Ecological EconomicsLecture 08

Tiago DomingosAssistant Professor

Environment and Energy SectionDepartment of Mechanical Engineering

Doctoral Program and Advanced Degree in Sustainable Energy SystemsDoctoral Program in Mechanical Engineering

Doctoral Program in Environmental Engineering

Present Value of Money

• Present Value– Conversion of money flows to their present value

• NPV: Net Present Value

• i: interest rate

• VFt(t): value at instant t

• If VF is in current prices then i is the nominal interest rate

• If VF is in constant prices then i is the real interest rate

t

T

ttVF

iNPV

0 1

1

Nominal vs. real interest ratesThe Fisher relation

)inflation1)(real1(nominal1

For low rates, this is approximately equal to

inflationrealnominal

Present Value of Utility

• Welfare– Discrete time

– Continuous time

T

tt tUW

0 1

1

T

t

t- dttUW0

e

Discount RateJustification and Components

• The same monetary flow at different instants does not have the same value (time preference)

– CONSUMPTION: Uncertainty• Being alive in the future (individual vs. society)

• Preferences in the future

• Value of the benefit or the cost

– CONSUMPTION: Impatience

– PRODUCTION: Capital productivity (opportunity cost of capital)

• Under certain conditions, the discount rate is equal to the real market interest rate

consumption discount rate

per capita consumption growth rate

elasticity of the marginal utility of consumption

utility discount rate

Turner et al. (1994), pp. 102-106.

.

p L

pure time preference rate

variation in survival probability

C

Cr

Discount RateCalculation Methods

• Pure rate of time preference– “ A universal point of view must be impartial about time, and impartiality

about time means that no time can count differently from any other. In overall good, judged from a universal point of view, good at one time cannot differ from good at another. Hence...the [pure time] discount rate...must be nought”

Broom (1992, p. 92) cit. in Pearce e Ulph (1998, p. 273)• Variation in survival probability

– Increase in mortality risk with age or– Average population mortality rate

• Elasticity of the marginal utility of consumption– Individual saving behaviour– Social judgement on income transfers between people

• Per capita consumption growth rate– Long run average of growth rate in real per capita consumption

Discount RateElasticity of the Marginal Utility of Consumption

U(C)

C

U(C)

C

0 0

U(C)>0

Utility of consumption

1

1C

aCU

U’(C)>0

Marginal utility of consumption

aCCU '

U’’(C)<0

Variation in marginal utility of consumption

1'' CaCU

CUCU

C''

'

Elasticity of the marginal utility of consumption

Discount RateEthical Interpretation of the Elasticity of Marginal Utility

• Consider two families, with consumption resp. equal to C1 and C2, with C1 = 2C2. The ratio of the marginal utilities of consumption is:

22

1

aC

aC

• For different values of μ , this ratio is equal to:

μ 0,5 0,7 1,0 1,5 2,0 5,0 10,0

2- μ 0,7 0,6 0,5 0,35 0,25 0,03 negl.

Discount RateEstimate for the United Kingdom

Pearce, D., D. Ulph (1998). A social discount rate for the United Kingdom. In D. Pearce, Economics and Environment, Edward Elgar, Cheltenham, UK, pp. 268-285.

Estimate

Pure rate of time

preference

Variation in survival

probability

Elasticity of marginal

utility

Per capita consumption growth rate

Consump. discount

rate

Lower bound

0,0 0,0 0,7 1,3 0,9

Best estimate

0,3 -1,1 0,8 1,3 2,4

Upper bound

0,5 -1,2 1,5 2,2 5,0

p.

L

.

r p L c

rc

Discount RateCriticisms

• The future is given a very low value

• Limits to growth– It may not make sense to assume that economic growth will

continue indefinitely (i.e., at a constant rate, i.e., exponentially)

• Negative discount rates – Countries with economic de-growth

– The future has more value than the present

Multisector Optimal Growth

• m-dimensional consumption bundle, including everything that influences well-being.

– Includes all non-market commodities, e.g, produced at home, environmental services, …

• n-dimensional capital vector:– Includes man-made capital, natural resources, human capital

(education and knowledge) and foreign capital. Time is included as a capital, to depict technological progress in production.

• Attainable production possibilities

• The model

0max ( ( )) t

cU C t e dt

C( ),I( ) (K( ), )t t S t t

s.t.K

Id

dt

C( ),I( ) (K( ), )t t S t t

Criteria for Sustainability, Pezzey (2004) EDE

• An economy is sustainable at time t if and only if the representative agent’s current utility does not exceed the maximum level of utility which can be sustained forever from t onwards.

• One-sided sustainability test:

un-sustainable development.

• Multisector results in real terms.– Real Net Income,

– Genuine Saving,

–

0 0dY

QI ordt

P C Q IY

dY R dWR

dt dt Q I

Q IConsumption Investment

Variation in Real Net Income

Variation in Welfare

Welfare Relationships

• Both Genuine Savings and Green NNI are related to future consumption.

