this case? How does it differ from the total cost computed in (c), and why?
(e) Following a report by the President’s Council of Economic Advisers, Congress is persuaded to introduce an emissions tax intended to reduce NOz from power plants and automobiles by a total of 15 million tons annually. What is the amount of the tax per ton of NOz emissions that it should set? Explain your answer.
5. Assume an interest rate of 7% in answering the following question.
(a) You would be indifferent between getting $12 now and X dollars two years from now.
What is X?
(b) What is the present value of an asset that pays $20 one year from now, $15 two years
from now, and $45 ten years from now?
(c) What is the formula for the present value of an asset that pays $8 per year every year for
the next 10 years, and nothing thereafter? Use the formula to calculate the present value
of this asset.
(d) What is the formula for the present value of an asset that pays $8 per year forever? Use
the formula to calculate the present value of this asset.