AIM/CGE V2.0 Model Formula

Abstract

This chapter describes the (1) model structure of AIM/CGE (Asia-Pacific Integrated Model/Computable General Equilibrium), (2) data structure (social accounting matrix (SAM)), and (3) formula and list of sets, parameters, equations, and variables. The aim of this chapter is to present all equations written in the model which is used in the other chapter’s analysis and make the analysis made in this book transparent.

Mathematical Statement

12.1.1 Sets

a ∈ A :

:  a set of activities

a ∈ ACES(⊂A):

:  a set for nonenergy transformation

a ∈ ACES_ENE(⊂A):

:  a set of activities with a CES function at energy nest

a ∈ ALEO(⊂A):

:  a set for energy transformation

a ∈ ALEO_ENE(⊂A):

:  a set of activities with a CES function at energy nest

aagg ∈ Aagg :

:  a set of aggregated activity

c ∈ C :

:  a set of commodities (also referred to as c’ and C’)

C_CCS :

:  a set of CCS service

c ∈ CD(⊂C):

:  a set of commodities with domestic sales of domestic output

c ∈ CDN(⊂C):

:  commodities without domestic market sales of domestic output (complement of CD)

c ∈ CE(⊂C):

:  a set of exported commodities (with domestic production)

c ∈ CEN(⊂C):

:  non-exported commodities (complement of CE)

c ∈ CM(⊂C):

:  a set of imported commodities

c ∈ CMN(⊂C):

:  a set of nonimported commodities

c ∈ CNEN :

:  a set of nonenergy commodities

c ∈ C_TRS :

:  a set of transport service

c ∈ CX(⊂C):

:  a set of commodities with domestic output

c ∈ ENE :

:  a set of energy commodities (COM_COA, COM_OIL, COM_GAS, COM_P_P, COM_COP, COM_ELY, COM_GDT)

c ∈ ENEENDMAP(c, K_END):

:  Mapping for enduse energy kinds and commodity

ch ∈ CH :

:  household commodity category ch

emcm ∈ EMCM :

:  a subset of emission reduction countermeasures

emcm ∈ EMCM0(⊂EMCM):

:  a subset of emission reduction countermeasures which are for nonenergy-related emissions

emcm ∈ EMCM1(⊂EMCM):

:  a subset of emission reduction countermeasures which are for energy-related emissions

emcm ∈ EMCM2(⊂EMCM):

:  a subset of emission reduction countermeasures which are for biomass power plant absorption

emcm ∈ EMCM :

:  a set of emission reduction countermeasures (CCS)

f ∈ F(=F ^′):

:  a set of factors

f ∈ FCAP(=F):

:  a set of capital (new and old, “ncap” and “cap”)

f ∈ F _lab :

:  labor (skilled and unskilled labor)

g ∈ G :

:  a set of emission gases

h ∈ H(⊂INSDNG):

:  a set of households

i ∈ INS :

:  a set of institutions (domestic and rest of the world)

i ∈ INSD(⊂INS):

:  a set of institutions (domestic and rest of the world)

i ∈ INSDNG(⊂INSD):

:  a set of domestic nongovernment institutions

emsc ∈ EMSC :

:  a set of emission sources

i ∈ I :

:  energy service i

k ∈ K_END :

:  energy kind for end-use device

l ∈ L :

:  end-use device l

LI(l, i):

:  mapping device l and energy service i

r ∈ R :

:  a set of regions

ragg ∈ Ragg :

:  a set of aggregated regions

t ∈ T :

:  a set of time series

tc ∈ TC :

:  a set of technology

tr ∈ TR :

:  a set of transport mode

12.1.2 Parameters

12.1.2.1 Latin Letters

ad _r,ac,l,i :

:  supply output of service i per operating unit of device l in sector ac (same as specific service output)

${aeei}_{r, c, ac}^t$ :

:  annual AEEI rate of energy commodity c, sector ac, time t, and region r

Baseyear :

:  base year

bioc _r,ac :

:  biomass consumption coefficient to the activity level of sector ac

biod _r,ac :

:  decreasing rate of biomass consumption of sector ac

careneeff _r,h :

:  household passenger car energy coefficient

cdst_wd :

:  conversion factor for carbon density

cf_v2t :

:  conversion factor from volume to ton

CPI_base _r :

:  base year’s CPI

crt_in _r :

:  transfer from rest of the world

crt_out _r :

:  transfer to rest of the world

cwts _r,c :

:  weight of commodity c in the consumer price index

${dep}_r^t$ :

:  capital depreciation rate in time t and region r

dfpq _r,c,I :

:  price differences of commodity price among inputs sectors

dis_exp _r,c :

:  price difference of the export commodity c

dis_imp _r,c :

:  price difference of the import commodity c

dwts _r,c :

:  weight of commodity c in the producer price index

ecfneng _r,g :

:  emission coefficient of nonenergy-related emissions

ecf_gdpela _r,r :

:  elasticity of Fgas to GDP increase in region r, gas g.

ecoefluc _,fl,sprl :

:  land-use change emission coefficient AEZ fl, region r, land classification sprl

efacl _r,ac,g,emsc :

:  emission factors for emissions related to activity level by sector ac, energy source emsc,

efbio _r,ac,g :

:  emission factors for emissions fossil fuel combustion by sector ac

efffc _r,c,ac,g :

:  emission factors for emissions fossil fuel combustion by sector ac consuming of goods c

efint_trs _tr,c,g :

:  international transport emissions coefficients

EH_base _r,h :

:  household expenditure of base year

${el}_{r, c, h}^{carh}$ :

:  price elasticity parameter of Logit function for transport mode energy source selection

${el}_{r, c, a}^{inden}$ :

:  price elasticity parameter of Logit function for industrial activity energy source selection

${el}_{r, tr}^{pssincome}$ :

:  passenger transport income elasticity

${el}_{r, c, a}^{trsen}$ :

:  price elasticity parameter of Logit function for transport mode energy source selection

${el}_{r, tr}^{trspr}$ :

:  transport energy demand price elasticity

emcoef_end _{r,ac,K_END,g} :

:  emission coefficient for end-use device

end_ped_base _{r,K_END,ac} :

:  base energy price of end-use stock

enur _r,c,ac :

:  energy-used ratio (1-nonenergy-use ratio)

ewts _r,c :

:  weight of commodity c in the export price index

faceff _r,c,a,* :

:  old and new capital efficiency parameter (only used for power sectors)

$fac\_{gr}_{r, f}^t$ :

:  expected factor input growth rate (calculated by 12.5.1 and 12.5.2)

fcmult _r,f,a :

:  productivity shifter of factor f in activity a

$gdp\_{gr_r^t}^{\ast }$ :

:  expected GDP growth target (annual growth rate)

gdp_base _r :

:  base-year GDP of region r.

$\overline{ghgc_r}$ :

:  GHG emission constraint

$\overline{{ghgt\_\mathit{\exp}\_ cap}_r}$ :

:  GHG emission trading (export) limit

$\overline{{ghgt\_ imp\_ cap}_r}$ :

:  GHG emission trading (import) limit

gwp _g :

:  global warming potential of gas g

gwts _r,c :

:  weight of commodity c in the government price index

ica _r,c,a :

:  quantity of c per unit of aggregate intermediate input a

ied _{r,ac,l,K_END} :

:  energy use of energy kind k per operating unit (or specific energy input) of device l in sector ac region r

iena _r,a :

:  quantity of aggregate energy input per activity unit

iene _r,c,a :

:  energy commodity consumption ratio

indserincel _r,a :

:  output elasticity of energy service demand of industry

inta _r,a :

:  quantity of aggregate nonenergy intermediate input per activity unit

inttrenecoeft _r,c :

:  international transport energy coefficient

invc _r,ac,l :

:  annualized investment cost per unit of combination of device l in sector ac and region r

ires _r,a :

:  quantity of aggregate resource input per activity unit

iva _r,a :

:  quantity of value added per activity unit

ivae _r,a :

:  quantity of value-added energy composite per activity unit

ivfa _r,f,a :

:  input coefficient of factors for Leontief inputs

iwts _r,c :

:  weight of commodity c in the capital formation price index

${labor\_ stock}_r^t$ :

:  labor stock in time t and region r

${lab\_ gr}_r^t$ :

:  labor stock (annual) growth rate in time t and region r

landeff _r,f,a :

:  land productivity coefficient

loss _r,c :

:  distribution loss rate

mps01_r,i :

:  0–1 parameter with 1 for institutions with potentially flexed direct tax rates

mwts _r,c :

:  weight of commodity c in the import price index

oped _r,ac,l :

:  operating cost except for energy per unit of combination of device l in sector ac and region r

pasch _r,h :

:  income elasticity of passenger car service demand

pcaru _r,h :

:  household passenger car service demand in base year

pene_tr_base _r,tr :

:  energy price of transport mode tr in base year

plandt_ini _{, r,fl} :

:  total unused land price

poph _r,h :

:  population of household h

pres_base _r,a :

:  resource price (normally 1)

prluch _y,r,fl :

:  prior year’s land-use change

Pyear :

:  the calculation year

qe_up _r,c :

:  export constraint

qfrspre _r,fl,sprl :

:  previous year’s primary land area AEZ fl, region r, land classification sprl

qlandtotara _r,fl :

:  total AEZ arable land

quotaqa _ragg,aagg :

:  quota of aggregated region ragg and aggregated activity aagg

renew_up _r,a :

:  capacity of the activity level a (for power sector energy)

resserincel _r,h :

:  income elasticity of energy service demand of household

sd_base _r,a,i :

:  base service demand coefficient of industry

sd_base _r,h,i :

