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Who pays for climate change mitigation:
Integrated assessment of equitable emissions budgets
in ETSAP-TIAM-MACRO
James Glynn, Socrates Kypreos, Antti Lehtila, Maurizio Gargiulo, Brian Ó’GallachΓ³ir
68th ETSAP Workshop
Sophia Antipolis, FRANCE | 23rd October 2015
Acknowledgements
β€’ ETSAP TIAM Project Group
β€’ MSA Developers Socrates Kypreos (PSI) & Antti
Lehtila (VTT)
Outline
β€’ Overview of ETSAP-TIAM Macro Stand Alone
(MSA)
β€’ 2Β°C Cumulative CO2 Budget Scenario
β€’ Regional Macroeconomic losses
β€’ Post Optimisation Analysis (POA)
β€’ Equitable Efficient Burden Sharing
β€’ Appropriate capital transfers?
β€’ Contract & Convergence Grandfathering to equal/Cap
β€’ Compensation rules
β€’ Fund technology transfer to LDCs
β€’ Equity based on historical emissions
GLOBAL ETSAP-TIAM model
Built with the TIMES model generator
β€’ The Integrated MARKAL-EFOM System of IEA-ETSAP
β€’ Linear programming bottom-up energy system model
β€’ Integrated model of the entire energy system
β€’ Prospective analysis on medium to long term horizon
(2100)
β€’ Demand driven by exogenous energy service demands
β€’ Partial and dynamic equilibrium (perfect market)
β€’ Hybrid General Equilibrium using MSA
β€’ Optimal technology selection
β€’ Minimizes the total system cost
β€’ Environmental constraints
β€’ Integrated Climate Model
β€’ 15 Region Global Model
β€’ Price-elastic demands in the TIMES-ED version
β€’ Not included in Macro-Stand-Alone runs
ETSAP-TIAM 15 Regions
AFR
CAN
USA
MEX
CSA
WEU
EEU
MEA
IND
CHI
SKO
JPN
AUS
ODA
Res Heat
Ind Heat
Person Km
Freight Km…
Transformation
Refinery,
Power Plants,
Gas Network,
Briquetting...
Primary energy prices,
Resource availability
Primary energy Final energy Service Demands
GDP, Population,
Industrial Activity
TIMES-MACRO
Domestic
sources
Imports
Consumption
Industry,
Services,
Transport,
Residential...
MACRO Stand Alone (MSA)
General Equilibrium
Macroeconomic Model
Energy Costs
Labour
ConsumptionInvestmentCapital
Demand
Response
CrudeOil
RawGas
Gasoline
NaturalGas
Electrcity
π‘€π‘Žπ‘₯ π‘ˆ =
𝑑=1
𝑇
π‘Ÿ
𝑛𝑀𝑑 π‘Ÿ . 𝑝𝑀𝑑𝑑. π‘‘π‘“π‘Žπ‘π‘‘ π‘Ÿ,𝑑. 𝑙𝑛 πΆπ‘Ÿ,𝑑
οƒ₯ οƒ₯ο€½ οƒŽ
ο€­

R
r YEARSy
yREFYR
yr yrANNCOSTdNPVMin
1
, ),()1(
Coal
Heat
Light
Motion
Partial Equilibrium
Scenario Outline
β€’ BASE
β€’ Reference energy system, least cost optimal without
policy constraints
β€’ Assumes rational optimising choices: not equal to
business as usual
β€’ 2DS – Remaining CO2 Emission Quota Budget
β€’ BASE with a cumulative on CO2 emissions constraint
to achieve the target 2Β°C (50% probability) set in
Friedlingston et al.
