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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. 𝐡 = 𝛼𝐴 + πœ’πΊ Two criterion emissions, G and A, measured as emission reductions. Benefits, B, of emission reduction: Emission controls, R and S, affect both: 𝐺 = πœ‹π‘† + πœŒπ‘…, 𝜌 ≫ πœ‹ 𝐴 = πœŽπ‘† + πœπ‘…, 𝜎 ≫ 𝜏 Costs, C, of emission reduction: 𝐢 = 0.5πœ…π‘†2 + 0.5πœ†π‘…2 Rework benefits: 𝐡 = 𝛼 πœŽπ‘† + πœπ‘… + πœ’ πœ‹π‘† + πœŒπ‘… = 𝑆 π›ΌπœŽ + πœ’πœ‹ + 𝑅 π›Όπœ + πœ’πœŒ
  2. 2. Benefits, B, of emission reduction: Costs, C, of emission reduction: 𝐢 = 0.5πœ…π‘†2 + 0.5πœ†π‘…2 𝐡 = 𝛼 πœŽπ‘† + πœπ‘… + πœ’ πœ‹π‘† + πœŒπ‘… = 𝑆 π›ΌπœŽ + πœ’πœ‹ + 𝑅 π›Όπœ + πœ’πœŒ Optimal control for R: πœ•π΅ πœ•π‘… = π›Όπœ + πœ’πœŒ = πœ†π‘… = πœ•πΆ πœ•π‘… β‡’ 𝑅′ = π›Όπœ + πœ’πœŒ πœ† The secondary benefit, 𝜏>0, increases the optimal rate of abatement. πœ•π΅ πœ•π‘† = π›ΌπœŽ + πœ’πœ‹ = πœ…π‘… = πœ•πΆ πœ•π‘† β‡’ 𝑆′ = π›ΌπœŽ + πœ’πœ‹ πœ…
  3. 3. 𝐡 = π›Όβˆšπ΄ + πœ’πΊ Now make the secondary benefits less than linear. Benefits, B, of emission reduction: Emission controls, R and S, affect both: 𝐺 = πœ‹π‘† + πœŒπ‘…, 𝜌 ≫ πœ‹ 𝐴 = πœŽπ‘† + πœπ‘…, 𝜎 ≫ 𝜏 Costs, C, of emission reduction: 𝐢 = 0.5πœ…π‘†2 + 0.5πœ†π‘…2 Rework benefits: 𝐡 = π›Όβˆš πœŽπ‘† + πœπ‘… + πœ’ πœ‹π‘† + πœŒπ‘…
  4. 4. Benefits, B, of emission reduction: Costs, C, of emission reduction: 𝐢 = 0.5πœ…π‘†2 + 0.5πœ†π‘…2 Optimal control for R: πœ•π΅ πœ•π‘… = π›Όπœ 2√ πœŽπ‘† + πœπ‘… + πœ’πœŒ = πœ†π‘… = πœ•πΆ πœ•π‘… β‡’ 𝑅′ = π›Όπœ 2πœ†βˆš πœŽπ‘†β€² + πœπ‘…β€² + πœ’πœŒ πœ† The secondary benefit, 𝜏>0, increases the optimal rate of abatement R, but that increase falls with abatement of the other criterion emission S. 𝐡 = π›Όβˆš πœŽπ‘† + πœπ‘… + πœ’ πœ‹π‘† + πœŒπ‘…
  5. 5. Optimal control: 𝑅′ = π›Όπœ 2πœ†βˆš πœŽπ‘†β€² + πœπ‘…β€² + πœ’πœŒ πœ† Without the primary benefit, πœ’=0, the optimal rate of abatement R is small, and abatement of the other criterion emission S increases. 𝑆′ = π›ΌπœŽ 2πœ…βˆš πœŽπ‘†β€² + πœπ‘…β€² + πœ’πœ‹ πœ… If climate change is a hoax, πœ’=0: 𝑅" = π›Όπœ 2πœ†βˆš πœŽπ‘†" + πœπ‘…" β‰ͺ 𝑅′ 𝑆" = π›ΌπœŽ 2πœ…βˆš πœŽπ‘†" + πœπ‘…" < 𝑆′
  6. 6. 𝐡 = 𝛼 ln 𝐴 + πœ’πΊ Now make the secondary benefits less than linear. Benefits, B, of emission reduction: Emission controls, R and S, affect both: 𝐺 = πœ‹π‘† + πœŒπ‘…, 𝜌 ≫ πœ‹ 𝐴 = πœŽπ‘† + πœπ‘…, 𝜎 ≫ 𝜏 Costs, C, of emission reduction: 𝐢 = 0.5πœ…π‘†2 + 0.5πœ†π‘…2 Rework benefits: 𝐡 = 𝛼 ln(πœŽπ‘† + πœπ‘…) + πœ’ πœ‹π‘† + πœŒπ‘…
  7. 7. Benefits, B, of emission reduction: Costs, C, of emission reduction: 𝐢 = 0.5πœ…π‘†2 + 0.5πœ†π‘…2 Optimal control for R: πœ•π΅ πœ•π‘… = π›Όπœ πœŽπ‘† + πœπ‘… + πœ’πœŒ = πœ†π‘… = πœ•πΆ πœ•π‘… β‡’ π›Όπœ + πœŽπœ’πœŒπ‘† = πœŽπ‘†πœ† βˆ’ πœπœ’πœŒ 𝑅 + πœπœ†π‘…2 β‡’ 𝑅′ = πœπœ’πœŒ βˆ’ πœŽπ‘†πœ† Β± (πœŽπ‘†πœ† βˆ’ πœπœ’πœŒ)2+4πœπœ†(π›Όπœ + πœŽπœ’πœŒπ‘†) βˆ’2(π›Όπœ + πœŽπœ’πœŒπ‘†) 𝐡 = 𝛼 ln πœŽπ‘† + πœπ‘… + πœ’ πœ‹π‘† + πœŒπ‘…
  8. 8. Optimal control for R: 𝑅′ = πœπœ’πœŒ βˆ’ πœŽπ‘†πœ† βˆ’ (πœŽπ‘†πœ† βˆ’ πœπœ’πœŒ)2+4πœπœ†(π›Όπœ + πœŽπœ’πœŒπ‘†) βˆ’2(π›Όπœ + πœŽπœ’πœŒπ‘†) The secondary benefit, 𝜏>0, increases the optimal rate of abatement R, but that increase falls with abatement of the other criterion emission S. ??? 𝑅′ = βˆ’πœŽπ‘†πœ† βˆ’ πœŽπ‘†πœ† 2 βˆ’2 πœŽπœ’πœŒπ‘† = πœ† πœ’πœŒ No secondary benefit, 𝜏 =0 No abatement of the other criterion emission S 𝑅′ = πœπœ’πœŒ βˆ’ πœπœ’πœŒ 2 + 4𝜏2 πœ†π›Ό βˆ’2π›Όπœ = πœ’πœŒ βˆ’ πœ’πœŒ 2 + 4πœ†π›Ό βˆ’2𝛼
  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.

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