The document discusses the benefits and costs associated with emission reduction strategies, modeling the relationships between various controls and their effectiveness. It emphasizes the impact of secondary benefits on the optimal rates of abatement for different criteria emissions. Additionally, it critiques the effectiveness of using greenhouse gas emission reduction as a solution to other environmental issues, suggesting that it may not be the most efficient approach.

2. 𝐵 = 𝛼𝐴 + 𝜒𝐺
Two criterion emissions, G and A, measured as emission reductions.
Benefits, B, of emission reduction:
Emission controls, R and S, affect both:
𝐺 = 𝜋𝑆 + 𝜌𝑅, 𝜌 ≫ 𝜋
𝐴 = 𝜎𝑆 + 𝜏𝑅, 𝜎 ≫ 𝜏
Costs, C, of emission reduction:
𝐶 = 0.5𝜅𝑆2
+ 0.5𝜆𝑅2
Rework benefits:
𝐵 = 𝛼 𝜎𝑆 + 𝜏𝑅 + 𝜒 𝜋𝑆 + 𝜌𝑅 = 𝑆 𝛼𝜎 + 𝜒𝜋 + 𝑅 𝛼𝜏 + 𝜒𝜌

3. Benefits, B, of emission reduction:
Costs, C, of emission reduction:
𝐶 = 0.5𝜅𝑆2 + 0.5𝜆𝑅2
𝐵 = 𝛼 𝜎𝑆 + 𝜏𝑅 + 𝜒 𝜋𝑆 + 𝜌𝑅 = 𝑆 𝛼𝜎 + 𝜒𝜋 + 𝑅 𝛼𝜏 + 𝜒𝜌
Optimal control for R:
𝜕𝐵
𝜕𝑅
= 𝛼𝜏 + 𝜒𝜌 = 𝜆𝑅 =
𝜕𝐶
𝜕𝑅
⇒ 𝑅′ =
𝛼𝜏 + 𝜒𝜌
𝜆
The secondary benefit, 𝜏>0, increases the optimal rate of abatement.
𝜕𝐵
𝜕𝑆
= 𝛼𝜎 + 𝜒𝜋 = 𝜅𝑅 =
𝜕𝐶
𝜕𝑆
⇒ 𝑆′ =
𝛼𝜎 + 𝜒𝜋
𝜅

4. 𝐵 = 𝛼√𝐴 + 𝜒𝐺
Now make the secondary benefits less than linear.
Benefits, B, of emission reduction:
Emission controls, R and S, affect both:
𝐺 = 𝜋𝑆 + 𝜌𝑅, 𝜌 ≫ 𝜋
𝐴 = 𝜎𝑆 + 𝜏𝑅, 𝜎 ≫ 𝜏
Costs, C, of emission reduction:
𝐶 = 0.5𝜅𝑆2
+ 0.5𝜆𝑅2
Rework benefits:
𝐵 = 𝛼√ 𝜎𝑆 + 𝜏𝑅 + 𝜒 𝜋𝑆 + 𝜌𝑅

5. Benefits, B, of emission reduction:
Costs, C, of emission reduction:
𝐶 = 0.5𝜅𝑆2 + 0.5𝜆𝑅2
Optimal control for R:
𝜕𝐵
𝜕𝑅
=
𝛼𝜏
2√ 𝜎𝑆 + 𝜏𝑅
+ 𝜒𝜌 = 𝜆𝑅 =
𝜕𝐶
𝜕𝑅
⇒
𝑅′ =
𝛼𝜏
2𝜆√ 𝜎𝑆′ + 𝜏𝑅′
+
𝜒𝜌
𝜆
The secondary benefit, 𝜏>0, increases the optimal rate of abatement R, but
that increase falls with abatement of the other criterion emission S.
𝐵 = 𝛼√ 𝜎𝑆 + 𝜏𝑅 + 𝜒 𝜋𝑆 + 𝜌𝑅

6. Optimal control:
𝑅′ =
𝛼𝜏
2𝜆√ 𝜎𝑆′ + 𝜏𝑅′
+
𝜒𝜌
𝜆
Without the primary benefit, 𝜒=0, the optimal rate of abatement R is small,
and abatement of the other criterion emission S increases.
𝑆′ =
𝛼𝜎
2𝜅√ 𝜎𝑆′ + 𝜏𝑅′
+
𝜒𝜋
𝜅
If climate change is a hoax, 𝜒=0:
𝑅" =
𝛼𝜏
2𝜆√ 𝜎𝑆" + 𝜏𝑅"
≪ 𝑅′
𝑆" =
𝛼𝜎
2𝜅√ 𝜎𝑆" + 𝜏𝑅"
< 𝑆′

7. 𝐵 = 𝛼 ln 𝐴 + 𝜒𝐺
Now make the secondary benefits less than linear.
Benefits, B, of emission reduction:
Emission controls, R and S, affect both:
𝐺 = 𝜋𝑆 + 𝜌𝑅, 𝜌 ≫ 𝜋
𝐴 = 𝜎𝑆 + 𝜏𝑅, 𝜎 ≫ 𝜏
Costs, C, of emission reduction:
𝐶 = 0.5𝜅𝑆2
+ 0.5𝜆𝑅2
Rework benefits:
𝐵 = 𝛼 ln(𝜎𝑆 + 𝜏𝑅) + 𝜒 𝜋𝑆 + 𝜌𝑅

8. Benefits, B, of emission reduction:
Costs, C, of emission reduction:
𝐶 = 0.5𝜅𝑆2 + 0.5𝜆𝑅2
Optimal control for R:
𝜕𝐵
𝜕𝑅
=
𝛼𝜏
𝜎𝑆 + 𝜏𝑅
+ 𝜒𝜌 = 𝜆𝑅 =
𝜕𝐶
𝜕𝑅
⇒ 𝛼𝜏 + 𝜎𝜒𝜌𝑆 = 𝜎𝑆𝜆 − 𝜏𝜒𝜌 𝑅 + 𝜏𝜆𝑅2
⇒ 𝑅′ =
𝜏𝜒𝜌 − 𝜎𝑆𝜆 ± (𝜎𝑆𝜆 − 𝜏𝜒𝜌)2+4𝜏𝜆(𝛼𝜏 + 𝜎𝜒𝜌𝑆)
−2(𝛼𝜏 + 𝜎𝜒𝜌𝑆)
𝐵 = 𝛼 ln 𝜎𝑆 + 𝜏𝑅 + 𝜒 𝜋𝑆 + 𝜌𝑅

9. Optimal control for R:
𝑅′ =
𝜏𝜒𝜌 − 𝜎𝑆𝜆 − (𝜎𝑆𝜆 − 𝜏𝜒𝜌)2+4𝜏𝜆(𝛼𝜏 + 𝜎𝜒𝜌𝑆)
−2(𝛼𝜏 + 𝜎𝜒𝜌𝑆)
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′ =
−𝜎𝑆𝜆 − 𝜎𝑆𝜆 2
−2 𝜎𝜒𝜌𝑆
=
𝜆
𝜒𝜌
No secondary benefit, 𝜏 =0
No abatement of the other criterion emission S
𝑅′
=
𝜏𝜒𝜌 − 𝜏𝜒𝜌 2 + 4𝜏2 𝜆𝛼
−2𝛼𝜏
=
𝜒𝜌 − 𝜒𝜌 2 + 4𝜆𝛼
−2𝛼

10. Secondary benefits
• If greenhouse gas emission reduction helps solving other
problems (air pollution, energy security), then we should do more
of it
• 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
• Other problems justify a lot of other problem solving.