:  base service demand coefficient of household

sh_ely_up _r,a :

:  power generation share of activity a

shii_resource _r,I :

:  a ratio of transfer to institution i of total transfer in a country

shii_use _r,I :

:  share of net income of i

shif _r,i,f :

:  share of domestic institution i in income of factor f

shincome _r,I :

:  total income share of GHG emission cost for institution i

shres _r,I :

:  resource income share of institution i

stch _r,c :

:  stock change of commodity c (positive)

stch2 _r,c :

:  stock change of commodity c (negative)

stka_pre _r,ac,l :

:  previous year’s stock of combination of device l in sector ac

ta _r,a :

:  tax rate for activity

te _r,c :

:  export tax rate

tf _r,f :

:  direct tax rate for factor f

tins01_r,i :

:  0.1 parameter with 1 for institutions with potentially flexed direct tax rates

tm _r,c :

:  import tariff rate

tq _r,c,ac :

:  rate of sales tax (as share of composite price inclusive of sales tax). Suffix ac includes activity a and institution i

transfr_crt_in _r :

:  current transfer from rest of the world

transfr_crt_out _r :

:  current transfer to rest of the world

transfr _r,f :

:  factor transfer to abroad

transfr_f _r,f :

:  factor transfer from abroad

trscvf _r,tr,ac :

:  transport service demand by modes

trseneeffi _r,tr :

:  transport energy efficiency

trspc_enecoef _r,h,c :

:  passenger transport industry and residential efficiency difference

trscef _r,tr :

:  passenger transport demand coefficient

tsh _c :

:  share of international trade service to world total international trade service

tva _r,a :

:  rate of value-added tax for activity a

tw _r,c :

:  international trade cost ratio

Year _y :

:  year order (ex; base year is 1)

12.1.2.2 Greek Letters

${\alpha}_{r, c}^{ac}$ :

:  shift parameter for domestic commodity aggregation function

${\alpha}_{r, c}^q$ :

:  an Armington function shift parameter

${\alpha}_{r, c}^t$ :

:  a CET function shift parameter

${\alpha}_{a, tc}^{tech}$ :

:  share parameter for technology Logit selection function

${\alpha}_{r, a}^{va}$ :

:  efficiency parameter in the CES value-added function

${\alpha_{r, a}^{va}}^{\ast }$ :

:  adjusted efficiency parameter in the CES value-added function

${\alpha}_{r, a}^{vae}$ :

:  efficiency parameter in the CES energy and value-added function

α ^bms _fl :

:  a parameter of biomass stock

${\beta}_{r, c, h}^{carh}$ :

:  share parameter of Logit function for household car energy source selection

${\beta}_{r, c, a}^{inden}$ :

:  share parameter of Logit function for industrial activity energy source selection

${\beta}_{r, ch, h}^m$ :

:  marginal share of consumption spending on marketed commodity ch for household h

${\beta}_{r, a, tc}^{tech}$ :

:  exponent of technology Logit selection

${\beta}_{r, c, tr}^{trsen}$ :

:  share parameter of Logit function for transport mode energy source selection

${\lambda}_{r, ac, l}^d$ :

:  operating rate of device l in sector ac

${\lambda}_c^w$ :

:  depreciation rate of traded commodity c

${\rho}_{r, c}^{ac}$ :

:  domestic commodity aggregation function exponent

${\rho}_{r, fl}^{ara}$ :

:  exponent parameter of arable land input

${\rho}_{r, a}^{ltc}$ :

:  exponent parameter crop input

${\rho}_{r, fl}^{ltc}$ :

:  exponent parameter grazing input

${\rho}_{r, fl}^{ltf}$ :

:  exponent parameter agriculture and forestry input

${\rho}_{r, c}^q$ :

:  an Armington function exponent

${\rho}_{r, c}^t$ :

:  a CET function exponent

${\rho}_{r, a}^{ls}$ :

:  exponent parameter of AEZ input function

${\rho}_{r, fl}^{ltt}$ :

:  exponent parameter crop and grazing input

${\rho}_{r, a}^{va}$ :

:  CES value-added function exponent

${\rho}_{r, a}^{vae}$ :

:  CES energy and value-added function exponent

${\delta}_{r, a, c}^{ac}$ :

:  shift parameter for domestic commodity aggregation function

${\delta}_{r, fl,\ast}^{ara}$ :

:  share parameter of arable land input

${\delta}_{r, fl}^{ltc}$ :

:  share parameter of crop AEZ input

${\delta}_{r, fl}^{ltc}$ :

:  share parameter of grazing AEZ input

${\delta}_{r, fl, a}^{ls}$ :

:  share parameter of AEZ input

${\delta}_{r, fl}^{ltf}$ :

:  share parameter of agriculture and forestry input

${\delta}_{r, fl}^{ltt}$ :

:  share parameter of crop and grazing input

${\delta}_{r, c}^q$ :

:  an Armington function share parameter

${\delta}_{r, c}^t$ :

:  a CET function share parameter

${\delta}_{r, a}^{va}$ :

:  CES value-added function share parameter for factor f in activity a

${\delta}_{r, a}^{vae}$ :

:  CES energy and value-added function share parameter in activity a

θ _r,a,c :

:  yield of output c per unit of activity a

${\psi}_{r, a, c}^{ac}$ :

:  share parameter

${\psi}_{r, c}^m$ :

:  scale parameter for import share of commodity c

${\psi_2}_{r, c}^m$ :

:  scale parameter for domestically produced goods share of commodity c

${\psi}_{r, c}^t$ :

:  scale parameter for export share of commodity c

${\psi_2}_{r, c}^t$ :

:  scale parameter for domestically produced share of commodity c

${\eta}_{r, a, c}^{ac}$ :

:  elasticity of domestic commodity aggregation

${}^{\eta_{r, ac, l}^{end}}$ :

:  exponent of Logit function

${\eta}_{r, c}^m$ :

:  elasticity of domestic consumption commodity aggregation

${\eta}_{r, c}^t$ :

:  elasticity of domestic produced commodity aggregation

${\sigma}_{r, a, g, emsc}^{ghg}$ :

:  elasticity of the additional emission reductions of nonenergy-related emissions

σghg_int :

:  parameter for a MAC curve of international transport CO2 reduction

σghg_hfc _r,g :

:  parameter for a MAC curve of international transport CO2 reduction

ς _r,a :

:  a parameter for operation ratio

θh _r,ch,h :

:  subsistence consumption of household commodity category ch for household h

αh _r,ch,h :

:  a parameter for AIDADS

βh _r,ch,h :

:  a parameter for AIDADS

τ _l :

:  lifetime of device l

φ _r,ac,i :

:  a measure of service efficiency of service type i in sector ac region r

12.1.3 Exogenous Variables

$\overline{DTINS_{r, i}}$ :

:  change in domestic institution tax share (= 0 for base; exogenous variable)

$\overline{FSAV_r}$ :

:  foreign savings (FCU) (exogenous variable)

$\overline{GADJ_r}$ :

:  government consumption adjustment factor (exogenous variable)

$\overline{ghgc_r}$ :

:  GHG emission constraint

$\overline{{ghgt\_ imp\_ cap}_r}$ :

:  GHG emission trading (import) limit

$\overline{{ghgt\_\mathit{\exp}\_ cap}_r}$ :

:  GHG emission trading (export) limit

$\overline{ghgtot\_ c}$ :

:  global GHG emission constraint

$\overline{mps_{r, i}}$ :

:  base savings rate for domestic institution i

$\overline{MPSADJ_r}$ :

:  savings rate scaling factor (= 0 for base)

${\overline{QFS}}_{r, f}$ :

:  quantity supplied of factor (exogenous variable)

$\overline{qg_{r, c}}$ :

:  government consumption adjustment factor (exogenous variable)

$\overline{qinv_{r, c}}$ :

:  base-year quantity of fixed investment demand

$\overline{tins_{r, i}}$ :

:  rate of direct tax on domestic institutions i

$\overline{TINSADJ_r}$ :

:  direct tax scaling factor (= 0 for base; exogenous variable)

$\overset{-}{{trnsfr\_ CRT}_{r," gov"}}$ :

:  governmental transfer in base year

12.1.4 Endogenous Variables

BFRATIO _r,ac,i :

:  end-use biofuel ratio

COPR _r,a :

:  operation ratio

CPI _r :

:  consumer price index (exogenous variable)

DELTA_AD2 _r,c :

:  adjustment variable for export constraint

DMPS _r :

:  0–1 parameter with 1 for institutions with potentially flexed direct tax rates

DPI _r :

:  producer price index for domestically marketed output

EG _r :

:  government expenditures

EH _r,h :

:  household consumption expenditures

EH_base _r,h :

:  household expenditure of base year

EMALI _r,a,g,emsc :

:  emissions nonenergy-related emission by industrial activity a, energy source emsc

EMALH _r,h,g.emsc :

:  emissions related to activity level by household h, emission source emsc

EMBIH _r,h,g :

:  emissions related to biomass combustion emitted by household h

EMBII _r,a,g :

:  emissions related to biomass combustion emitted by industrial activity a

EMFFH _r,c,h,g :

:  emissions related to fossil fuel combustion emitted by household h consumption of goods c

EMFFI _r,c,a,g :

:  emissions related to fossil fuel combustion emitted by industrial activity a consuming of goods c

EMFFINT _tr,g :

:  gas g emissions from international transport

EMNEG _r,g :

:  nonenergy-related emissions C2F6, SF6, CF4, and HFCs

END_ENE _{r,ac,i,K_END} :

:  energy use of service i in end-use energy

END_PCOST _r,ac,l :

