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Question Croissance, Energie et Technologie
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On Economic Growth, EnergyConsumption and Technological
ChangeJussieu 24 Avril 2006
Dr Benjamin Warr Professor Robert Ayres
Sommaire
• Critique de l’approche «neo-classique » de la croissance économique
• Considération de la rôle d’énergie• Estimation d’une « proxy » mesure de
Technologie• Développement d’une méthode pour
estimer la croissance du Produit Intérieur Brut.
Problématique
• L’approche neo-classique économique
– Ignore l’environnement et des ressources naturelles
• Comme facteur de production• Comme bien collectif
– Considère la technologie comme exogène, continue et perpétuelle.
• Mais le progrès technologique est plutôt non linéaire (learning by doing) avec des limites
Une fonction de production
• Décrit les relations entre le « output »(PIB) et les « inputs », (les facteurs de production)
• Cobb-Douglas ont développe la forme le plus utilisé,
Y = A K ααααLββββ where αααα + ββββ = 1• Y=PIB, A=technology multiplier, K=capital,
L=labour, α et β les élasticités de production
Quelques problèmes
• Les ressources naturelles exclus….• Constant returns to scale (rendement constant)• Le dérivative défini la productivité marginal de
chaque facteur en tant que constant, égal au « factor cost » α =0.3 capital, β =0.7 labour.
• Static substitution• Rendu dynamique avec multiplicateur
technologie (A), l’erreur d’une modèle OLS.• PAS de RETROACTION suites aux
changements dans le quantité et qualité du bilan énergétique.
PIB et les facteurs de production, K, L, B, US 1900 -2000
0
5
10
15
20
25
2000199019801970196019501940193019201910
année
inde
x (1
900=
1)
PIB (Y)Capital (K)Labour (L)Ressources Naturelles (B)
PIB empirique et estimé, et l'erreur (le progres te chnologique)
0
5
10
15
20
25
2000199019801970196019501940193019201910
année
inde
x (1
900=
1)
PIB empirique
PIB estimé (Cobb-Douglas)
Erreur (technological progress)
Observations
• Même avec inclusion des ressources naturelles (B) le PIB estimé est inférieur au valeur empirique si on utilise les « factor costs » pour définir les paramètres.
• Le progrès technologique (l’erreur) est responsable pour plus que 80% de la croissance.
• Si on utilise pour prévision on est obligé de faire l’hypothèse que la technologie va développer comme avant. La croissance économique est assuré malgré nos actions.
Industrial Metabolism(Ayres and Simonis 1994)
• New conceptualisation of society’s relation to and pressures on the environment.
• The economy is physically embedded into the environment.
• The economy is an open-system with regards matter & energy.
• Matter and energy societal throughputs must => minimum requirements = technological progress.
• RESOURCE SCARCITY: Societies intervene withpurpose to gain better access to supplies of naturalresources (through technology and resourcesubstitutions .i.e. energy) – a supply-side problem.
• ASSIMILATIVE CAPACITY: Societies must restrictwaste flows to the environment (output side).
The Salter Cycle, an engine for growth.
Lower Prices of
Materials &
Energy
INCREASED REVENUES
Increased Demand for
Final Goods and Services
R&D Substitution of
Knowledge for Labour;
Capital; and Exergy
Product
Improvement
Substitution of
Exergy for Labour
and Capital
Process
Improvement
Lower Limits to
Costs of
Production
Economies of
Scale
Criteria for EnvironmentalAccounting
• Environmental accounting must be:– Politically relevant – strength of the concept to
provide information for policy decision and public discourse.
– Feasibility often requires reduced complexity
– Definition of scale and then system boundaries
– Accurate source information
– Methods to estimate stocks & flows
Energie comme facteur de production – quel mesure faut il?• Pas tout l’énergie utilisé est utile dans
l’économie – conséquence du 2eme loi de Thermodynamique.
• Faut considérer la quantité plus qualité de l’énergie utilisé
• Faut quantifier le progrès technologique et l’effet sur la quantité et le façon qu’on utilise énergie.
Task efficiency: specify service & define the task
• The first objective of any technical study of energy use isto establish a standard of performance.