β€’ 1400Gt CO2e 2020 – 2100
β€’ No Significant policy action to 2020
β€’ Macro Stand Alone (MSA) active to re-estimate
energy service demands relative to available capital &
investment
Global Energy Balance - 2012
Data: IEA Energy Balances of OECD Countries, IEA Energy Balance of Non-OECD Countries
Final Energy - 2DS 2100
Net CO2 Emissions & CO2 Price
-10
0
10
20
30
40
50
60
70
BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS
2010 2020 2030 2040 2050 2060 2070 2080 2090 2100
GtCO2
WEU
USA
SKO
ODA
MEX
MEA
JPN
IND
FSU
EEU
CSA
CHI
CAN
AUS
AFR
CSA
AFR
USA
CHI
IND
MEA
WEU
FSU
$66 $108 $175 $286 $465
$758
$1,235
$2,012
$3,277
$-
$1,000
$2,000
$3,000
$4,000
2020 2030 2040 2050 2060 2070 2080 2090 2100
$/tCo2
Post Optimisation Analysis –
Burden Sharing Rules
β€’ Efficiency [Eff]
β€’ Least Cost Optimal Energy System with Maximised
Discounted Utility under cumulative emission quota of
1,400GtCO2e
β€’ TIAM-MSA Result without Post Optimisation Analysis
β€’ Rule 1 – Equalitarian Emissions Per Capita
β€’ Rule 2 – Equalise GDP loss per region
β€’ Rule 3 – Compensate Developing countries for any
increases in energy costs
β€’ Rule 4 – Compensate Developing Countries for GDP
loss
β€’ Rule 6 – Equalise cumulative emissions per capita
β€’ Rule 7 – Budget of future emissions inversely based
on historical cumulative emissions per capita
Rule 1 (R1) – Equalitarian
Grandfathering to 2050 then equal
emission/capita
CAN
USA
SKO, AUS
JPN, WEU, FSU
MEA, EEU, CHI
CSA, MEX
ODA, IND, AFR
-5
0
5
10
15
20
2020 2030 2040 2050 2060 2070 2080 2090 2100
GtCO2/Capita
Rule 1 - Equalitarian
-6
-4
-2
-
2
4
6
2020
2030
2040
2050
2060
2070
2080
2090
2100
GtCO2/yr
Carbon Traded
$-20
$-15
$-10
$-5
$-
$5
$10
$15
$20
2020
2030
2040
2050
2060
2070
2080
2090
2100
TnUSD
Capital Transfers WEU
USA
SKO
ODA
MEX
MEA
JPN
IND
FSU
EEU
CSA
CHI
CAN
AUS
AFR
-20.0% 0.0% 20.0%
GDP Change
-20.0%
-10.0%
0.0%
10.0%
20.0%
AFR AUS CAN CHI CSA EEU FSU IND JPN MEA MEX ODA SKO USA WEU World
%GDPChange
Efficient Rule 1
Rule 3/4 – Compensate Developing
countries for increased energy costs or
GDP Loss
-0.5
-0.4
-0.3
-0.2
-0.1
-
0.1
0.2
0.3
0.4
0.5
2020
2030
2040
2050
2060
2070
2080
2090
2100
GtCO2/yr
Rule 3 - Carbon Traded
-$2
-$1
-$1
$-
$1
$1
$2
2020
2030
2040
2050
2060
2070
2080
2090
2100
TnUSD
Rule 3 - Capital Transfers WEU
USA
SKO
ODA
MEX
MEA
JPN
IND
FSU
EEU
CSA
CHI
CAN
AUS
AFR
-8
-6
-4
-2
0
2
4
6
8
2020
2030
2040
2050
2060
2070
2080
2090
2100
GtCO2/yr
Rule 4 - Carbon Traded
$-10
$-8
$-6
$-4
$-2
$-
$2
$4
$6
$8
$10 2020
2030
2040
2050
2060
2070
2080
2090
2100
TnUSD
Rule 4 – Capital Transfers
WEU
USA
SKO
ODA
MEX
MEA
JPN
IND
FSU
EEU
CSA
CHI
CAN
AUS
AFR
-20.0% 0.0% 20.0%
% GDP Change
-20.0% 0.0% 20.0%
Interpreting the Brazilian Proposal
Historical and Future emissions
What is an equitable budget allocation?