:  end-use device price

END_PED _{r , K_END , ac} :

:  end-use energy price

END_QEOR _r,ac,i :

:  end-use device (not working)

END_QR _r,ac,l :

:  end-use device new investment

END_QRT _r,ac,i :

:  end-use total new investment for service

END_QXD _r,ac,l :

:  end-use device stock operation

END_STK _r,ac,l :

:  end-use device stock

EPI _r :

:  export price index

EXR _r :

:  exchange rate country r

GDP _r :

:  GDP of region r

GHGCA_NENE _r,a :

:  GHG emission cost related biomass burning and CCS negative emissions of activity a in region r

GHGCA_NENE _r,a :

:  GHG emission cost related to nonenergy consumption

GHGTCOST _r :

:  GHG emission cost

GHGT_CT _r :

:  GHG emission from region r (CO₂ equivalent) includes emission permit import

GHGT _r :

:  GHG emission from region r (CO₂ equivalent)

GHG_IMP _r :

:  GHG emission credit import (net)

GPI _r :

:  government price index

GSAV _r :

:  government savings

IADJ _r :

:  investment adjustment factor (exogenous variable)

IPI _r :

:  capital formation price index

MPI _r :

:  import price index

MPS _r,I :

:  marginal propensity to save for domestic nongovernment institution (exogenous variable)

NERED _r,a,g,emsc :

:  emission reduction caused by the GHG emission price, energy source emsc

PAGRT _r,fl :

:  agriculture AEZ-aggregated land price

PA _r,a :

:  activity price (gross revenue per activity unit)

PCROP _r,fl :

:  crop field AEZ-aggregated land price

PDD _r,c :

:  demand price for commodity produced and sold domestically

PDS _r,c :

:  supply price for commodity produced and sold domestically

PENE _r,a :

:  price of (aggregate) energy input

PE_base _r,c :

:  base year’s PE

PE _r,c :

:  export price of commodity c

${PENE}_{r, a}^{bau}$ :

:  energy price (BaUcase)

PENE_TR _r,tr :

:  energy price of transport mode tr

PGHG_EXP_QUO _r :

:  GHG emission price generated by export quota

PGHG_G :

:  GHG emission price corresponding to the global emission constraint

PGHG_G _r :

:  global GHG emission price

PGHG_IMP_QUO _r :

:  GHG emission price generated by import quota

PGHG _r :

:  GHG emission price in region r (US$/tCO₂)

PGRZ _r,fl :

:  grazing AEZ-aggregated land price

PINTA _r,a :

:  aggregate intermediate input price for activity a

PLANDT _r,fl :

:  total AEZ-aggregated land price

PLAND _r,fl,a :

:  land price of activity a and AEZ fl

PM_base _r,c :

:  base year’s PM

PM _r,c :

:  composite commodity price (including import tax and transaction costs)

PQD_base _r,c :

:  base year’s PQD

PQD _r,c :

:  composite commodity price excluding sales tax

PQH _r,ch,h :

:  price of household category commodity ch

PQ _r,c :

:  composite commodity price excluding sales tax

PRES _r,a :

:  price of resource input

PTRS _c :

:  price of international trade service

PVAE _r,a :

:  price of (aggregate) energy and value-added bundle (nonenergy transformation sector)

PVA _r,a :

:  price of (aggregate) value added

PWE _c :

:  f.o.b. export world price

PWM _c :

:  world import price (c.i.f) of commodity c

PX2 _r,c :

:  aggregate producer price for commodity including stock change effects

PXAC _r,a,c :

:  producer price of commodity c for activity a

PX _r,c :

:  aggregate producer price for commodity

QAGRT _r,fl :

:  agriculture AEZ-aggregated land use

QA _r,a :

:  quantity (level) of activity

QCARU _r,h :

:  household passenger car service demand

QCARUENET _r,h :

:  household passenger car energy use

QCH _r,ch,h :

:  household consumption of household commodity category ch

QCROP _r,fl :

:  crop field AEZ-aggregated land use

QDTRST _r,tr :

:  total transport service demand by modes

QDTRS _r,tr,ac :

:  freight transport service demand by sector ac and modes

QD _r,c :

:  quantity sold domestically of domestic output

QENE _r,a :

:  quantity of (aggregate) energy input

QEND_ENE _r,c,ac,i :

:  energy use of service i in CGE energy

QE _r,c :

:  quantity of exports

QF _r,f,a :

:  quantity demanded of factor f from activity a

QGRZ _r,fl :

:  grazing AEZ-aggregated land use

QG _r,c :

:  government consumption demand for commodity

QH _r,c,h :

:  quantity of consumption of marketed commodity c for household h

QINTA _r,a :

:  quantity of aggregate intermediate input

QINT _r,c,a :

:  quantity of commodity c as intermediate input to activity a

QINV _r,c :

:  quantity of fixed investment demand for commodity

QLAND _r,fl,a :

:  land quantity of activity a and AEZ fl

QLANT _r,fl :

:  total AEZ-aggregated land use

QM _r,c :

:  quantity of imports of commodity

QPRMLANDT _r,fl :

:  primary land area AEZ fl, region r

QQ _r,c :

:  quantity of goods supplied to domestic market (composite supply)

QRED _r,emcm,a :

:  input of counter emission reduction countermeasures of activity a and measure emcm

QRES _r,a :

:  quantity of resource input

QSD _r,ac,i :

:  service demand

QTRS _c :

:  quantity of international trade service

QVAE _r,a :

:  quantity of (aggregate) energy and value-added bundle (nonenergy transformation sector)

QVA _r,a :

:  quantity of (aggregate) value added

QWE _r,c :

:  quantity of exports of commodity

QWM _r,c :

:  quantity of imports of commodity

QX2 _r,c :

:  aggregate marketed quantity of domestic output of commodity including stock change

QXAC _r,a,c :

:  marketed output quantity of commodity c from activity a

QX _r,c :

:  aggregate marketed quantity of domestic output of commodity

RQUOQA _r,a :

:  shadow subsidies of the fixed activity level

SHAC _r,a,c :

:  share of the commodity c produced by activity a

SHQE _r,c :

:  share of domestically sold and export commodity c

SHQM :

:  share of domestically sold and imported commodity c

TBH _r,h :

:  biomass consumption by household h

TBI _r,a :

:  biomass consumption by activity a

TINS _r,I :

:  direct tax rate for institution i

TRII_Resource _r,I :

:  transfers to institution i

TRII_Use _r,I :

:  transfers from institution i

TRS_ENE_FL _r,c,tr :

:  transport energy demand by modes and energy sources

TRS_ENE _r,tr :

:  transport energy demand by modes

TSCT _r,a,tc :

:  technology tc’s share in sector a and region r

VRENCAP _r,a :

:  rent of electricity capacity activity a in region r

VRENCAPTOT _r :

:  rent related to electricity capacity

Vu _r,h :

:  utility of household h defined by AIDADS

Vμ _r,ch,h :

:  marginal share of consumption spending on household commodity category ch for household h

WFDIST _r,f,a :

:  factor price distortion factor for factor f in activity a

WF _r,f :

:  average price of factor

YF _r,f :

:  income of factor f

YG _r :

:  government revenue

YI _r,I :

:  income of institution i (in the set INSDNG)

YIF _r,i,f :

:  income to domestic institution i from factor f

12.1.5 Equation

• Import price:

$$ {PM}_{r, c}={PWM}_c\cdot {dis\_ imp}_{r, c}\cdot \left(1+{tm}_{r, c}\right)\cdot {EXR}_r,\kern2em \forall c\in CM $$

• Export price:

$$ {PE}_{r, c}={PWE}_c\cdot {dis\_\mathit{\exp}}_{r, c}\cdot \left(1-{te}_{r, c}\right)\cdot \overline{EXR_r},\kern2em \forall r\in R, c\in CE $$

• Demand price of domestic nontraded goods:

$$ {PDD}_{r, c}={PDS}_{r, c},\kern2em \forall r\in R, c\in CD $$

• Absorption:

$$ {PQ}_{r, c}\cdot {QQ}_{r, c}={PDD}_{r, c}\cdot {QD}_{r, c}+{PM}_{r, c}\cdot {QM}_{r, c},\kern2em \forall r\in R, c\in \left( CD\cup CM\right) $$

• Commodity market monetary balance:

$$ \begin{array}{l}{PQ}_{r,c}\cdot {QQ}_{r,c}={ PQ D}_{r,c}\cdot \left(\begin{array}{l}\sum_{a\in A}{\mathit{\mathrm{dfpq}}}_{r,c,a}\cdot {\mathit{\mathrm{QINT}}}_{r,c,a}+\sum_{h\in H}{\mathit{\mathrm{pfdq}}}_{r,c,h}\cdot {QH}_{r,c,h}\\ {}+{\mathit{\mathrm{pfdq}}}_{r,c," gov"}\cdot {QG}_{r,c}+{\mathit{\mathrm{pfdq}}}_{r,c,"S-I"}\cdot {\mathit{\mathrm{QINV}}}_{r,c}\end{array}\right),\\ {}\kern6.5em \forall r\in R,c\in CX\end{array} $$

• Marketed output with stock change:

$$ QX{2}_{r, c}={QX}_{r, c}+{stch}_{r, c},\kern2em \forall r\in R, c\in CX $$

• Marketed output value with stock change:

$$ PX{2}_{r, c}\cdot QX{2}_{r, c}={PX}_{r, c}\cdot {QX}_{r, c},\kern2em \forall r\in R, c\in CX $$

• Marketed output value:

$$ PX{2}_{r, c}\cdot QX{2}_{r, c}={PDS}_{r, c}\cdot {QD}_{r, c}+{PE}_{r, c}\cdot {QE}_{r, c},\kern2em \forall r\in R, c\in CX $$

