Dust, Cement and the Price of Clean Air
A cement plant is the largest private employer in a town of 40,000 people. It produces 500,000 tonnes a year and sells at N$1,000 a tonne. Its private marginal cost is constant at N$700 a tonne. Independent consultants put the marginal external cost at N$350 a tonne, arising from respiratory illness, dust on crops and cleaning costs for households downwind. Demand is such that every N$10 rise in the price of cement reduces quantity demanded by 10,000 tonnes a year. The plant says the estimate is exaggerated and that a levy would force it to cut shifts. The environment ministry proposes either a Pigouvian tax per tonne or an auctioned cap-and-trade scheme limiting the town's cement output to the socially efficient level. Abatement engineers say the cost of reducing dust per tonne varies from N$150 to N$600, depending on whether filters are upgraded or the kiln is run more slowly.
1. Explain why output of 500,000 tonnes is not allocatively efficient, and calculate the deadweight loss assuming marginal external cost is constant at N$350 a tonne.
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Allocative efficiency requires marginal social benefit to equal marginal social cost. The price is a measure of marginal social benefit, assuming no other distortions. Marginal social cost is private marginal cost plus marginal external cost: 700 + 350 = N$1,050 a tonne.
At 500,000 tonnes the price is N$1,000, which is below MSC of N$1,050. The last tonnes cost society more than consumers value them, so too much cement is produced and too much dust is emitted. The gap at the margin is N$50 a tonne.
To find the efficient output, the price must rise until it equals MSC, that is by N$50. Demand falls by 10,000 tonnes for every N$10, so a N$50 rise reduces quantity by 50,000 tonnes, to 450,000 tonnes. The efficient outcome is therefore N$1,050 and 450,000 tonnes.
The deadweight loss is the triangle between MSC and demand over the excess output: 1/2 x 50,000 x 50 = N$1.25m a year. This is small relative to turnover of N$500m, but that is because the marginal gap is only N$50; the inframarginal external cost borne by residents is much larger. A small deadweight loss does not mean the pollution is unimportant, only that the last units are not greatly overproduced at this constant-cost assumption.
2. Calculate the Pigouvian tax that would achieve the efficient output and the revenue it raises, and explain how the plant is likely to respond.
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The tax per tonne should equal marginal external cost at the efficient output, N$350. This raises the firm's private marginal cost from N$700 to N$1,050, which is exactly MSC. Facing a market price of N$1,050, the firm supplies 450,000 tonnes, which is the efficient quantity.
Tax revenue is 350 x 450,000 = N$157.5m a year.
The plant has two margins of response. It can cut output by 50,000 tonnes, or it can abate emissions and pay tax only on residual dust. Because abatement costs range from N$150 to N$600 a tonne, the firm will adopt measures costing less than N$350 and pay the tax on the rest. This is the strength of a tax: it directs abatement to the cheapest options and equalises marginal abatement cost with the tax across sources. If filters cost N$200 a tonne of dust removed, installing them is cheaper than paying N$350.
The tax also has costs. It raises the local price of cement by up to N$50, which may encourage imports from plants with weaker standards, shifting output and emissions elsewhere (leakage) and threatening local jobs. Revenue of N$157.5m could fund a health clinic, monitoring or compensation, but compensation does not itself reduce emissions. The plant may also argue that the N$350 figure is uncertain, so the tax should be reviewed as monitoring data improve.
3. Evaluate whether an auctioned cap-and-trade scheme would be a better instrument than the tax in this town.
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The choice depends on whether it is more important to control quantity or cost, and on how steeply damage and abatement costs rise.
A cap at 450,000 tonnes guarantees the emissions quantity. If damage rises sharply above a health threshold, quantity certainty is valuable and permits are superior. A tax fixes the marginal cost facing the firm; if abatement turns out to cost N$600 a tonne rather than N$150, output may fall much more than expected, with larger job losses, or if abatement is cheap, emissions may fall less than expected because the tax is too low.
But this is a single major source in a small town, so a permit market would be thin. With only one buyer, an auction is effectively a licence fee set by the cap and the firm's demand; the permit price would be volatile and could be manipulated. Monitoring, verification and enforcement costs are similar to a tax, but market design is more complex. Free allocation would soften the employment blow and reduce leakage, but it creates windfall gains and weakens the polluter-pays principle; auctioning raises revenue but may accelerate closure.
A workable compromise is a cap with free initial allocation plus a ring-fenced health fund, reviewed annually, because the health threshold makes quantity certainty valuable. A tax is simpler and more predictable and is preferable if damage is roughly linear. Judgement: the case for permits is strongest where damage is steep and monitoring is credible; in a one-plant town, administrative simplicity and predictable cost may make the tax the safer instrument.