-100.0
0.0
100.0
200.0
300.0
400.0
500.0
600.0
700.0
AFR AUS CAN CHI CSA EEU FSU IND JPN MEA MEX ODA SKO USA WEU
CarbonDioxideEmissions(GtCO2)
Historical Emissions (1751-2010) Future 2D CO2 Emissions
Equal CO2 Budget Population Weighted CO2 Budget
Cumulative regional CO2 emissions budgets for efficient, regional equalisation of cumulative emissions, and regional per capita
equalisation of cumulative emissions (Historical Data source: Carbon Dioxide Information Analysis Center http://cdiac.ornl.gov/).
Rule 6 & Rule 7 explained
β€’ Rule 6
β€’ Allocates future emissions permits on a cumulative equal budget
per capita between 1790 and 2100. Regions that emit more than
their allocated CO2 budget must purchase permits from those
that have not broken their budget in any given time step.
Regions that have already spent their cumulative CO2 budget
pay into a clean development mechanism (CDM), which
distributes their carbon debt equally per time step at the given
marginal cost of carbon at that time step.
β€’ Rule 7
β€’ Interprets the Brazil proposal as a combination of an
interpolation grandfathering rule from the current emissions per
capita regionally to allocation of future emissions based on
population intensity per cumulative emissions. This balances
historical cumulative emissions responsibility and population
growth. This allows developing countries a larger share of future
emission based on low historical emissions, but become bound
by an increasing share of a declining global emission budget per
year.
What is an Equitable Rule?
Brazilian Rule 6 & 7
-20.0%
-10.0%
0.0%
10.0%
20.0%
USA JPN CAN WEU AUS SKO EEU MEX MEA CSA FSU CHI ODA IND AFR World
GDPChange%
Efficient
Rule 6
Rule 7
Rule (6)
Rule (7)
0
1
2
3
4
5
6
7
202020302040205020602070208020902100
tCO2/yr
Carbon Traded Capital Transfers % GDP Change Brazilian Proposal for burden sharing.
Carbon Permits GtCO2 (Left), Capital
Transfers Tn US Dollars (Centre) per region
per time period and Cumulative (2010 –
2100) GDP loss per region (Right). Rule (6)
Regional allocation of cumulative population
weighted emissions permits and Rule (7)
Brazil rule allocation weighted to population
per cumulative emissions.
Conclusions
β€’ The 2 Degree goal is barely technically feasible and comes with
prohibitively expensive marginal abatement costs.
β€’ The technologically efficient global cumulative cost of the 2 degree
goal is 5% GDP on aggregate with regional variations of between
2.5% and 11% GDP.
β€’ Equitable burden sharing rules require massive capital transfers of
trillions US $ (undiscounted) per year in the second half of the
century.
β€’ Emissions per capita budgets are not necessarily in the best
interests of developing countries
β€’ China is best off when the burden sharing rules focus on equalisation for
economic losses,
β€’ India, Other developing Asia and Africa have greater economic benefits
when rules focus on equitable cumulative emissions per capita.
β€’ These burden sharing rules are politically infeasible given the scale
of capital transfers
β€’ Compensating LDCs for relative energy cost losses has the smallest
capital transfers and potentially the most politically favourable rule?