• What is the difference between a service and a task?– (service) keeping warm, (task) providing heat to a home– (service) structures in society, (task) making aluminium– (service) mobility, (task) moving a vehicle
• Services must consider non-technical trade-offs, tasksrequire only a physics perspective.
• This permits,a) Evaluation of the efficiency of present uses.b) Definition of goals towards which technical
innovation can strive .
Thermodynamics and « available work »
Necessary to define a Minimum Task Energy to allow consideration of :
• Interchanging devices or systems (mass transport vs. Cars)• Seeking technological innovations (aluminium for steel)
• The 1st Law (convervation of energy) isinadequate for considering minimimum taskenergy.
• The 2nd law (the entropy law) indicates that « in any process involving heat, there is an inexorable increase of entropy (disorder), meaning that not all the energy is available in useful form »
The 1st Law (conservation of energy) isinadequate for considering minimimum
task energy.• η = energy transfer (of desired kind) /
energy input• Maximum value may be greater than 1.• No explicit consideration of the quality of
the energy and its ability to do useful work.• Cannot be generalised to complex
systems with work and heat outputs.
The 2nd law (the entropy law)
• indicates that « in any process involving heat, there is an inexorable increase of entropy(disorder), meaning that not all the energy isavailable in useful form »
• For any device or system the 2nd Law Efficiencyε is the ratio of the minimum exergy that couldperform the task (Bmin), to the exergy actuallyconsumed in doing the job (Bactual).
• Its maximum value is 1.• Maximising ε minimises exergy demand and
wastes generated for a given task.
Exergy and Exergy Balance
• Exergy is the useful part of the energy.• There are 4 components:
– Kinetic exergy of bulk motion– Potential gravitational or electro-magnetic field
differentials– Physical exergy from temperature and pressure
differentials– Chemical exergy arising from differences in
chemical composition
• We can ignore the first two for many industrialand economic applications.
Exergy or « Available Work »
• So, not all energy can be made available in useful form(consequence of 2nd Law).
• Available work is an energy measure that is actuallyconsumed in a process.
• Work is the highest quality (lowest entropy) form of energy. It is often called exergy.
• Exergy = The maximum amount of work that a subsystem can do on it’s surroundings as it approachesthermodynamic equilibrium reversibly.
• Exergy is proportional to the future entropy production, but has units of energy.
• Exergy is gained or lost in physical processes.• Minimising exergy consumption is a measureable
objective to optimise energy consuming tasks.
Example: Chemical exergy
• Production of pure iron (Fe2) from iron oxide(Fe2O3)
• This requires exergy from burning coke (pure carbon)
• Carbon dioxide (CO2) is the waste product2Fe2O3 + 3C � 4Fe + 3CO2
Correct mass balance – all atoms in ome out. Conversion of mass causes inevitable joint product CO2
• 0.75 moles of CO2 per Kg of Fe.
Iron production 1
1. 2Fe2O3 + 3C � 4Fe + 3CO2
2. Making 4 moles of Fe requires generation of 3 moles of CO2
3. And 1505.6 Kj whichcomes from thisoxidation of carbon
4. But 3 moles of C contain only 1230.9
5. We need 0.76 C extra. 4.432O2
19.944CO2
410.312C
16.5160Fe2O3
376.456Fe
kJ/moleexergy
Weight
Iron Production 2
2Fe2O3 + 3C � 4Fe + 3CO2Correct mass balance, incorrect exergy balance
2 Fe2O3 + 3.76 C + 0.76 O2 � 4 Fe + 3.76 CO2(33.0) (1542.7) (3.0) (1505.6) (74.8)
On the input side oxygen has been added to fulfill the balance of the extra C required
1580 kJ in � 1580 kJ out• This is for an ideal reversible transformation. No entropy
generated or exergy lost.• Hence 0.94 moles of waste CO2 are inevitable per mole
Fe produced (corresponds to 0.74kg CO2 per kg Fe)• This is the thermodynamic minimum.
Iron Production: Reality
• The 410.3 kJ/mole from source C is never used100% efficiently
• Blast furnace average have efficiencies of 33%.• So, one mole of C one obtains only 135.4kJ• As a result need 12.42 moles of C instead of
3.76.2 Fe2O3 + 12.42 C + 9.42 O2 � 4 Fe + 12.42 CO2+ heat(33.0) (5095.9) (37.7) (1505.6) (247.2)
• B lost = 3413.8 kJ• 2/3 rd of waste produced is unecessary.