• Activity price:

$$ {PA}_{r, a}\cdot {QA}_{r, a}\cdot \left(1+{RQUOQA}_{r, a}\right)=\sum_{c\in C}{PXAC}_{r, a, c}\cdot {QXAC}_{r, a, c},\kern2em \forall r\in R, a\in A $$

• Aggregate Nonenergy intermediate input price:

$$ \begin{array}{l}{\mathit{\mathrm{QINT}\mathrm{A}}}_{r,a}\cdot {\mathit{\mathrm{PINTA}}}_{r,a}=\sum_{c\in \mathit{\mathrm{CNEN}}}{\mathit{\mathrm{dfpq}}}_{r,c,a}\cdot {PQD}_{r,c}\cdot {\mathit{\mathrm{QINT}}}_{r,c,a}\cdot \left(1+{tqd}_{r,c,a}\right)\\ {}\kern9.4em \forall r\in R,a\in A,c\in \mathit{\mathrm{CNEN}}\end{array} $$

• Activity revenue and costs (nonenergy transformation sector):

$$ \begin{array}{ll}{PA}_{r,a}\cdot \left(1-{ta}_{r,a}\right)\cdot {QA}_{r,a}=\kern-0.7em & {\mathit{\mathrm{PVAE}}}_{r,a}\cdot {\mathit{\mathrm{QVAE}}}_{r,a}+{\mathit{\mathrm{PINTA}}}_{r,a}\cdot {\mathit{\mathrm{QINTA}}}_{r,a}\hfill \\ {}& +{\mathit{\mathrm{PRES}}}_{r,a}\cdot {\mathit{\mathrm{QRES}}}_{r,a}+{\mathit{\mathrm{GHGCA}}\_\mathit{\mathrm{NENE}}}_{r,a}\hfill \\ {}& +{\mathit{\mathrm{VRENCAP}}}_{r,a}\cdot {QA}_{r,a}+\sum_{\mathit{\mathrm{emcm}}\in \mathit{\mathrm{EMCM}}}{\mathit{\mathrm{QRED}}}_{r,\mathit{\mathrm{emcm}},a},\hfill \\ {}& \forall r\in R,a\in \mathit{\mathrm{ACES}}\hfill \end{array} $$

• Activity revenue and costs (energy transformation sector):

$$ \begin{array}{ll}{PA}_{r,a}\cdot \left(1-{ta}_{r,a}\right)\cdot {QA}_{r,a}=\kern-0.8em & {PVA}_{r,a}\cdot {QVA}_{r,a}+{\mathit{\mathrm{PINTA}}}_{r,a}\cdot {\mathit{\mathrm{QINTA}}}_{r,a}\hfill \\ {}& +{\mathit{\mathrm{PENE}}}_{r,a}\cdot {\mathit{\mathrm{QENE}}}_{r,a}+{\mathit{\mathrm{PRES}}}_{r,a}\cdot {\mathit{\mathrm{QRES}}}_{r,a}\hfill \\ {}& +{\mathit{\mathrm{GHGCA}}\_\mathit{\mathrm{NENE}}}_{r,a}\hfill \\ {}& +{\mathit{\mathrm{VRENCAP}}}_{r,a}\cdot {QA}_{r,a}\sum_{\mathit{\mathrm{emcm}}\in \mathit{\mathrm{EMCM}}}{\mathit{\mathrm{QRED}}}_{r,\mathit{\mathrm{emcm}},a},\hfill \\ {}& \forall r\in R,a\in \mathit{\mathrm{ALEO}}\hfill \end{array} $$

• Resource input price:

$$ {pres\_ base}_{r, a}={PRES}_{r, a},\kern2em \forall r\in R, a\in A $$

• Consumer price index:

$$ \begin{array}{ll}\hfill & \kern-0.8em {CPI}_r=\sum_{c\in C}\left({PQD}_{r,c}\cdot {\mathit{\mathrm{dfpq}}}_{r,c,"\mathit{\mathrm{hurb}}"}\cdot \left(1+{tqd}_{r,c,"\mathit{\mathrm{hurb}}"}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_{r,g}\cdot {\mathit{\mathrm{efffc}}}_{r,c,"\mathit{\mathrm{hurb}}",g}\right)\cdot {\mathit{\mathrm{cwts}}}_{r,c}\\ {}& \kern2.6em \forall r\in R,\forall g\in G\hfill \end{array} $$

• Producer price index for nontraded market output:

$$ {DPI}_r=\sum_{c\in C}{PDS}_{r, c}\cdot {dwts}_{r, c}\kern2em \forall r\in R $$

• Export price index:

$$ {EPI}_r=\sum_{c\in C}{PE}_{r, c}\cdot {ewts}_{r, c}\kern1.5em \forall r\in R $$

• Import price index:

$$ {MPI}_r=\sum_{c\in C}{PM}_{r, c}\cdot {mwts}_{r, c}\kern1.5em \forall r\in R $$

• Governmental consumption price index:

$$ {GPI}_r=\sum_{c\in C}{PQD}_{r, c}\cdot {dfpq}_{r, c," gov"}\cdot \left(1+{tqd}_{r, c," gov"}\right)\cdot {gwts}_{r, c}\kern1.5em \forall r\in R $$

• Capital formation price index:

$$ {IPI}_r=\sum_{c\in C}{PQD}_{r, c}\cdot {dfpq}_{r, c," S- I"}\cdot \left(1+{tqd}_{r, c," S- I"}\right)\cdot {iwts}_{r, c}\kern1.5em \forall r\in R $$

• Leontief technology: demand for aggregate value added (energy transformation sector)

$$ {QVA}_{r, a}={iva}_{r, a}\cdot {QA}_{r, a},\kern2em \forall r\in R, a\in ALEO $$

• Leontief technology: demand for aggregate energy input (energy transformation sector)

$$ {QENE}_{r, a}={iena}_{r, a}\cdot {QA}_{r, a},\kern2em \forall r\in R, a\in ALEO $$

• Energy and value-added bundle (nonenergy transformation sector):

$$ {QVAE}_{r, a}={ivae}_{r, a}\cdot {QA}_{r, a},\kern2em \forall r\in R, a\in ACES $$

• Leontief technology: demand for aggregate nonenergy intermediate input

$$ {QINTA}_{r, a}={inta}_{r, a}\cdot {QA}_{r, a},\kern2em \forall r\in R, a\in A $$

• Leontief technology: demand for resource input:

$$ {QRES}_{r, a}={ires}_{r, a}\cdot {QA}_{r, a},\kern2em \forall r\in R, a\in A $$

• Energy and value-added composite:

$$ \begin{array}{ll}{ QVA E}_{r, a}=& {\alpha}_{r, a}^{vae}\cdot {\left({\delta}_{r, a}^{vae}\cdot {QVA_{r, a}}^{-{\rho}_{r, a}^{vae}}+\left(1-{\delta}_{r, a}^{vae}\right)\cdot {QENE_{r, a}}^{-{\rho}_{r, a}^{vae}}\right)}^{-\frac{1}{\rho_{r, a}^{vae}}},\kern1.5em \forall r\in R,\hfill \\ {}& a\in ACES\hfill \end{array} $$

• Energy and value-added input CES technology: energy – value-added input ratio

$$ {QVA}_{r, a}={QENE}_{r, a}\cdot {\left(\frac{\delta_{r, a}^{vae}}{1-{\delta}_{r, a}^{vae}}\cdot \frac{PENE_{r, a}}{PVA_{r, a}}\right)}^{\frac{1}{1+{\rho}_{r, a}^{vae}}},\kern2em \forall r\in R, a\in ACES $$

• Energy and value-added composite balance:

$$ { QVA E}_{r, a}\cdot {PVA E}_{r, a}={QENE}_{r, a}\cdot {PENE}_{r, a}+{QVA}_{r, a}\cdot {PVA}_{r, a},\kern1.5em \forall r\in R, a\in ACES $$

• Energy and value-added composite (nonenergy use sector):

$$ { QVA E}_{r, a}={QVA}_{r, a},\kern1.5em \forall r\in R, a\in ACES $$

• Value-added and factor demands: non-power supply activities

$$ {QVA}_{r, a}={\alpha}_{r, a}^{va}\cdot {\left(\sum_{f\in F}{\delta}_{r, a}^{va}\cdot {\left({ f cmult}_{r, f, a}\cdot {QF}_{r, f, a}\right)}^{-{\rho}_{r, a}^{va}}\right)}^{-\frac{1}{\rho_{r, a}^{va}}},\kern1.5em \forall r\in R, a\in A $$

• Value-added and factor demands: power supply activities

$$ {PVA}_{r, a}\cdot \left(1-{tva}_{r, a}\right)\cdot {QVA}_{r, a}=\sum_{f\in F}{WF}_{r, f}\cdot { WF DIST}_{r, f, a},\kern1em \forall r\in R, a\in A $$

• Factor demand: non-power supply activities

$$ \begin{array}{ll}{WF}_{r,f}\cdot {\mathit{\mathrm{WFDIST}}}_{r,f,a}=& {PVA}_{r,a}\cdot \left(1-{tva}_{r,a}\right)\cdot {QVA}_{r,a}\cdot \hfill \\ {}& \kern-8.8em {\left(\sum_{f\in F\hbox{'}}{\delta}_{r,a}^{va}\cdot {\left({\mathit{\mathrm{fcmult}}}_{r,f,a}\cdot {QF}_{f\ r,a}\right)}^{-{\rho}_{r,a}^{va}}\right)}^{-1}\kern-0.8em \cdot {\delta}_{r,a}^{va}\cdot {{\mathit{\mathrm{fcmult}}}_{r,f,a}}^{-{\rho}_{r,a}^{va}}\cdot {QF_{r,f,a}}^{-{\rho}_{r,a}^{va}-1},\hfill \\ {}& \kern-8.5em \forall r\in R,a\in A,f\in F\hfill \end{array} $$