β€’ Rule 6 or Rule 7 is probably the most equitable, but politically
difficult messaging and possibly counter productive by induced
delayed action
Environmental Research Institute
InstiΓΊd Taighde Comshaoil
Energy Policy and Modelling Group
www.ucc.ie/energypolicy
@james_glynn
james.glynn@umail.ucc.ie
Model Emissions Scenarios
1150 scenarios from the IPCC Fifth Assessment Report are shown
Data Source: AR5 Emissions Database
https://secure.iiasa.ac.at/web-apps/ene/AR5DB/
Cumulative Emissions Budget
EU28
USA
CHI
IND
ROW
ETSAP-TIAM MSA (TMSA)
Macro Stand Alone
π‘€π‘Žπ‘₯ π‘ˆ =
𝑑=1
𝑇
π‘Ÿ
𝑛𝑀𝑑 π‘Ÿ . 𝑝𝑀𝑑𝑑. π‘‘π‘“π‘Žπ‘π‘‘ π‘Ÿ,𝑑. 𝑙𝑛 πΆπ‘Ÿ,𝑑 (1) (MSA OBJz)
π‘Œπ‘Ÿ,𝑑 = πΆπ‘Ÿ,𝑑 + πΌπ‘π‘‰π‘Ÿ,𝑑 + πΈπΆπ‘Ÿ,𝑑 + 𝑁𝑇𝑋(π‘›π‘šπ‘Ÿ) π‘Ÿ,𝑑 (2)
π‘Œπ‘Ÿ,𝑑 = π‘Žπ‘˜π‘™ π‘Ÿ βˆ™ πΎπ‘Ÿ,𝑑
π‘˜π‘π‘£π‘  π‘Ÿβˆ™πœŒ π‘Ÿ
βˆ™ 𝑙 π‘Ÿ,𝑑
(1βˆ’π‘˜π‘π‘£π‘  π‘Ÿ)𝜌 π‘Ÿ
+
π‘˜
𝑏 π‘Ÿ,π‘˜ βˆ™ π·πΈπ‘€π‘Ÿ,𝑑,π‘˜
𝜌 π‘Ÿ
1
𝜌 π‘Ÿ
(3)
β€’ nwt – Negishi Weights
β€’ pwt – weight Multiplier
β€’ dfact – utility discount factor
β€’ C - Consumption
β€’ Y – Production
β€’ INV – Investment
β€’ EC – Energy Cost
β€’ NTX – Net exports
β€’ akl – production fn constant
β€’ K – Capital
β€’ kpvs – capital value share
β€’ l - Labour annual growth
β€’ b – Demand coefficient
β€’ p – elasticity of substitution
β€’ DEM - Energy Demands
οƒ₯ οƒ₯ο€½ οƒŽ
ο€­

R
r YEARSy
yREFYR
yr yrANNCOSTdNPVMin
1
, ),()1( (TIAM OBJz)

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Who pays for climate change mitigation? Integrated Assessment of equitable emissions budgets in ETSAP-TIAM-MACRO

  • 1. Who pays for climate change mitigation: Integrated assessment of equitable emissions budgets in ETSAP-TIAM-MACRO James Glynn, Socrates Kypreos, Antti Lehtila, Maurizio Gargiulo, Brian Ó’GallachΓ³ir 68th ETSAP Workshop Sophia Antipolis, FRANCE | 23rd October 2015
  • 2. Acknowledgements β€’ ETSAP TIAM Project Group β€’ MSA Developers Socrates Kypreos (PSI) & Antti Lehtila (VTT)
  • 3. Outline β€’ Overview of ETSAP-TIAM Macro Stand Alone (MSA) β€’ 2Β°C Cumulative CO2 Budget Scenario β€’ Regional Macroeconomic losses β€’ Post Optimisation Analysis (POA) β€’ Equitable Efficient Burden Sharing β€’ Appropriate capital transfers? β€’ Contract & Convergence Grandfathering to equal/Cap β€’ Compensation rules β€’ Fund technology transfer to LDCs β€’ Equity based on historical emissions
  • 4. GLOBAL ETSAP-TIAM model Built with the TIMES model generator β€’ The Integrated MARKAL-EFOM System of IEA-ETSAP β€’ Linear programming bottom-up energy system model β€’ Integrated model of the entire energy system β€’ Prospective analysis on medium to long term horizon (2100) β€’ Demand driven by exogenous energy service demands β€’ Partial and dynamic equilibrium (perfect market) β€’ Hybrid General Equilibrium using MSA β€’ Optimal technology selection β€’ Minimizes the total system cost β€’ Environmental constraints β€’ Integrated Climate Model β€’ 15 Region Global Model β€’ Price-elastic demands in the TIMES-ED version β€’ Not included in Macro-Stand-Alone runs
