Diese Präsentation wurde erfolgreich gemeldet.
Wir verwenden Ihre LinkedIn Profilangaben und Informationen zu Ihren Aktivitäten, um Anzeigen zu personalisieren und Ihnen relevantere Inhalte anzuzeigen. Sie können Ihre Anzeigeneinstellungen jederzeit ändern.
Nächste SlideShare
×

# Secondary benefits

142 Aufrufe

Veröffentlicht am

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

Veröffentlicht in: Bildung
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Als Erste(r) kommentieren

• Gehören Sie zu den Ersten, denen das gefällt!

### Secondary benefits

1. 1. 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
2. 2. 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
3. 3. 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
4. 4. 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
5. 5. 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′
6. 6. 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
7. 7. 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
8. 8. 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
9. 9. 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.