• Factor demand: power supply activities

$$ {QF}_{r, f, a}={ivfa}_{r, f, a}\cdot {QVA}_{r, a},\kern1em \forall r\in R, a\in A, f\in F $$

• Factor cost: power supply activities

$$ \sum_f{WF}_{r, f}\cdot { WF DIST}_{r, f, a}\cdot {QF}_{r, f, a}={PVA}_{r, a}\cdot \left(1-{tva}_{r, a}\right)\cdot {QVA}_{r, a},\kern1em \forall r\in R, a\in A $$

• Capital aggregation: perfect substitution

$$ {QF}_{r," ccap", a}={QF}_{r," ncap", a}+{QF}_{r," cap", a}\cdot {COPR}_{r, a},\kern1em \forall r\in R, a\in A $$

• Capital aggregation: new industry

$$ {QF}_{r," ccap", a}={QF}_{r," ncap", a},\kern2em \forall r\in R, a\in A $$

• Capital aggregation: base year

$$ {QF}_{r," ccap", a}={QF}_{r," cap", a},\kern1em \forall r\in R, a\in A $$

• Capital cost balance:

$$ \begin{array}{ll}{QF}_{r, f, a}\cdot {WF}_{r, f}\cdot {WF DIST}_{r, f, a}=\kern-0.8em & {QF}_{r," ncap", a}\cdot {WF}_{r," ncap"}\cdot {WF DIST}_{r," ncap", a}\hfill \\ {}& +{QF}_{r," cap", a}\cdot {COPR}_{r, a}\cdot {WF}_{r," cap"}\cdot {WF DIST}_{r," cap", a},\hfill \\ {}& \forall r\in R, a\in A, f\in FCCAP\hfill \end{array} $$

• Capital rate of return for new and old:

$$ \begin{array}{l}{WF}_{r," ncap"}\cdot {WF DIST}_{r," ncap", a}\ge {WF}_{r," cap"}\cdot {WF DIST}_{r," cap", a}\perp {QF}_{r," ncap", a}\ge 0,\\ {}\kern1em \forall r\in R, a\in A\end{array} $$

• Capital operation ratio

$$ {COPR}_{r, a}={\left(\frac{WF_{r," cap"}\cdot { WF DIST}_{r," cap", a}}{WF_{r," ncap"}\cdot { WF DIST}_{r," ncap", a}}\right)}^{\varsigma_{r, a}},\kern1em \forall r\in R, a\in A $$

• Disaggregated intermediate input demand:

$$ {QINT}_{r, c, a}\cdot \frac{faceff_{r, c, a," old"}\cdot {QF}_{r," CAP", a}+{faceff}_{r, c, a," new"}\cdot {QF}_{r," NCAP", a}}{QF_{r," CAP", a}+{QF}_{r," NCAP", a}}={ica}_{r, c, a}\cdot {QINT A}_{r, a},\kern2em \forall r\in R, a\in A, c\in CNEN $$

• CCS service intermediate input demand:

$$ {QINT}_{r, c, a}=\sum_{emcm\in C CSMAP}{QRED}_{r, emcm, a},\kern1em \forall r\in R, a\in A, c\in C\_ CCS $$

• Reduction measures (for nonenergy-related GHG emissions):

$$ \begin{array}{c}{QRED}_{r, emcm, a}={\xi}_{emcm, a}^{\max}\cdot {\eta}_{emcm, a}\cdot \sum_{g\in G}{ g wp}_g\cdot {EMALI}_{r, a, g},\\ {}\kern3.7em \forall r\in R, a\in A, emcm\in EMCM0\end{array} $$

• Reduction measures (for energy-related GHG emissions):

$$ \begin{array}{ll}{QRED}_{r, emcm, a}=\kern-0.8em & {\xi}_{emcm, a}^{\max}\cdot {\eta}_{emcm, a}\cdot \sum_{c\in ENE}\sum_{g\in G}{ g wp}_g\cdot {QINT}_{r, c, a}\cdot {enur}_{r, c, a}\cdot {efffc}_{r, c, a, g},\hfill \\ {}& \forall r\in R, a\in A, emcm\in EMCM1\hfill \end{array} $$

• Reduction measures (for biomass power plant GHG absorption):

$$ \begin{array}{l}{QRED}_{r, emcm, a}={\xi}_{emcm, a}^{\max}\cdot {\eta}_{emcm, a}\cdot \sum_{g\in G}{ g wp}_g\cdot {EMBII}_{r, a, g},\\ {}\kern7em \forall r\in R, a\in A, emcm\in EMCM2\end{array} $$

• CCS-equipped share:

$$ {\mathit{\mathrm{TSCT}}}_{r,a, tc}={\alpha}_{a, tc}^{\mathit{\mathrm{tech}}}\cdot {{\mathit{\mathrm{PGHG}}}_r}^{\beta_{r,a, tc}}\cdot {\left(\sum_{tc\in TC}{\alpha}_{a, tc}^{\mathit{\mathrm{tech}}}\cdot {{\mathit{\mathrm{PGHG}}}_r}^{\beta_{r,a, tc}^{\mathit{\mathrm{tech}}}}\right)}^{-1},\kern1em \forall r\in R,a\in A, tc\in TC $$

• Energy input technology share:

$$ \begin{array}{ll}{\mathit{\mathrm{QINT}}}_{r,c,a}=\kern-0.8em & {\mathit{\mathrm{QENE}}}_{r,a}\cdot \hfill \\ {}& \kern-4.5em \frac{\beta_{r,c,a}^{\mathit{\mathrm{inden}}}\cdot {\left\{{PQD}_{r,c}\cdot \left(1+{tqd}_{r,c,a}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r,c,a}\cdot {\mathit{\mathrm{efffc}}}_{r,c,a,g}\right\}}^{el_{r,c,a}^{\mathit{\mathrm{inden}}}}}{\sum_{cp\in ENE}{\beta}_{r, cp,a}^{\mathit{\mathrm{inden}}}\cdot {\left\{{PQD}_{r, cp}\cdot \left(1+{tqd}_{r, cp,a}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r, cp,a}\cdot {\mathit{\mathrm{efffc}}}_{r, cp,a,g}\right\}}^{el_{r, cp,a}^{\mathit{\mathrm{inden}}}}},\hfill \\ {}& \kern-4.5em \forall r\in R,c\in ENE,a\in A\hfill \end{array} $$

• Energy input costs:

$$ \begin{array}{ll}\hfill & \kern-1.5em {\mathit{\mathrm{PENE}}}_{r,a}\cdot {\mathit{\mathrm{QENE}}}_{r,a}\\ {}& =\sum_{c\in C\_ ENE}\left\{{PQD}_{r,c,a}\cdot \left(1+{tqd}_{r,c,a}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r,c,a}\cdot {\mathit{\mathrm{efffc}}}_{r,c,a,g}\right\}\cdot \hfill \\ {}& {\mathit{\mathrm{QINT}}}_{r,c,a},\hfill \\ {}& \kern0em \forall r\in R,a\in A\hfill \end{array} $$

• Energy consumption of energy transformation sector:

$$ {QINT}_{r, c, a}={QENE}_{r, a}\cdot {iene}_{r, c, a},\kern2em \forall r\in R, a\in ALEO\_ ENE, c\in ENE $$

• Freight transport generated by industrial activity:

$$ {QDTRS}_{r, tr, a}={QINT}_{r," COM\_ TRS", a}\cdot {trscvf}_{r, tr, a},\kern2em \forall r\in R, a\in A, tr\in TR\_ FRT\kern1em $$

• Freight transport generated by household consumption:

$$ {QDTRS}_{r, tr, h}={QH}_{r," COM\_ TRS", h}\cdot {trscvf}_{r, tr, h},\kern2em \forall r\in R, h\in H, tr\in TR\_ FRT\kern1em $$

• Total freight transport:

$$ { QDTRS T}_{r, tr}=\sum_{ac\in AC}{QDTRS}_{r, tr, ac},\kern2em \forall r\in R, tr\in TR\_ FRT\kern1em $$

• Passenger transport (excluding household passenger car):

$$ {QDTRST}_{r, tr}={trspss\_ base}_{r, tr}\cdot {\left(\frac{GDP_r}{{GDP\_ base}_r}\right)}^{el_{r, tr}^{pssincome}},\kern1em \forall r\in R, tr\in TR\_ PSS\kern1em $$

• Transport energy demand:

$$ {TRS\_ ENE}_{r, tr}={QDTRST}_{r, tr}\cdot {trseneeffi}_{r, tr}\cdot {\left(\frac{{PENE\_ TR}_{r, tr}}{{pene\_ tr\_ base}_{r, tr}}\right)}^{el_{r, tr}^{trspr}},\kern1em \forall r\in R, a\in A, tr\in TR $$

• Transport energy price by mode:

$$ \begin{array}{ll}\hfill & \kern-1em {\mathit{\mathrm{PENE}}\_ TR}_{r, tr}\\ {}& =\frac{\sum_{c\in C}{TRS\_ ENE\_ FL}_{r, tr,c}\cdot \left\{{PQD}_{r,c}\cdot \left(1+{tqd}_{r,c," TRS"}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r,c," trs"}\cdot {\mathit{\mathrm{efffc}}}_{r,c," trs",g}\right\}}{\sum_c{TRS\_ ENE\_ FL}_{r, tr,c}},\hfill \\ {}& \kern1em \forall r\in R,a\in A, tr\in TR\hfill \end{array} $$