  • 6. Res Heat Ind Heat Person Km Freight Km… Transformation Refinery, Power Plants, Gas Network, Briquetting... Primary energy prices, Resource availability Primary energy Final energy Service Demands GDP, Population, Industrial Activity TIMES-MACRO Domestic sources Imports Consumption Industry, Services, Transport, Residential... MACRO Stand Alone (MSA) General Equilibrium Macroeconomic Model Energy Costs Labour ConsumptionInvestmentCapital Demand Response CrudeOil RawGas Gasoline NaturalGas Electrcity π‘€π‘Žπ‘₯ π‘ˆ = 𝑑=1 𝑇 π‘Ÿ 𝑛𝑀𝑑 π‘Ÿ . 𝑝𝑀𝑑𝑑. π‘‘π‘“π‘Žπ‘π‘‘ π‘Ÿ,𝑑. 𝑙𝑛 πΆπ‘Ÿ,𝑑 οƒ₯ οƒ₯ο€½ οƒŽ ο€­  R r YEARSy yREFYR yr yrANNCOSTdNPVMin 1 , ),()1( Coal Heat Light Motion Partial Equilibrium
  • 7. Scenario Outline β€’ BASE β€’ Reference energy system, least cost optimal without policy constraints β€’ Assumes rational optimising choices: not equal to business as usual β€’ 2DS – Remaining CO2 Emission Quota Budget β€’ BASE with a cumulative on CO2 emissions constraint to achieve the target 2Β°C (50% probability) set in Friedlingston et al. β€’ 1400Gt CO2e 2020 – 2100 β€’ No Significant policy action to 2020 β€’ Macro Stand Alone (MSA) active to re-estimate energy service demands relative to available capital & investment
  • 8. Global Energy Balance - 2012 Data: IEA Energy Balances of OECD Countries, IEA Energy Balance of Non-OECD Countries
  • 9. Final Energy - 2DS 2100
  • 10. Net CO2 Emissions & CO2 Price -10 0 10 20 30 40 50 60 70 BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS BASE 2DS 2010 2020 2030 2040 2050 2060 2070 2080 2090 2100 GtCO2 WEU USA SKO ODA MEX MEA JPN IND FSU EEU CSA CHI CAN AUS AFR CSA AFR USA CHI IND MEA WEU FSU $66 $108 $175 $286 $465 $758 $1,235 $2,012 $3,277 $- $1,000 $2,000 $3,000 $4,000 2020 2030 2040 2050 2060 2070 2080 2090 2100 $/tCo2
  • 11. Post Optimisation Analysis – Burden Sharing Rules β€’ Efficiency [Eff] β€’ Least Cost Optimal Energy System with Maximised Discounted Utility under cumulative emission quota of 1,400GtCO2e β€’ TIAM-MSA Result without Post Optimisation Analysis β€’ Rule 1 – Equalitarian Emissions Per Capita β€’ Rule 2 – Equalise GDP loss per region β€’ Rule 3 – Compensate Developing countries for any increases in energy costs β€’ Rule 4 – Compensate Developing Countries for GDP loss β€’ Rule 6 – Equalise cumulative emissions per capita β€’ Rule 7 – Budget of future emissions inversely based on historical cumulative emissions per capita
  • 12. Rule 1 (R1) – Equalitarian Grandfathering to 2050 then equal emission/capita CAN USA SKO, AUS JPN, WEU, FSU MEA, EEU, CHI CSA, MEX ODA, IND, AFR -5 0 5 10 15 20 2020 2030 2040 2050 2060 2070 2080 2090 2100 GtCO2/Capita
  • 13. Rule 1 - Equalitarian -6 -4 -2 - 2 4 6 2020 2030 2040 2050 2060 2070 2080 2090 2100 GtCO2/yr Carbon Traded $-20 $-15 $-10 $-5 $- $5 $10 $15 $20 2020 2030 2040 2050 2060 2070 2080 2090 2100 TnUSD Capital Transfers WEU USA SKO ODA MEX MEA JPN IND FSU EEU CSA CHI CAN AUS AFR -20.0% 0.0% 20.0% GDP Change -20.0% -10.0% 0.0% 10.0% 20.0% AFR AUS CAN CHI CSA EEU FSU IND JPN MEA MEX ODA SKO USA WEU World %GDPChange Efficient Rule 1
