Climate change and economic analysis

Climate change and

economic

analysis

by

Finn R. Førsund

Department of Economics

University of Oslo

*

Slides prepared for the Symposium on Energy and CO₂ Emission/Policies – Global CO₂ Economics

Global warming and CO

₂

• Svante Arrhenius

1896, Nobel prize 1903 • Studied causes of ice

ages

• Predicted correctly the change in temperature of doubling of CO₂

• Predicted it would take 3000 years

Global warming threatening

human existence

• Intergovernmental Panel on Climate

Change (IPCC)

– First time the human race is capable of

destroying life on earth as we know it with peaceful means

• Increased surface temperature

– Massive extinction of species – Change in weather patterns

The fundamental stock – flow

trade-off

• Haavelmo (Nobel prize 1989) (1971):

Social entropy

– Positive utility of current consumption, but negative utility of build-up of social entropy – Social entropy: index for accumulation of

pollution caused by current production and consumption

– Social entropy causes negative impacts due to various types of discomforts, and global

Haavelmo’s social entropy model

• Social utility function

• Accumulation of social entropy

• The present value of utility

x _x Z _Z

u x t Z t

( ( ), ( )),

u

′

>

0,

u

′′

₂

<

0,

u

′

<

0,

u

′′

₂

<

0

t

Z t

=

k N

∫

x

d

0

( )

( ) ( )

τ

τ τ

t t

V t

e

u x

k N s x s ds d

∞ −

=

∫

( )

∫

( )

[ ( ),

( ) ( ) ]

τ ρ τ

τ

τ

Z

• x: consumption per capita

• N: population

• k: contribution to social entropy per unit of production/

consumption • Z: index for

accumulated amount

The dynamics of social entropy

Flow of pollutants, kNx t time Accumulated amount Catastrophe level

Sustainability

• Depreciation of social entropy as pollutants

– Natural processes of dilution, decaying,

chemical processes changing the nature of stocks of pollutants, carbon sinks

• Fundamental factors for unit additions

– Population, consumption- and production technology including purification, mix of consumption goods

• Sustainability

– Current additions to social entropy

• Introducing decay of social entropy

• Sustainability:

– It must be possible to obtain a steady state for social entropy

• Emissions are balanced by decay

• Technology influences

k

, maybe

α

Z t kN t x t Z t • = − ( ) ( ) ( ) α ( ) Z t kN t x t Z t • = ⇒ = ( ) 0 ( ) ( ) α ( )

Formal sustainability

The optimisation problem

• Introducing a separable utility function

• The social problem

u x t Z t( ( ), ( )) = B x t( ( )) − D Z t( ( )), B′ > 0, B′′ < 0, D′ > 0, D′′ > 0 ( ) 0 Max [ ( ( )) ( ( ))] subject to ( ) ( ) ( ) 0, rt x t o N B x t D Z t e dt Z t kNx t Z t Z α ∞ − • − = − ≥

∫

Solving the problem

• The current-value Hamiltonian

• First-order condition for the flow variable

• First-order condition for the stock variable

( ( ( ))

( ( )))

( )(

( )

( ))

H

=

N B x t

−

D Z t

+

μ

t kNx t

−

α

Z t

( ( )) ( ( )) ( ) 0 ( ) ( ) H B x t NB x t t kN t x t μ k μ ′ ∂ _′ = + = ⇒ = − ∂ ( ) ( ) ( ( )) ( ) ( ) ( ) H t r t ND Z t t r t Z t

μ

•

μ

μ α

μ

• ∂ _′ = − + = + + ⇒ ∂

Steady state

• No change in the shadow price on social

entropy

• Steady state for social entropy

0 ( ( )) ( )( ) ( ( )) ( ) ND Z t t r ND Z t t r μ α μ α ′ = + + ⇒ ′ − = + ( ) 0 kNx t( )

α

Z t( ) Z t( ) kNx t

α

= − ⇒ =

The role of population growth

• Total population

N

– The steady state level of social entropy increases in N

– The constant marginal damage of social entropy in steady state increases in N

• Possible link between level of

Z

and

population growth

N t

n Z t

n

′

=

<

( )

( ( )),

0

( )

Health effects of climate change

London smog disaster 1952

• 4000 premature dead in one week • In total 12000 dead • Caused by particles, soot, SO₂ from heating/cooking with coal • Air inversion • Lead to prohibition of using coal in London

Global health effects

• IPCC Fourth Assessment Report (2007),

Stern Review (2007)

• Changing weather patterns

– More frequent extreme rains, hurricanes, draughts

• Spread of tropical diseases

• Death from drowning, dehydration,

malnutrition

Local health effects

• Heat waves

– Premature death among elderly and babies

• London smog equivalents

– Reduced air quality due to pollution of particles, , soot, SO2, ozone

• Loss of productivity due to ill health, costs of

prevention and hospital treatment

• Finding willingness to pay for reduced air

Solving local and global problems

jointly

• The GAINS model of IASA

– Finding purification cost synergies between purifying local air pollutants and global GHG

– Index i is region,e_i1 is local air pollution, e_i2 is global air pollution

1 1 2 2 1,2 ( , ) , 1,..., 0 , 1, 2 , 0 o o i i i i i i is i c c e e e e i N c s c = − − = ′ > = ′′ >

The cooperative GAINS model

1 1 2 2 1 * 1 1 min 1 1 1 * 2 2 1 min ( , ) . . , 1,.., , 1,.., , 1,.., N o o i i i i i i N ij i j j i o i i i N i i o Min c e e e e s t a e b d j R e e e i N e e e e e i N = = = − − + ≤ = ≤ ≤ = ≤ ≤ ≤ =

∑

∑

∑

The optimal solution

• Necessary conditions

• Local pollutants: marginal cost equal to

weighted marginal damage

• Global pollutants: marginal costs equal for

all regions and equal to shadow price on

constraint on global pollutant

1 1 1 1 1 2 2 1 2 2 2 1 1 2 2 ( , ) 0 1 ( , ) 0 1 R o o j ij _{i i} i i i i i j= o o i i i i i i i c e e e e +_a , i = ,.., N c e e e e + , i = ,.., N

μ γ λ σ μ γ ′ − − − − = ′ − − − − =

∑

Illustration

S(e₁min₎ e₂*<e₂o e₂=e₂o c₁’ c1’ S(e₁o₎ c₁’* e o Emissions Marginal costs e * μ₁ γ₁ c₁’

Challenges and strategies 1

• Population growth

– Resource availability, biodiversity, pollution: all problems easier to solve with fewer people

• Technological change

– New energy technologies most important; renewables, nuclear, increased efficiency in using raw materials

• Change of composition of consumption

– A change from material goods to services; culture, education, leisure

Challenges and strategies 2

• Control of population growth must be

introduced

• Vulnerability to climate change

– Sea level rise: the coastal zone, salt water intrusion→ happens in poor countries→

pressure for migration of people on a large scale

– Melting of glaziers, floods, draughts

– Health effects, pollution, urban heat waves

Challenges and strategies 3

• Developing alternative technologies to

coal-fired electricity production

– Renewables, hydropower, wind power, solar, nuclear

• Promoting efficiency of use of energy in

industry, housing and transport

• International cooperation, the next Kyoto

protocol

– Equity issues versus cost efficiency – Technology transfers, cooperation on