• Transport energy source:

$$ \begin{array}{ll}{TRS\_ ENE\_ FL}_{r,c, tr}=& {TRS\_ ENE}_{r, tr}\cdot \hfill \\ {}& \kern-7.9em \frac{\beta_{r,c, tr}^{\mathit{\mathrm{trsen}}}\cdot {\left\{{PQD}_{r,c}\cdot \left(1+{tqd}_{r,c," TRS"}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r,c," trs"}\cdot {\mathit{\mathrm{efffc}}}_{r,c," trs",g}\right\}}^{el_{r,c, tr}^{\mathit{\mathrm{trsen}}}}}{\sum_{cp\in ENE}{\beta}_{r, cp, tr}^{\mathit{\mathrm{trsen}}}\cdot {\left\{{PQD}_{r, cp}\cdot \left(1+{tqd}_{r, cp," TRS"}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r, cp," trs"}\cdot {\mathit{\mathrm{efffc}}}_{r, cp," trs",g}\right\}}^{el_{r, cp, tr}^{\mathit{\mathrm{trsen}}}}},\hfill \\ {}& \kern-7.8em \forall r\in R,c\in ENE, tr\in TR\kern1em \hfill \end{array} $$

• Transport total energy consumption:

$$ {QENE}_{r, a}=\sum_{tr\in TR}{TRS\_ ENE}_{r, tr},\kern1em \forall r\in R, a\in A\_ TRS $$

• Transport total energy consumption by fuel:

$$ {QINT}_{r, c, a}=\sum_{tr\in TR}{TRS\_ ENE\_ FL}_{r, c, tr},\kern1em \forall r\in R, c\in ENE, a\in A\_ TRS $$

• Commodity production and allocation:

$$ {QXAC}_{r, a, c}={\theta}_{r, a, c}\cdot {QA}_{r, a},\kern1em \forall r\in R, a\in A, c\in CX $$

• Commodity production and allocation (nonenergy commodities):

$$ {QX}_{r, c}={\alpha}_{r, c}^{a c}\cdot {\left(\sum_{a\in A}{\delta}_{r, a, c}^{a c}\cdot {{ QX AC}_{r, a, c}}^{-{\rho}_{r, c}^{a c}}\right)}^{-\frac{1}{\rho_{r, c}^{a c}}},\kern1em \forall r\in R, c\in \left( CX- ENE\right) $$

• First-order condition for output aggregation function (nonenergy commodities):

$$ \begin{array}{l}{\mathit{\mathrm{PXAC}}}_{r,a,c}={PX}_{r,c}\cdot {QX}_{r,c}\cdot {\left(\sum_{ap\in A}{\delta}_{r, ap,c}^{ac}\cdot {{\mathit{\mathrm{QXAC}}}_{r, ap,c}}^{-{\rho}_{r, ap}^{ac}}\right)}^{-1}\cdot {\delta}_{r,a,c}^{ac}\cdot {{\mathit{\mathrm{QXAC}}}_{r,a,c}}^{-{\rho}_{r,a}^{ac}-1},\\ {}\kern5.5em \forall r\in R,a\in A,c\in \left( CX- ENE\right)\end{array} $$

• Single sector commodity source:

$$ { PX AC}_{r, a, c}={PX}_{r, c},\kern1em \forall r\in R, a\in A, c\in \left( CX- ENE\right) $$

• Perfect substitution commodity sources:

$$ \sum_{a\in A}{ QX AC}_{r, a, c}={QX}_{r, c},\kern1em \forall r\in R, a\in A $$

• Share of commodity production and allocation (energy commodities):

$$ {SHAC}_{r, a, c}=\frac{\psi_{r, a, c}^{ac}{PXAC_{r, a, c}}^{\eta_{r, a, c}^{ac}}}{\sum_{ap\in A}{\psi}_{r, a p, c}^{ac}{PXAC_{r, a p, c}}^{\eta_{r, a p, c}^{ac}}},\kern1em \forall r\in R, c\in \left( CX\cap ENE\right) $$

• Commodity production and allocation (energy commodities):

$$ { QX AC}_{r, a, c}={QX}_{r, c}\cdot {SHAC}_{r, a, c},\kern2em \forall r\in R, a\in A, c\in \left( CX\cap ENE\right) $$

• Balance of the output and commodity aggregate (energy commodities):

$$ \sum_{a\in A}{ QX AC}_{r, a, c}\cdot { PX AC}_{r, a, c}={QX}_{r, c}{PX}_{r, c},\kern2em \forall r\in R, c\in \left( CX\cap ENE\right) $$

• Output transformation (CET) function (nonenergy commodities):

$$ \begin{array}{ll} QX{2}_{r,c}=\kern-0.7em & {\alpha}_{r,c}^t\cdot {\left({\delta}_{r,c}^t\cdot \mathit{\mathrm{DELTA}}\_ AD{2}_{r,c}\cdot {QE_{r,c}}^{\rho_{r,c}^t}+\left(1-{\delta}_{r,c}^t\cdot \mathit{\mathrm{DELTA}}\_ AD{2}_{r,c}\right)\cdot {QD_{r,c}}^{\rho_{r,c}^t}\right)}^{\frac{1}{\rho_{r,c}^t}},\hfill \\ {}& \forall r\in R,c\in \left( CE\cap CD- ENE\right)\hfill \end{array} $$

• Export constraint:

$$ {qe\_ up}_{r, c}\ge {QE}_{r, c}\perp DELTA\_ AD{2}_{r, c}\ge 1,\kern1em \forall r\in R, c\in C\left\{ qe\_{up}_{r, c}\ge 0\right\} $$

• Export-domestic supply ratio (nonenergy commodities):

$$ \begin{array}{l}\frac{QE_{r,c}}{QD_{r,c}}={\left(\frac{PE_{r,c}}{PDS_{r,c}}\cdot \frac{1-{\delta}_{r,c}^t\cdot \mathit{\mathrm{DELTA}}\_ AD{2}_{r,c}}{\delta_{r,c}^t\cdot \mathit{\mathrm{DELTA}}\_ AD{2}_{r,c}}\right)}^{\frac{1}{\rho_{r,c}^t-1}},\kern2em \forall r\in R,c\in \left( CE\cap CD- ENE\right)\end{array} $$

• Output transformation for domestically sold outputs without exports and for exports without domestic sales:

$$ QX{2}_{r, c}={QD}_{r, c}+{QE}_{r, c},\kern2em \forall r\in R, c\in \left( CE\cap CEN\right)\cup \left( CD\cap CDN\right) $$

• Share of the domestically sold and export (energy commodities):

$$ {SHQE}_{r, c}=\frac{\psi_{r, c}^t{PE_{r, c}}^{\eta_{r, c}^t}}{\psi_{r, c}^t{PE_{r, c}}^{\eta_{r, c}^t}+{\psi_2}_{r, c}^t{PDS_{r, c}}^{\eta_{r, c}^t}},\kern2em \forall r\in R, c\in \left( CE\cap CD\cap ENE\right) $$

• Exported energy commodities:

$$ {QE}_{r, c}= QX{2}_{r, c}\cdot {SHQE}_{r, c},\kern2em \forall r\in R, c\in \left( CE\cap CD\cap ENE\right) $$

• Domestically sold energy commodities:

$$ {QD}_{r, c}= QX{2}_{r, c}\cdot \left(1-{SHQE}_{r, c}\right),\kern2em \forall r\in R, c\in \left( CE\cap CD\cap ENE\right) $$

• Composite supply (Armington) function (nonenergy commodities):

$$ \begin{array}{ll}{QQ}_{r,c}=\kern-0.8em & {\alpha}_{r,c}^q\cdot {\left({\delta}_{r,c}^q\cdot {QM_{r,c}}^{-{\rho}_{r,c}^q}+\left(1-{\delta}_{r,c}^q\right)\cdot {QD_{r,c}}^{-{\rho}_{r,c}^q}\right)}^{-\frac{1}{\rho_{r,c}^q}},\hfill \\ {}& \kern0em \forall r\in R,c\in \left( CM\cap CD- ENE\right)\hfill \end{array} $$

• Import-domestic demand ratio (nonenergy commodities):

$$ \frac{QM_{r, c}}{QD_{r, c}}={\left(\frac{PDD_{r, c}}{PM_{r, c}}\cdot \frac{\delta_{r, c}^q}{1-{\delta}_{r, c}^q}\right)}^{\frac{1}{\rho_{r, c}^q+1}},\kern2em \forall r\in R, c\in \left( CM\cap CD- ENE\right) $$

• Composite supply for nonimported outputs and non-produced imports:

$$ {QQ}_{r, c}={QD}_{r, c}+{QM}_{r, c},\kern2em \forall r\in R, c\in \left( CD\cap CMN\right)\cup \left( CM\cap CDN\right) $$

• Share of the domestically sold and imported (energy commodities):

$$ {SHQM}_{r, c}=\frac{\psi_{r, c}^m{PM_{r, c}}^{\eta_{r, c}^m}}{\psi_{r, c}^m{PM_{r, c}}^{\eta_{r, c}^m}+{\psi_2}_{r, c}^m{PDD_{r, c}}^{\eta_{r, c}^m}},\kern2em \forall r\in R, c\in \left( CM\cap CD\cap ENE\right) $$

• Imported energy commodities:

$$ {QM}_{r, c}={QQ}_{r, c}\cdot {SHQM}_{r, c},\kern2em \forall r\in R, c\in \left( CM\cap CD\cap ENE\right) $$