  • 14. Rule 3/4 – Compensate Developing countries for increased energy costs or GDP Loss -0.5 -0.4 -0.3 -0.2 -0.1 - 0.1 0.2 0.3 0.4 0.5 2020 2030 2040 2050 2060 2070 2080 2090 2100 GtCO2/yr Rule 3 - Carbon Traded -$2 -$1 -$1 $- $1 $1 $2 2020 2030 2040 2050 2060 2070 2080 2090 2100 TnUSD Rule 3 - Capital Transfers WEU USA SKO ODA MEX MEA JPN IND FSU EEU CSA CHI CAN AUS AFR -8 -6 -4 -2 0 2 4 6 8 2020 2030 2040 2050 2060 2070 2080 2090 2100 GtCO2/yr Rule 4 - Carbon Traded $-10 $-8 $-6 $-4 $-2 $- $2 $4 $6 $8 $10 2020 2030 2040 2050 2060 2070 2080 2090 2100 TnUSD Rule 4 – Capital Transfers WEU USA SKO ODA MEX MEA JPN IND FSU EEU CSA CHI CAN AUS AFR -20.0% 0.0% 20.0% % GDP Change -20.0% 0.0% 20.0%
  • 15. Interpreting the Brazilian Proposal Historical and Future emissions What is an equitable budget allocation? -100.0 0.0 100.0 200.0 300.0 400.0 500.0 600.0 700.0 AFR AUS CAN CHI CSA EEU FSU IND JPN MEA MEX ODA SKO USA WEU CarbonDioxideEmissions(GtCO2) Historical Emissions (1751-2010) Future 2D CO2 Emissions Equal CO2 Budget Population Weighted CO2 Budget Cumulative regional CO2 emissions budgets for efficient, regional equalisation of cumulative emissions, and regional per capita equalisation of cumulative emissions (Historical Data source: Carbon Dioxide Information Analysis Center http://cdiac.ornl.gov/).
  • 16. Rule 6 & Rule 7 explained β€’ Rule 6 β€’ Allocates future emissions permits on a cumulative equal budget per capita between 1790 and 2100. Regions that emit more than their allocated CO2 budget must purchase permits from those that have not broken their budget in any given time step. Regions that have already spent their cumulative CO2 budget pay into a clean development mechanism (CDM), which distributes their carbon debt equally per time step at the given marginal cost of carbon at that time step. β€’ Rule 7 β€’ Interprets the Brazil proposal as a combination of an interpolation grandfathering rule from the current emissions per capita regionally to allocation of future emissions based on population intensity per cumulative emissions. This balances historical cumulative emissions responsibility and population growth. This allows developing countries a larger share of future emission based on low historical emissions, but become bound by an increasing share of a declining global emission budget per year.
  • 17. What is an Equitable Rule? Brazilian Rule 6 & 7 -20.0% -10.0% 0.0% 10.0% 20.0% USA JPN CAN WEU AUS SKO EEU MEX MEA CSA FSU CHI ODA IND AFR World GDPChange% Efficient Rule 6 Rule 7 Rule (6) Rule (7) 0 1 2 3 4 5 6 7 202020302040205020602070208020902100 tCO2/yr Carbon Traded Capital Transfers % GDP Change Brazilian Proposal for burden sharing. Carbon Permits GtCO2 (Left), Capital Transfers Tn US Dollars (Centre) per region per time period and Cumulative (2010 – 2100) GDP loss per region (Right). Rule (6) Regional allocation of cumulative population weighted emissions permits and Rule (7) Brazil rule allocation weighted to population per cumulative emissions.
