Optimal Emission Reduction• The problem• The solution

– What will it cost?– What to do?

How deep?The ultimate objective of [the United Nations Framework Convention on Climate Change] [...] is to achieve [...] stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference with the climate system. Such a level should be achieved within a time-frame sufficient to allow ecosystems to adapt naturally, to ensure that food production is not threatened and to enable economic development to proceed in a sustainable manner.

How deep?• Concentration

1 1

1Stabilization:

1

t t t

t t

M M EM M

EM M E M

How deep?• Maier-Reimer & Hasselmann

5

,1

5

, , 1 11

1 2 3

54

; 1

1 1/ 2; 1 1/ 17; 1 1/ 74;1 1/ 363; 1

Stabilization: 0

t i ti

i t i i ii t ti

M M

M M E

E

Optimal Climate Policy• In a static optimum, the marginal costs

should equal the marginal benefits• In a situation like climate change, where

the benefits are a stock and the costs are a flow, the marginal costs should equal the net present value of the marginal benefits

Optimal Climate Policy• In a static optimum, the marginal costs

should equal the marginal benefitsmax ( ) ( ) ( )

EW E B E C E

0 0W B C B CE E E E E

Optimal Climate Policy• In a situation like climate change, where

the benefits are a stock and the costs are a flow, the marginal costs should equal the net present value of the marginal benefits

0 1

1

1, ,...

( , ,...) ( )max ( ) ( )t t t t t

tE E t

B E E C EW Er

11( )

t s ts

s t t

B C tr E E

0

50

100

150

200

250

2005 2025 2045 2065 2085 2105

Car

bon

tax

(200

0 $

per t

on ca

rbon

)

350

400

450

500

550

600

650

700

750

2005 2025 2045 2065 2085 2105

Atm

osph

eric

con

cent

ratio

n of

car

bon

diox

ide

(ppm

)

Optimal Emission Control• If the world were ruled by a benevolent

dictator, what would she do?• A little emission reduction in the beginning,

more later, but not enough to stabilise concentrations

• The first part is robust, the second part is very sensitive to assumptions

• The last part is robust, unless there is a cheap alternative to fossil fuels

• If we consider many countries, optimal emission reduction goes down!

Gain

Emissions

Marginal private gainsf rom emissions

Marginal social lossesf rom emissions

Marginal net social gainsf rom emissions

Optimal Emission Control• If the world were ruled by a benevolent

dictator, what would she do?• A little emission reduction in the beginning,

more later, but not enough to stabilise concentrations

• The first part is robust, the second part is very sensitive to assumptions

• The last part is robust, unless there is a cheap alternative to fossil fuels

• If we consider many countries, optimal emission reduction goes down!