• Domestically sold energy commodities:

$$ {QD}_{r, c}={QQ}_{r, c}\cdot \left(1-{SHQM}_{r, c}\right),\kern2em \forall r\in R, c\in \left( CM\cap CD\cap ENE\right) $$

• Land input of activity:

$$ {QF}_{r, f, a}={landeff}_{r, f, a}\cdot {QA}_{r, a},\kern2em \forall r\in R, f\in FLND, a\in A $$

• AEZ aggregation for activity a:

$$ {QF}_{r,f,a}\cdot {WF}_{r,f}\cdot {\mathit{\mathrm{WFDIST}}}_{r,f,a}=\sum_{fl\in FL}{\mathit{\mathrm{PLAND}}}_{r, fl,a}\cdot {\mathit{\mathrm{QLAND}}}_{r, fl,a},\kern2em \forall r\in R,f\in \mathit{\mathrm{FLND}},a\in A $$

• AEZ selection for activity a:

$$ {QLAND}_{r, fl, a}={QF}_{r," lnd", a}\cdot \frac{\delta_{r, fl, a}^{ls}\cdot {PLAND_{r, fl, a}}^{\rho_{r, a}^{ls}}}{\sum_{flp\in FL}{\delta}_{r, fl p, a}^{ls}\cdot {PLAND_{r, fl p, a}}^{\rho_{r, a}^{ls}}},\kern2em \forall r\in R, fl\in FL, a\in A $$

• Crop land price:

$$ {QCROP}_{r, fl}\cdot {PCROP}_{r, fl}=\sum_{a\in AAGR}{PLAND}_{r, fl, a}\cdot {QLAND}_{r, fl, a},\kern2em \forall r\in R, fl\in FL $$

• AEZ land crop selection:

$$ {\mathit{\mathrm{QLAND}}}_{r, fl,a}={\mathit{\mathrm{QCROP}}}_{r, fl}\cdot \frac{\delta_{r, fl,a}^{ltc}\cdot {{\mathit{\mathrm{PLAND}}}_{r, fl,a}}^{\rho_{r, fl}^{ltc}}}{\sum_{ap\in \mathit{\mathrm{AAGR}}}{\delta}_{r, fl, ap}^{ltc}\cdot {{\mathit{\mathrm{PLAND}}}_{r, fl, ap}}^{\rho_{r, fl}^{ltc}}},\kern2em \forall r\in R, fl\in FL,a\in \mathit{\mathrm{AAGR}} $$

• Grazing land price:

$$ {QGRZ}_{r, fl}\cdot {PGRZ}_{r, fl}=\sum_{a\in ALIV}{PLAND}_{r, fl, a}\cdot {QLAND}_{r, fl, a},\kern2em \forall r\in R, fl\in FL $$

• AEZ land grazing selection:

$$ {\mathit{\mathrm{QLAND}}}_{r, fl,a}={\mathit{\mathrm{QGRZ}}}_{r, fl}\cdot \frac{\delta_{r, fl,a}^{ltc}\cdot {{\mathit{\mathrm{PLAND}}}_{r, fl,a}}^{\rho_{r, fl}^{ltc}}}{\sum_{ap\in \mathit{\mathrm{ALIV}}}{\delta}_{r, fl, ap}^{ltc}\cdot {{\mathit{\mathrm{PLAND}}}_{r, fl, ap}}^{\rho_{r, fl}^{ltc}}},\kern1.5em \forall r\in R, fl\in FL,a\in \mathit{\mathrm{ALIV}} $$

• Crop and grazing selection for AEZ (crop):

$$ \begin{array}{l}{\mathit{\mathrm{QCROP}}}_{r, fl}={\mathit{\mathrm{QAGRT}}}_{r, fl}\cdot \frac{\delta_{r, fl,"\mathit{\mathrm{CROP}}"}^{ltt}\cdot {{\mathit{\mathrm{PCROP}}}_{r, fl}}^{\rho_{r, fl}^{ltt}}}{\delta_{r, fl,"\mathit{\mathrm{CROP}}"}^{ltt}\cdot {{\mathit{\mathrm{PCROP}}}_{r, fl}}^{\rho_{r, fl}^{ltt}}+{\delta}_{r, fl," GRZ"}^{ltt}\cdot {{\mathit{\mathrm{PGRZ}}}_{r, fl}}^{\rho_{r, fl}^{ltt}}},\\ {}\kern5.7em \forall r\in R, fl\in FL\end{array} $$

• Crop and grazing selection for AEZ (grazing):

$$ \begin{array}{l}{\mathit{\mathrm{QGRZ}}}_{r, fl}={\mathit{\mathrm{QAGRT}}}_{r, fl}\cdot \frac{\delta_{r, fl," GRZ"}^{ltt}\cdot {{\mathit{\mathrm{PGRZ}}}_{r, fl}}^{\rho_{r, fl}^{ltt}}}{\delta_{r, fl,"\mathit{\mathrm{CROP}}"}^{ltt}\cdot {{\mathit{\mathrm{PCROP}}}_{r, fl}}^{\rho_{r, fl}^{ltt}}+{\delta}_{r, fl," GRZ"}^{ltt}\cdot {{\mathit{\mathrm{PGRZ}}}_{r, fl}}^{\rho_{r, fl}^{ltt}}},\\ {}\kern5.1em \forall r\in R, fl\in FL\end{array} $$

• Aggregation of agriculture (in case missing either crop or graze):

$$ {QAGRT}_{r, fl}={QCROP}_{r, fl}+{QGRZ}_{r, fl},\kern2em \forall r\in R, fl\in FL $$

• Aggregated agricultural price:

$$ {\mathit{\mathrm{QAGR}}}_{r, fl}\cdot {\mathit{\mathrm{PAGRT}}}_{r, fl}={\mathit{\mathrm{QCROP}}}_{r, fl}\cdot {\mathit{\mathrm{PCROP}}}_{r, fl}+{\mathit{\mathrm{QGRZ}}}_{r, fl}\cdot {\mathit{\mathrm{PGRZ}}}_{r, fl},\kern2em \forall r\in R, fl\in FL $$

• Agriculture and forestry selection for AEZ (agriculture):

$$ \begin{array}{l}{\mathit{\mathrm{QAGRT}}}_{r, fl}={\mathit{\mathrm{QLANT}}}_{r, fl}\cdot \frac{\delta_{r, fl," AGR"}^{ltf}\cdot {{\mathit{\mathrm{PAGRT}}}_{r, fl}}^{\rho_{r, fl}^{ltf}}}{\delta_{r, fl," AGR"}^{ltf}\cdot {{\mathit{\mathrm{PAGRT}}}_{r, fl}}^{\rho_{r, fl}^{ltf}}+{\delta}_{r, fl," FRS"}^{ltf}\cdot {{\mathit{\mathrm{PLAND}}}_{r, fl," FRS"}}^{\rho_{r, fl}^{ltf}}},\\ {}\kern5.8em \forall r\in R, fl\in FL\end{array} $$

• Agriculture and forestry selection for AEZ (forestry):

$$ \begin{array}{l}{\mathit{\mathrm{QLAND}}}_{r, fl,a}={\mathit{\mathrm{QLAND}\mathrm{T}}}_{r, fl}\cdot \frac{\delta_{r,\kern0.05em fl," AGR"}^{ltf}\cdot {{\mathit{\mathrm{PLAND}}}_{r,\kern0.05em fl," FRS"}}^{\rho_{r,\kern0.05em fl}^{ltf}}}{\delta_{r,\kern0.05em fl," AGR"}^{ltf}\cdot {{\mathit{\mathrm{PAGRT}}}_{r, fl}}^{\rho_{r,\kern0.05em fl}^{ltf}}+{\delta}_{r,\kern0.05em fl," FRS"}^{ltf}\cdot {{\mathit{\mathrm{PLAND}}}_{r,\kern0.05em fl," FRS"}}^{\rho_{r,\kern0.05em fl}^{ltf}}},\\ {}\kern6.3em \forall r\in R, fl\in FL,A\in \mathit{\mathrm{AFRS}}\end{array} $$

• Aggregation of agriculture (in case missing agriculture):

$$ { QLAND T}_{r, fl}={QLAND}_{r, fl," FRS"},\kern2em \forall r\in R, fl\in FL $$

• Aggregation of agriculture (in case missing forestry):

$$ {QLANDT}_{r, fl}={QAGRT}_{r, fl},\kern2em \forall r\in R, fl\in FL $$

• Aggregated total land price:

$$ \begin{array}{l}{\mathit{\mathrm{QLAND}\mathrm{T}}}_{r, fl}\cdot {\mathit{\mathrm{PLAND}\mathrm{T}}}_{r, fl}={\mathit{\mathrm{QAGRT}}}_{r, fl}\cdot {\mathit{\mathrm{PAGRT}}}_{r, fl}+{\mathit{\mathrm{QLAND}}}_{r, fl," FRS"}\cdot {\mathit{\mathrm{PLAND}}}_{r, fl," FRS"},\\ {}\kern11.5em \forall r\in R, fl\in FL\end{array} $$

• Total land:

$$ \begin{array}{l}{\mathit{\mathrm{QLANDT}}}_{r, fl}={\mathit{\mathrm{qlandtotara}}}_{r, fl}\cdot \frac{\delta_{r, fl," USE"}^{ara}\cdot {{\mathit{\mathrm{PLANDT}}}_{r, fl}}^{\rho_{r, fl}^{ara}}}{\delta_{r, fl," USE"}^{ara}\cdot {{\mathit{\mathrm{PLANDT}}}_{r, fl}}^{\rho_{r, fl}^{ara}}+{\delta}_{r,\kern0.07em fl," NUS"}^{ara}\cdot \mathit{\mathrm{plandt}}\_{ini_{r, fl}}^{\rho_{r, fl}^{ara}}},\\ {}\kern6.2em \forall r\in R, fl\in FL\end{array} $$

