The Fertilizer Plant and the Downstream Fishery
A fertilizer plant discharges runoff into a river. The plant's profit is $2,000,000 per year. The runoff reduces the catch of a downstream fishery, cutting its profit by $600,000 per year. The plant could install a treatment system costing $350,000 per year that would eliminate the damage entirely. Alternatively, the fishery could build a water-filtration system for $500,000 per year that would restore its catch. A regulator is considering a Pigouvian tax, a liability rule making the plant pay for measured damage, or simply assigning clear property rights to one party and letting them bargain. Transaction costs of bargaining are estimated at $50,000.
1. Identify the efficient outcome and compare the three policy instruments in terms of whether they reach it.
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The efficient outcome minimizes total cost. Options: plant does nothing → $600,000 fishery damage; plant treats → $350,000; fishery filters → $500,000. The cheapest is treatment at $350,000, so efficiency requires the plant to install treatment (or an equivalent burden of $350,000 or less).
- Pigouvian tax: set at marginal external damage. If the tax is set at $600,000/year (the damage), the plant prefers treatment ($350,000) to paying $600,000, so it treats. Efficient, provided the regulator knows the damage. If the tax is set too low, the plant pollutes.
- Liability rule: the plant pays measured damage of $600,000, so it again prefers treatment at $350,000. Efficient, but requires measuring damage accurately and enforcing payment.
- Property rights + bargaining (Coase): if the fishery has the right to clean water, it can demand the plant stop; the plant will pay up to $600,000 to be allowed to pollute but will instead treat for $350,000, so treatment results. If the plant has the right to pollute, the fishery will pay up to $600,000 to stop it; the plant will accept any payment above $350,000, so treatment again results - provided bargaining costs ($50,000) are small relative to the $250,000 gap between treatment and damage. They are, so Coase holds either way. The distribution of who pays differs, but efficiency does not.
2. Suppose the regulator sets the Pigouvian tax at $200,000 per year. Predict the plant's behavior and the welfare loss, and explain why the tax level matters more than the instrument label.
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At a $200,000 tax, the plant compares paying $200,000 to treating for $350,000. It pollutes and pays the tax, saving $150,000 privately. But the fishery still bears $600,000 in damage, and the tax revenue is a transfer, not a benefit. Social cost = $200,000 tax (transfer) + $600,000 damage = $600,000 real resource loss, versus $350,000 under treatment. The deadweight loss is $250,000 per year (the difference between damage and treatment cost).
The lesson: a tax only changes behavior if it exceeds the abatement cost. The instrument label ('Pigouvian tax') is not what produces efficiency - the level relative to marginal abatement cost is. A liability rule set at actual damage ($600,000) would have worked; a tax set at $200,000 fails. A good answer also notes the plant's profit is $2,000,000, so it can afford treatment, and that the regulator could alternatively set the tax at the marginal damage and let the plant choose treatment. The fishery's filtration option ($500,000) is never efficient here because treatment is cheaper.