• These relationships can be used to empirically check the theory.

• If genuine saving is negative (or green NNI deacreases) then current consumption will decrease in the future.

Small Open Economy

• Include – stocks of commercial forests,

– welfare costs of air emissions,

• The capital stocks are :– Domestic man-made capital,

– Net foreign capital held privately or by the government,

– Stock of commercial natural resources

• Production

K : ( , ,S)fK K

dKI CFC

dt

ff R X MdK

rK X Mdt

Q (R R )

d XdS

dt G(S) R R

d M d XI F K M X C a f ( , R R ) (R R ,S)

r – interest rate

Small Open Economy

• Households’ utility function depends on material consumption rate and (negatively) on the flow of emissions

• The vector of emissions depends on production and abatement expenditure.

• Maximize welfare subject to the above relations and having as controls consumption, , all forms of extraction, , abatement expenditure and trade balance .

• Conventional (SNA) NNI:

• Green Net National Income:

• Genuine Saving (Adjusted Net Saving):

(C) : ( ,E)U U C

E( ( ),a)F

( )C t R ( ), R ( ), R ( )d X Mt t ta( )t ( ) ( )M t X t

: fNNI C K K

R(Q f ) S e ER tY NNI Q

R(Q f ) St R tQ K Q NNI C Q

Small Open Economy – Table of symbols( )C t Consumption rate at time t

( )U Utility

E( ) Rate of emissions of air pollutants

( )F Production function

a Abatement expenditure

, , ,iR i d X M Extraction of natural resources for domestic use, exports and from imports.

M X Imports - Exports

r Constant nominal interest rate

S Stock of resources

K Man-made capital,

RQ Resource price

R Constant real interest rate

(R R ,S)d Xf Cost of extraction of resource

e Marginal cost of abatement = Marginal damage cost

Rf Marginal cost of abatement

fK Net foreign capital

Small Open Economy

• Starting from conventional SNA aggregates:– Deduct the damage from flow pollution emissions,

– Deduct (add) the value of rents from resource depletion (or not),

e E

R(Q f ) SR

-20000

0

20000

40000

60000

80000

100000

120000

140000

1990 1995 2000 2005

Mill

ion

€

GNI

CFC

Air emissions

Forest Depl.

Tech. Progress

GNNI

Pot GNNI

GNNI, T=100

• Models point to measure emissions at the – Marginal cost of abatement (MCA), or

– Marginal social cost (MSC) = Marginal benefit of abatement (MBA), a.k.a. Marginal Damage Costs (MDC)

• Measurement away from the optimum– c, over-polluting (assumed current state) => a is upper bound

– d, under-polluting => b is lower bound

Social costs vs Marginal abatement

Constant MDC

GNNI and GS in Portugal – Air Emissions

• How to value a unit of emissions?– Marginal benefit of avoided emission,– Marginal cost of emission (MDC), or– Marginal abatement costs?

• Marginal cost of emission per emitted pollutant [€2000/ton]:

[€2000/t] Best Low High

SO2 6872 3472 9972

NH3 7399 3699 10999

NOx 2040 1140 3040

VOC 1150 450 1550

PM2,5 44000 22000 64000

GNNI and GS in Portugal – Air Emissions

0

10

20

30

40

50

60

70

1990 1995 2000 2005

% o

f to

tal c

ost

SO2

NH3

NOx

VOC

PM2,5

GNNI and GS in Portugal – Forests

• National Forest Inventory 2005/06

• Average Volumes:

Conifers

Eucalyptus

95/98 05/06[m3/ha]

88.5

55 55

82.5

0

200

400

600

800

1000

1200

1400

1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005

10^3

ha

Conifers

Eucalyptus

GNNI and GS in Portugal – Forests

-200

-150

-100

-50

0

50

100

1990 1995 2000 2005

mill

ion

€ConiferousEucalyptus

The depreciation of commercial forests in Portugal is on average 10% of the contribution of forestry to national product (around 4%).

GS in Portugal

• Without the value of time – Decreasing tendency throughout the period and negative GS after 2002.

• With the value of time – Decreasing tendency until 2001, but GS are always positive.

-10000

-5000

0

5000

10000

15000

20000

25000

30000

35000

40000

1990 1995 2000 2005

Mill

ion

€GS, no Qt

GS

GS, T=100

Potential GS

• In 1993, SO2 costs of emissions, which represent around 30% of total emission costs, decreased substantially. Increases welfare but does not counteract the loss of production.

Sustainability Message

What’s Missing?

• The depletion of water resources.

• The depletion of biodiversity.

• Depletion of stocks of fish.

• Inclusion of the value of ecosystem services.

• Soil quality.

• Distributional issues (intragenerational concerns).

• ...