Types of Exergy Service
• Prime Movers ( electricity)• Transport• High Temperature Process Heat• Mid and Low Temperature Process Heat• Lighting• Non-Fuel
Petroleum Products
Apparent Consumption
Gasoline
Diesel
Aviation Fuel
Furnace Oil Heavy Fuel Oil
Kerosene
Feedstock
Petroleum Coke
Bitumen/ Waxes
Process Heat
Process Heat
Transport
Space Heating
Non Fuel
LPG
Lighting
Transport
Allocated to gas flows
Electricity
Petroleum Exergy Flows
Coal, Petroleum, Gas: Exergy breakdown by use, US 1900-2000
Figure 8. Coal consumption: Exergy allocation among types of work, USA 1900-1998
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000199019801970196019501940193019201910
year
Fra
ctio
n (%
)
HEATELECTRICITYPRIME MOVERSNON-FUEL
Figure 9. Petroleum and NGL consumption: Exergy allocation among types of work, USA 1900-1998
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
2000199019801970196019501940193019201910
year
Fra
ctio
n (%
)
HEATELECTRICITYPRIME MOVERSNON-FUELLIGHT
Figure 10. Natural Gas consumption: Exergy allocati on among types of work, USA 1900-1998
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2000199019801970196019501940193019201910
year
Fra
ctio
n (%
)
HEATELECTRICITYPRIME MOVERSNON-FUEL
Declining fraction to heat
Increasing fraction to electricity
Transport uses
Total Exergy Breakdown by Use, US 1900-2000
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
2000199019801970196019501940193019201910
year
Fra
ctio
n (%
)
HEATELECTRICITYPRIME MOVERSNON-FUELLIGHT
Heat
Other Prime Movers
Electricity
Non-Fuel
Efficiency (%) Year Kerosene Incandescent Fluorescent Average Efficiency Efficiency (%) 1% 5% 15% Market Share (%) 1900 20% 80% 0% 1.400% 1950 5% 70% 25% 2.433% 1972 1% 65% 33% 2.737% 2000 1% 60% 39% 2.953%
0.00%
0.50%
1.00%
1.50%
2.00%
2.50%
3.00%
3.50%
20001990198019701960195019401930192019101900
year
effic
ienc
y
Lighting Efficiency
Bauxite Ore 3.9kg (4.1MJ)
Cokes 1900 = 20 MJ/kg 2000 = 10 MJ/kg
Electricity 1900 = 190 MJ/kg
2000 = 66 MJ/kg
Aluminium 1kg (32.8MJ)
Refining
Electrolysis
Casting
Coal, Oil, Gas 1900 = 82 MJ/kg
2000 = 28 MJ/kg
Simplifiedprocess view:
Aluminium
MJ/1000kg % of total Coal 4092 5%
Oil 10912 14% Gas 8281 11%
Electricity 56559 70% Total 79845 100.00%
Table 1. Breakdown of total fuel exergy inputs for the production of 1 ton of primary aluminium (source: IAI LCS 2000).
Exergy consumption per kg of Al produced
0
50
100
150
200
250
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year
MJ/
kgBauxite
Coke
Coal, oil and gas
Electricity
Figure 1. Exergy consumed per kg primary aluminium produced. *electricity consumption adapted from Energy Implications of the Changing World of Aluminium Metal Supply (JOM 2004).
Efficiencies and GDP/Exergy Input
0%
5%
10%
15%
20%
25%
30%
35%
40%
2000199019801970196019501940193019201910year
effic
ienc
y
Low Temperature Space Heating
Mechanical Work
Medium Temperature Industrial Heat
High Temperature Industrial Heat
Electric Power Generation &Distribution
Technical efficiency, US 1900-2000
0
0,02
0,04
0,06
0,08
0,1
0,12
0,14
0,16
0,18
25 695 1486 2660 4677 7113
cumula tive prima ry exergy production (eJ)
tech
nica
l eff
icie
ncy
, f
empir ica l (U/ R)"
b ilogistic model
Source Data : Ayres, Ayres and Warr, 2003
Useful Work/GDP Ratios,US 1900-2000
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
5.0
2000199019801970196019501940193019201910
year
ratio
work (Ue) / GDP ratio
work (Ub) / GDP ratio
1st OilCrisis - US
Peak OilProduction
How does our model work ?
