Emissions Trading Versus a Uniform Standard Under Cost Uncertainty
Two cement plants each emit 100 units of CO2. The regulator wants total emissions capped at 120, so 80 units of abatement are required. Marginal abatement costs are MAC_A = 10 + 0.5q_A and MAC_B = 30 + q_B, where q is units abated and costs are in rupees per unit. The regulator is choosing between a uniform standard requiring each plant to abate 40 units and a tradable permit system allocating 60 permits to each plant. Industry lobbyists prefer the uniform standard. The regulator also worries that its estimate of B's costs may be too low: true MAC_B may be 50 + q_B. Monitoring is cheap, and the environmental damage function is steep once emissions exceed 120. You are asked to compare the cost-effectiveness of the instruments, to evaluate the permit price and distributional effects, and to advise on tax versus permits under the cost uncertainty.
1. Find the cost-effective abatement allocation and the permit price. Compare total abatement cost with the uniform standard.
Read the worked answer
Cost-effectiveness requires equal marginal abatement costs and q_A + q_B = 80. Set 10 + 0.5q_A = 30 + q_B, so q_B = 0.5q_A - 20. Substituting: q_A + 0.5q_A - 20 = 80, so 1.5q_A = 100 and q_A = 66.67. Then q_B = 13.33. The common MAC is 10 + 0.5(66.67) = 43.33, which is the permit price.
Under a uniform standard of 40 each: Cost A = ∫0^40 (10 + 0.5q)dq = 400 + 400 = 800. Cost B = ∫0^40 (30 + q)dq = 1,200 + 800 = 2,000. Total = 2,800.
Under the cost-effective allocation: Cost A = 10(66.67) + 0.25(66.67)^2 ≈ 666.7 + 1,111.1 = 1,777.8. Cost B = 30(13.33) + 0.5(13.33)^2 ≈ 400.0 + 88.9 = 488.9. Total ≈ 2,266.7.
The permit system saves about 533.3 compared with the uniform standard. Plant A abates more because its marginal cost is lower; plant B abates less. With 60 permits each, A emits 33.33 and sells 26.67 permits, while B emits 86.67 and buys 26.67 permits at 43.33.
2. Suppose the regulator's estimate is wrong and true MAC_B = 50 + q_B. Compare the outcome under a tax set at 43.33 with a permit cap of 120.
Read the worked answer
Under a tax of 43.33, plant A still sets 10 + 0.5q_A = 43.33, so q_A = 66.67. Plant B's marginal abatement cost at zero abatement is 50, which exceeds the tax, so B abates nothing: q_B = 0. Total abatement is 66.67 and total emissions are 200 - 66.67 = 133.33, above the 120 cap. The tax fails to protect the environmental target.
Under a permit cap of 120, the regulator requires q_A + q_B = 80. Equalising true marginal costs: 10 + 0.5q_A = 50 + q_B, so q_B = 0.5q_A - 40. Then q_A + 0.5q_A - 40 = 80, giving 1.5q_A = 120, q_A = 80 and q_B = 0. The permit price rises to 50. Plant A's cost is 10(80) + 0.25(80)^2 = 800 + 1,600 = 2,400; plant B's cost is zero. Total cost is 2,400, higher than the expected 2,266.7 but the emissions cap is exactly met.
The permit system is robust on quantity; the tax is not. The permit system pays a cost penalty when B's costs are high, while the tax pays an environmental penalty.
3. Given the steep damage function beyond 120 units, would you recommend a tax or tradable permits? How should the permit system be designed?
Read the worked answer
When the damage function is steep beyond 120, the regulator places a high value on not exceeding the cap. A quantity instrument is preferable because it guarantees emissions of 120 regardless of cost realisations. A tax set at the expected permit price would allow emissions to rise to 133.33 when abatement costs are higher than expected, which is exactly the outcome the damage function penalises most.
This is the Weitzman logic: quantity instruments dominate when marginal damages are steeper than marginal abatement costs, and price instruments dominate when costs are steeper than damages. Here damages are steep, so permits are the safer choice.
Design matters. Auctioning permits raises revenue that can be used for adaptation or reduced distortionary taxes, while grandparenting transfers rents to incumbents. The initial allocation affects distribution but not efficiency if trading is frictionless. Because cost uncertainty remains, a hybrid with a price ceiling (safety valve) and a price floor can bound compliance costs while preserving the cap. Monitoring is cheap, so a permit system is administratively feasible. The lobbyists' preference for a uniform standard should be rejected: it meets the cap but at higher cost and with no trading gains.