The Calder River Paper Mill: Tax, Permits or Regulation

Efficiency requires the marginal cost of abatement to equal the marginal damage from the remaining effluent. The marginal damage is $40 per tonne. Abatement should continue while the marginal abatement cost is below $40 and stop when it exceeds $40. The first 20 tonnes cost $10 each, which is below $40, so abate. The next 20 tonnes cost $25 each, still below $40, so abate. The third 20 tonnes cost $45 each, which is above $40, so do not abate. Therefore efficient abatement is 40 tonnes per day, leaving 80 - 40 = 40 tonnes of effluent. At that point the last tonne abated costs $25 and the next tonne would cost $45, so the marginal condition is satisfied at the boundary. Total abatement cost is 20 × $10 + 20 × $25 = $200 + $500 = $700 per day. Total damage from the remaining 40 tonnes is 40 × $40 = $1,600. The efficient outcome is not zero pollution, because the cost of eliminating the last 40 tonnes exceeds the damage avoided.

A Pigouvian tax set at $40 per tonne would make the mill pay for each tonne discharged. The mill would compare the tax with abatement cost. It would abate the first 40 tonnes because each costs less than $40, and it would discharge the remaining 40 tonnes and pay $40 per tonne. The tax therefore achieves the efficient 40 tonnes of effluent if the mill is a price taker and the regulator knows marginal damage. The mill pays 40 × $40 = $1,600 in tax, which raises revenue but also raises costs and may affect employment. A tradable permit scheme issuing 40 permits gives the same quantity directly. If permits are freely allocated, the mill can discharge 40 tonnes without paying, but it could sell permits if it abates more. If permits are auctioned, the effect is similar to a tax. The advantage of permits is quantity certainty: the regulator knows the cap. The disadvantage is that the permit price may be volatile if abatement costs change. With a limited monitoring budget, permits may be easier to enforce because the regulator only needs to check the cap and permit holdings, not every discharge tonne for tax liability. However, both require accurate monitoring of effluent. A tax gives the regulator less quantity certainty but more revenue; permits give more environmental certainty but may create windfall gains if given away free.

The regulation would require abatement of 60 tonnes, leaving 20 tonnes of effluent. The cost of the first 40 tonnes is $700. The next 20 tonnes cost $45 each, so the additional cost is $900. Total abatement cost is $1,600. The damage from the remaining 20 tonnes is 20 × $40 = $800. Total social cost is $1,600 + $800 = $2,400. At the efficient outcome, abatement cost is $700 and damage is $1,600, giving $2,300. So the strict regulation raises total social cost by $100 per day compared with the efficient outcome. That is a small efficiency loss, but the regulation has other costs. The mill may have to cut output or employment, which matters in a town with 9% unemployment. The fishing industry gains because damage falls from $1,600 to $800, but the mill and its workers lose. The regulation is also inflexible: if abatement technology improves, the mill still must meet 20 tonnes, and if costs rise, it cannot trade off. The regulator may prefer the regulation if monitoring is cheap and the environmental target is politically important. But economically, the tax or permit approach achieves a better balance unless the regulator believes the damage estimate is too low or the fishing industry's losses are undervalued.