Cobb-Douglas or LINEX
• At the ‘total factor productivity’ is REMOVED• Rt natural resource services replaced by Useful
Work, where U = F * R• Ft technical efficiency of energy to work conversion
( )( ) ( ) (
tttt RLKQY = ,,,
( ) ( ) ( ) γβαγβαtttttttt ULKRFLKY ==
−+
+−= 12expU
Lab
K
ULaUYt
REXS economic output module
CumulativeProductionMonetaryMonetary
Output
Gross Output
Labour Capital
Linexparameter a
Linexparameter b
Exe rgyServ ices
ICT Fraction ofCapital
LinexParameter c
ICT CapitalGrowth Rate
Labour supply feedback dynamics
Parameters for USA 1900-2000• Structural Shift Time C=1959, Structural Shift Time D=1920• F Labour Fire Rate A=0.108, F Labour Fire Rate B=0.120• F Labour Hire Rate A=0.124 F Labour Hire Rate B=0.135
LabourLabour Hire
RateLabour Fire
Rate
FractionalLabour Hire Rate
A
FractionalLabour Hire Rate
B
FractionalLabour Fire Rate
A
FractionalLabour Fire Rate
B
Structural ShiftTime C
<Time>
Structural ShiftTime D
Labour “hire and fire” parametersSimulated labour hire and fire rate, USA 1900-2000
0
0,05
0,1
0,15
0,2
0,25
0,3
0,35
0,4
0,45
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year
rate
(st
anda
rdis
ed la
bou
r un
its p
er y
ear)
Labour Hire Rate
Labour Fire Rate
Labour – validation by empirical fitSimulated and empirical labour, USA 1900-2000
0
0,5
1
1,5
2
2,5
3
3,5
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 2000
year
norm
alis
ed
labo
ur (
1900
=1)
empirical
simulated
Capital accumulation feedback loop
Parameters for USA 1900-2000• Investment Fraction A=0.081 Investment Fraction B=0.074
• Depreciation Rate A=0.059 Depreciation Rate B=0.106
• Structural Shift Time A=1970 Structural Shift Time B=1930
CapitalInvestment Depreciation
Inve stmentFraction
<Time>
DepreciationRate
<GrossOutput>
InvestmentFraction A
InvestmentFraction B
DepreciationRate A
DepreciationRate B
Structural ShiftTime A
Structural ShiftTime B
Capital investment and depreciationSimulated investment and depreciation, USA 1900-200 0
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year
norm
alis
ed c
apita
l (19
00=
1)
investment
depreciation
Capital – validation by empirical fitSimulated and empirical capital, USA 1900-2000
0
2
4
6
8
10
12
14
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year
norm
alis
ed c
apita
l (19
00=
1)
empirical
simulated
Output – validation of full model, US 1900-2000
0
2
4
6
8
10
12
14
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year
norm
alis
ed c
apita
l (19
00=1)
empirical
simulated
LINEX fits for GDP, Japan and US 1900-2000.
0
1000
2000
3000
4000
5000
6000
7000
8000
1900 1920 1940 1960 1980
year
GD
P (
thou
sand
bill
ion
1992
$)
empirical GDP, Japan
predicted GDP, Japan
empirical GDP, US
predicted GDP, US
Estimates of GDP, France 1960-2000
0
0.5
1
1.5
2
2.5
3
3.5
4
1963 1968 1973 1978 1983 1988 1993
outp
ut (
1960
=1)
YLINEXTime Dependent CDTime Average CD
A commonly used reference modeEnergy Intensity of Capital, USA 1900-2000.
