Factory Discharge and Oyster Farmers
A factory in an estuary produces industrial starch and discharges untreated wastewater into a river. Its annual private profit is HK$2.4 million. Thirty oyster farmers downstream earn HK$3.1 million in profit from clean water. The discharge reduces their combined profit to HK$0.9 million, so the external cost is HK$2.2 million per year. The factory can install a treatment plant for HK$1.5 million per year, which would eliminate the damage. The farmers could instead build a shared filtration system for HK$2.8 million per year. The factory and farmers have no history of cooperation, and each farmer fears that others will free-ride on any private agreement. The government is considering either a Pigouvian tax equal to the estimated external cost or a cap-and-trade permit scheme for discharge. Monitoring discharge is cheap, but estimating the exact marginal damage is difficult because oyster yields vary with rainfall.
1. Explain why the factory's private profit overstates the social gain from starch production, using the numbers. Calculate the social gain from treatment.
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The factory's private profit of HK$2.4 million counts only its own revenue and costs. The discharge imposes an external cost on the oyster farmers: their profit falls from HK$3.1 million to HK$0.9 million, a loss of HK$2.2 million. Without treatment, total social surplus is therefore HK$2.4 million plus HK$0.9 million, or HK$3.3 million. The private profit alone overstates the social gain because it ignores the HK$2.2 million loss suffered by the farmers.
With treatment, the factory's profit becomes HK$2.4 million minus HK$1.5 million, or HK$0.9 million, and the farmers' profit returns to HK$3.1 million. Total social surplus is HK$4.0 million. Treatment therefore raises social surplus by HK$0.7 million per year. The factory would not install the plant voluntarily because its private profit falls from HK$2.4 million to HK$0.9 million. This divergence between private and social incentives is the externality problem.
2. Compare a Pigouvian tax and a tradable permit scheme in this setting, given uncertain marginal damage.
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A Pigouvian tax sets a price per unit of discharge equal to the estimated marginal external damage. If the estimate is correct, the factory will abate up to the point where its marginal abatement cost equals the tax. If the estimate is too low, discharge will be too high; if it is too high, the factory may spend excessively on treatment. With rainfall-dependent oyster yields, the true marginal damage is uncertain, so a fixed tax may be inaccurate.
A cap-and-trade scheme sets a quantity cap and lets the permit price adjust. If the ecological threshold for the oyster beds is important, a quantity cap is safer because it directly limits discharge. Cheap monitoring makes permits workable. However, the initial allocation matters: giving permits free to the factory creates a windfall, while auctioning them raises revenue. A tax gives the government revenue and is simpler, but it does not guarantee the quantity limit. Judgement: permits are preferable if the damage rises sharply beyond a safe discharge level; a tax is preferable if damage is roughly linear and abatement-cost uncertainty is the main concern.
3. Would the Coase theorem predict that the factory and farmers will negotiate an efficient outcome without government? Explain with the free-rider problem.
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The Coase theorem says that if property rights are clearly defined and transaction costs are zero, the parties will bargain to an efficient outcome regardless of who initially holds the rights. Here the conditions are unlikely to hold. There are thirty farmers, and each has an incentive to free-ride: if one farmer pays the factory to treat the water, all farmers benefit from cleaner water. Each farmer therefore prefers to let others bear the cost. Holdout problems, monitoring costs, and the lack of a cooperation history raise transaction costs further.
Even if the farmers had the legal right to clean water, they might struggle to organise a collective payment to the factory. If the factory had the right to pollute, the farmers would still face the same collective-action problem in paying it to install treatment. Government can reduce transaction costs by clarifying liability, helping farmers form a collective agreement, or imposing a tax or permit scheme. Without such intervention, an efficient bargain is unlikely despite the potential HK$0.7 million social gain.