  • 18. Conclusions β€’ The 2 Degree goal is barely technically feasible and comes with prohibitively expensive marginal abatement costs. β€’ The technologically efficient global cumulative cost of the 2 degree goal is 5% GDP on aggregate with regional variations of between 2.5% and 11% GDP. β€’ Equitable burden sharing rules require massive capital transfers of trillions US $ (undiscounted) per year in the second half of the century. β€’ Emissions per capita budgets are not necessarily in the best interests of developing countries β€’ China is best off when the burden sharing rules focus on equalisation for economic losses, β€’ India, Other developing Asia and Africa have greater economic benefits when rules focus on equitable cumulative emissions per capita. β€’ These burden sharing rules are politically infeasible given the scale of capital transfers β€’ Compensating LDCs for relative energy cost losses has the smallest capital transfers and potentially the most politically favourable rule? β€’ Rule 6 or Rule 7 is probably the most equitable, but politically difficult messaging and possibly counter productive by induced delayed action
  • 19. Environmental Research Institute InstiΓΊd Taighde Comshaoil Energy Policy and Modelling Group www.ucc.ie/energypolicy @james_glynn james.glynn@umail.ucc.ie
  • 20. Model Emissions Scenarios 1150 scenarios from the IPCC Fifth Assessment Report are shown Data Source: AR5 Emissions Database https://secure.iiasa.ac.at/web-apps/ene/AR5DB/
  • 22. ETSAP-TIAM MSA (TMSA) Macro Stand Alone π‘€π‘Žπ‘₯ π‘ˆ = 𝑑=1 𝑇 π‘Ÿ 𝑛𝑀𝑑 π‘Ÿ . 𝑝𝑀𝑑𝑑. π‘‘π‘“π‘Žπ‘π‘‘ π‘Ÿ,𝑑. 𝑙𝑛 πΆπ‘Ÿ,𝑑 (1) (MSA OBJz) π‘Œπ‘Ÿ,𝑑 = πΆπ‘Ÿ,𝑑 + πΌπ‘π‘‰π‘Ÿ,𝑑 + πΈπΆπ‘Ÿ,𝑑 + 𝑁𝑇𝑋(π‘›π‘šπ‘Ÿ) π‘Ÿ,𝑑 (2) π‘Œπ‘Ÿ,𝑑 = π‘Žπ‘˜π‘™ π‘Ÿ βˆ™ πΎπ‘Ÿ,𝑑 π‘˜π‘π‘£π‘  π‘Ÿβˆ™πœŒ π‘Ÿ βˆ™ 𝑙 π‘Ÿ,𝑑 (1βˆ’π‘˜π‘π‘£π‘  π‘Ÿ)𝜌 π‘Ÿ + π‘˜ 𝑏 π‘Ÿ,π‘˜ βˆ™ π·πΈπ‘€π‘Ÿ,𝑑,π‘˜ 𝜌 π‘Ÿ 1 𝜌 π‘Ÿ (3) β€’ nwt – Negishi Weights β€’ pwt – weight Multiplier β€’ dfact – utility discount factor β€’ C - Consumption β€’ Y – Production β€’ INV – Investment β€’ EC – Energy Cost β€’ NTX – Net exports β€’ akl – production fn constant β€’ K – Capital β€’ kpvs – capital value share β€’ l - Labour annual growth β€’ b – Demand coefficient β€’ p – elasticity of substitution β€’ DEM - Energy Demands οƒ₯ οƒ₯ο€½ οƒŽ ο€­  R r YEARSy yREFYR yr yrANNCOSTdNPVMin 1 , ),()1( (TIAM OBJz)