8
10
12
14
16
18
20
22
24
26
28
20001990198019701960195019401930192019101900
year
inde
x
b/k - total primary exergy supply(energy carriers, metals, minerals and phytomass exergy)
e/k - total fuel exergy supply(energy carriers only)
Start of the Great Depression
End of World War II
The REXS alternativeSimulated and empirical primary exergy intensity of output,
USA 1900-2000
0
0.2
0.4
0.6
0.8
1
1.2
1900 1910 1920 1930 1940 1950 1960 1970 1980 1990
year
r/y
(190
0=1)
empirical
simulated
Average rate of decline 1.2% per annum
Declining resourceintensity of output
Continuing historicaltrends of technicale fficiency growth
Use ful worksupply
Economicoutput
cumulativeoutput
experience
cumulative exergyproductionexperience
The “dematerialising” dynamics
Primary exergy intensity ( B/GDP) of output decay feedback mechanism.
Parameters• Rate of Decay = Fractional
Decay Rate*Primary Exergy Intensity of Output
• Fractional Decay Rate=0.012
Primary Exe rgyIntensity of Output
Rate of Decay
FractionalDecay RatePrimary Exe rgy
Demand
<GrossOutput>
Lower Prices of
Materials &
Energy
INCREASED REVENUES
Increased Demand for
Final Goods and Services
R&D Substitution of
Knowledge for Labour;
Capital; and Exergy
Product
Improvement
Substitution of
Exergy for Labour
and Capital
Process
Improvement
Lower Limits to
Costs of
Production
Economies of
Scale
To the right:
Processes aggregated inthe REXS dynamics
Projections of future outputAltering the future rates of the energy intensity o f output
•The average decay rate of the exergy intensity of output ( R/GDP) for the period 1900-1998 is 1.2%
•The simulations involved increasing or decreasing this parameter from 1998 onwards, while keeping the values of all other parameters fixed.
•The following illustrations provide a summary of the results.
Varying rates of dematerialisation
Primary Exergy Intensity of Output Decline Rate
0
-0.5
-1
-1.5
-2 1900 1938 1975 2013 2050
Year
(%)
historical trend 50% 75% 95% 100%
The constant rate of exergy intensity decline was altered to vary between –0.55 and –1.65 % p.a.
Effects on ‘efficiency’ improvements
Technical Efficiency of Primary Exergy Conversion 0.4
0.3
0.2
0.1
0 1900 1938 1975 2013 2050
Year
historical data 50% 75% 95% 100%
effic
ienc
y
The ‘business as usual’ case:
If technical efficiency does not increase in pace with ‘de-materialisation’
The rate of growth slows .
GDP forecasts “dematerialisation scenarios” ,US 2000-2050
Gross Output 200
150
100
50
0 1900 1938 1975 2013 2050
Year
historical data 50% 75% 95% 100%
Inde
x (1
900=
1)
The sensitivity of future projections of GDP were assessed, the red line indicates the ‘business as usual’for a fractional decay rate of energy intensity of output –1.2 % per annum and technical efficiency at 1% p.a.
0
20
40
60
80
100
120
1950 1975 2000 2025 2050
year
GD
P (
1900
=1)
1.2% per annum1.3% per annum1.4% per annum1.5% per annumempirical
Historical and forecast GDP for alternative rates of decline of the energy intensity of
output, US 1900-2000
Forecast GDP growth rates for three alternative technology scenarios (US 2050).
2.63%1.23%1.75%0.89%0.92%0.62%Maximum
2.20%1.18%0.38%0.72%-1.29%0.40%Average
1.94%1.11%-1.89%0.43%-2.97%0.16%Minimum
GDPfGDPfGDPfGrowth rate
HighMidLow
Alternative Technology Scenarios
Note the feedback between f growth and GDP growth
Historical and forecast technical efficiency of ene rgy conversion, for 3 alternative rates of technical
efficiency growth, US 1950-2000.
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
1950 1975 2000 2025 2050
year
tech
nica
l effi
cien
cy (
f)
lowmidhighempirical
Historical and forecast GDP, for 3 alternative rates of technical efficiency growth, US 1950-
2050
0
10
20
30
40
50
60
70
1950 1975 2000 2025 2050
year
GD
P (
1900
=1)
lowmidhighempirical
Conclusions
• Travail utile comme facteur de production
• Application du 2°loi pour « proxy » de progrès technologique
• Fonction LINEX et représentation Systèmes Dynamique permettant– Estimation historique– « substitution dynamique » suite aux progrès– Feedback entre progrès technologique et le quantité
et qualité des sources énergétique et l’efficacitéd’utilisation