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# Secondary benefits

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Lecture on secondary benefits and climate policy. Will be in next edition of the Climate Economics textbook.

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### Secondary benefits

1. 1. π΅ = πΌπ΄ + ππΊ Two criterion emissions, G and A, measured as emission reductions. Benefits, B, of emission reduction: Emission controls, R and S, affect both: πΊ = ππ + ππ, π β« π π΄ = ππ + ππ, π β« π Costs, C, of emission reduction: πΆ = 0.5ππ2 + 0.5ππ2 Rework benefits: π΅ = πΌ ππ + ππ + π ππ + ππ = π πΌπ + ππ + π πΌπ + ππ
2. 2. Benefits, B, of emission reduction: Costs, C, of emission reduction: πΆ = 0.5ππ2 + 0.5ππ2 π΅ = πΌ ππ + ππ + π ππ + ππ = π πΌπ + ππ + π πΌπ + ππ Optimal control for R: ππ΅ ππ = πΌπ + ππ = ππ = ππΆ ππ β πβ² = πΌπ + ππ π The secondary benefit, π>0, increases the optimal rate of abatement. ππ΅ ππ = πΌπ + ππ = ππ = ππΆ ππ β πβ² = πΌπ + ππ π
3. 3. π΅ = πΌβπ΄ + ππΊ Now make the secondary benefits less than linear. Benefits, B, of emission reduction: Emission controls, R and S, affect both: πΊ = ππ + ππ, π β« π π΄ = ππ + ππ, π β« π Costs, C, of emission reduction: πΆ = 0.5ππ2 + 0.5ππ2 Rework benefits: π΅ = πΌβ ππ + ππ + π ππ + ππ
4. 4. Benefits, B, of emission reduction: Costs, C, of emission reduction: πΆ = 0.5ππ2 + 0.5ππ2 Optimal control for R: ππ΅ ππ = πΌπ 2β ππ + ππ + ππ = ππ = ππΆ ππ β πβ² = πΌπ 2πβ ππβ² + ππβ² + ππ π The secondary benefit, π>0, increases the optimal rate of abatement R, but that increase falls with abatement of the other criterion emission S. π΅ = πΌβ ππ + ππ + π ππ + ππ
5. 5. Optimal control: πβ² = πΌπ 2πβ ππβ² + ππβ² + ππ π Without the primary benefit, π=0, the optimal rate of abatement R is small, and abatement of the other criterion emission S increases. πβ² = πΌπ 2πβ ππβ² + ππβ² + ππ π If climate change is a hoax, π=0: π" = πΌπ 2πβ ππ" + ππ" βͺ πβ² π" = πΌπ 2πβ ππ" + ππ" < πβ²
6. 6. π΅ = πΌ ln π΄ + ππΊ Now make the secondary benefits less than linear. Benefits, B, of emission reduction: Emission controls, R and S, affect both: πΊ = ππ + ππ, π β« π π΄ = ππ + ππ, π β« π Costs, C, of emission reduction: πΆ = 0.5ππ2 + 0.5ππ2 Rework benefits: π΅ = πΌ ln(ππ + ππ) + π ππ + ππ
7. 7. Benefits, B, of emission reduction: Costs, C, of emission reduction: πΆ = 0.5ππ2 + 0.5ππ2 Optimal control for R: ππ΅ ππ = πΌπ ππ + ππ + ππ = ππ = ππΆ ππ β πΌπ + ππππ = πππ β πππ π + πππ2 β πβ² = πππ β πππ Β± (πππ β πππ)2+4ππ(πΌπ + ππππ) β2(πΌπ + ππππ) π΅ = πΌ ln ππ + ππ + π ππ + ππ
8. 8. Optimal control for R: πβ² = πππ β πππ β (πππ β πππ)2+4ππ(πΌπ + ππππ) β2(πΌπ + ππππ) The secondary benefit, π>0, increases the optimal rate of abatement R, but that increase falls with abatement of the other criterion emission S. ??? πβ² = βπππ β πππ 2 β2 ππππ = π ππ No secondary benefit, π =0 No abatement of the other criterion emission S πβ² = πππ β πππ 2 + 4π2 ππΌ β2πΌπ = ππ β ππ 2 + 4ππΌ β2πΌ
9. 9. Secondary benefits β’ If greenhouse gas emission reduction helps solving other problems (air pollution, energy security), then we should do more of it β’ However, greenhouse gas emission reduction would be a clumsy way to solve other problems and other problems do not justify a lot of greenhouse gas emission reduction β’ Other problems justify a lot of other problem solving.