• Positive land-use change emissions:

$$ \begin{array}{ll}\mathit{\mathrm{LUCHEM}}\_{P}_{r, fl}=& \max \left[0,\left({\mathit{\mathrm{qfrspre}}}_{r, fl}-{\mathit{\mathrm{QPRMLANDT}}}_{r, fl," frs"}\right)\cdot {\mathit{\mathrm{ecoefluc}}}_{r, fl," frs"}\right],\hfill \\ {}& \kern2em \forall r\in R, fl\in FL\hfill \end{array} $$

(EQ_LUCHEM_P)

• Negative land use-change emissions:

$$ \begin{array}{l}{\mathit{\mathrm{prluch}}}_{y,r, fl}\cdot cf\_v2t\cdot \mathit{\mathrm{cdst}}\_ wd\cdot 11/3\cdot \\ {}\mathit{\mathrm{LUCHEM}}\_{N}_{r, fl}=-\sum_{y\in \mathit{\mathrm{Yold}}}\left[ \exp \left[{\alpha}_{fl}^{bms}-\frac{30}{\left\{\left(\mathit{\mathrm{Pyear}}-\mathit{\mathrm{baseyear}}+1\right)-{\mathit{\mathrm{Year}}}_y\right\}}-\frac{30}{\left\{\left(\mathit{\mathrm{Pyear}}-\mathit{\mathrm{baseyear}}\right)-{\mathit{\mathrm{Year}}}_y\right\}}\right]\right],\hfill \\ {}\kern6.3em \forall r\in R, fl\in FL\hfill \end{array} $$

(EQ_LUCHEM_N)

• Factor income:

$$ {YF}_{r, f}=\sum_{a\in A}{WF}_{r, f}\cdot { WF DIST}_{r, f, a}\cdot {QF}_{r, f, a}+{transfr\_ f}_{r, f," ROW"}\cdot {EXR}_r,\kern1em \forall r\in R, f\in F $$

• Institutional factor incomes:

$$ {YIF}_{r,i,f}={\mathit{\mathrm{shif}}}_{r,i,f}\cdot \left(\left(1-{tf}_{r,f}\right)\cdot {YF}_{r,f}-{\mathit{\mathrm{transfr}}}_{r," ROW",f}\cdot {EXR}_r\right),\kern1em \forall r\in R,i\in \mathit{\mathrm{INSD}},f\in F $$

• Income of nongovernmental domestic institution:

$$ \begin{array}{ll}{YI}_{r,i}=& \sum_{f\in F}{YI F}_{r,i,f}+{\mathit{\mathrm{TRII}}\_\mathit{\mathrm{Resource}}}_{r,i}+{\mathit{\mathrm{shincome}}}_{r,i}\cdot {\mathit{\mathrm{GHGTCOST}}}_r\hfill \\ {}& +{\mathit{\mathrm{VRENCAPTOT}}}_{r,i}-\left(\mathit{\mathrm{PGHG}}\_G+{\mathit{\mathrm{PGHG}}\_ IMP\_ QUO}_r-{\mathit{\mathrm{PGHG}}\_ EXP\_ QUO}_r\right)\kern0.15em \cdot \hfill \\ {}& {GHG\_ IMP}_r{\times EXR}_r\cdot {\mathit{\mathrm{shincome}}}_{r,i}+{\mathit{\mathrm{shres}}}_{r,i}\cdot \sum_{a\in A}{\mathit{\mathrm{PRES}}}_{r,a}\cdot {\mathit{\mathrm{QRES}}}_{r,a}\hfill \\ {}& +{\mathit{\mathrm{shincome}}}_{r,i}\cdot \sum_{a\in A}{\mathit{\mathrm{QENE}}}_{r,a}\cdot {\mathit{\mathrm{PENE}}}_{r,a}\cdot \left(\frac{1}{1-{\mathit{\mathrm{ADEEI}}}_{r,a}}-1\right)\hfill \\ {}& \kern-4em +{\mathit{\mathrm{shincome}}}_{r,i}\cdot \sum_{a\in A}{\mathit{\mathrm{RQUOQA}}}_{r,a}\cdot {QA}_{r,a}\cdot {PA}_{r,a}\kern2em ,\forall r\in R,\hfill \\ {}& i\in \mathit{\mathrm{INSDNG}}\hfill \end{array} $$

• Total rent of electricity capacity:

$$ { VRENCAP TOT}_{r," ent"}=\sum_{a\in A}{VRENCAP}_{r, a}\kern1.25em \forall r\in R $$

• Household consumption expenditures:

$$ \begin{array}{ll}{EH}_{r,h}=\kern-0.8em & \left(1-{\mathit{\mathrm{shii}}\_ use}_{r,h}\right)\left(1-{MPS}_{r,h}\right)\cdot \left(1-{\mathit{\mathrm{TINS}}}_{r,h}\right)\cdot {YI}_{r,h}\hfill \\ {}& -{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_{r,g}\cdot \left({\mathit{\mathrm{EMALH}}}_{r,h,g}+{\mathit{\mathrm{EMBIH}}}_{r,h,g}\right)\hfill \\ {}& \forall r\in R,h\in H\hfill \end{array} $$

• Passenger car by household:

$$ {QCARU}_{r, h}={pcaru}_{r, h}\cdot {\left(\frac{EH_{r, h}/{CPI}_r}{EH\_{base}_{r, h}/ CPI\_{base}_r}\right)}^{pasch_{r, h}},\kern1em \forall r\in R, h\in H $$

• Energy consumption caused by passenger car in household ⁷:

$$ { QCARU ENET}_{r, h}={QCARU}_{r, h}\cdot {careneeff}_{r, h},\kern2em \forall r\in R, h\in H $$

• Energy price for passenger car in household:

$$ \begin{array}{ll}{\mathit{\mathrm{PENE}}\_H\_ CAR}_{r,h}\cdot {\mathit{\mathrm{QCARENET}}}_{r,h}=& \sum_{c\in C}{\mathit{\mathrm{QCARUENE}}}_{r,h,c}\hfill \\ {}& \kern-14.5em \cdot \left({PQD}_{r,c}\cdot {\mathit{\mathrm{dfpq}}}_{r,c,h}\cdot \left(1+{tqd}_{r,c,h}\right)+\sum_{g\in G}{\mathit{\mathrm{PGHG}}}_r\cdot {gwp}_g\cdot {\mathit{\mathrm{efffc}}}_{r,c,h,g}\right),\hfill \\ {}& \kern-14.3em \forall r\in R,h\in H\hfill \end{array} $$

• Energy fuel consumption caused by passenger car in household:

$$ \begin{array}{ll}\hfill & \kern-1em {\mathit{\mathrm{QCARUENE}}}_{r,h,c}\\ {}& \kern-1.5em ={\mathit{\mathrm{QCARUENE}\mathrm{T}}}_{r,h}\frac{\beta_{r,c,h}^{\mathit{\mathrm{carh}}}\cdot {\left\{{PQD}_{r,c}\cdot \left(1+{tqd}_{r,c,h}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r,c,h}\cdot {\mathit{\mathrm{efffc}}}_{r,c,h,g}\right\}}^{el_{r,c,h}^{\mathit{\mathrm{carh}}}}}{\sum_{cp}{\beta}_{r, cp,h}^{\mathit{\mathrm{carh}}}\cdot {\left\{{PQD}_{r, cp}\cdot \left(1+{tqd}_{r, cp,h}\right)++{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r, cp,h}\cdot {\mathit{\mathrm{efffc}}}_{r, cp,h,g}\right\}}^{el_{r, cp,h}^{\mathit{\mathrm{carh}}}}},\hfill \\ {}& \forall r\in R,h\in H,c\in ENE\kern1em \hfill \end{array} $$

• Household consumption spending (LES):

$$ \begin{array}{l}{PQH}_{r, ch}\cdot {QCH}_{r, ch,h}={PQH}_{r, ch}\cdot {\gamma}_{r, ch,h}^m\kern1em +{\beta}_{r, ch,h}^m\cdot \left({EH}_{r,h}-\sum_{c^{\prime}\in C}{PQH}_{r, ch\hbox{'}}\cdot {\gamma}_{r,{c}^{\prime }h,h}^m\right),\\ \kern-25.8em \forall r\in R,c\in C,h\in H\hfill \end{array} $$

• Household goods price:

$$ \begin{array}{ll}{QCH}_{r, c h, h}\cdot {PQH}_{r, c h, h}=\kern-1em & \sum_{c\in {wch}_{r, c h, c, h}}\kern-0.5em \left({QH}_{r, c, h}-{QCARENE}_{r, c, h}\right)\cdot \hfill \\ {}& \kern-8.5em \left({PQD}_{r, c}\cdot {dfpq}_{r, c, h}\cdot \left(1+{tqd}_{r, c, h}\right)+\sum_{g\in G}{PGHG}_r\cdot { g wp}_g\cdot {efffc}_{r, c, h, g}\right),\hfill \\ {}& \kern-8.3em \forall r\in R, c h\in CH, h\in H\kern0.48em \hfill \end{array} $$

• Household goods consumption mapping:

$$ {QH}_{r, c, h}=\sum_{ch\in {wch}_{r, c h, c, h}}{QCH}_{r, c h, h},\kern1em \forall r\in R, c\in C, h\in H $$

• Household energy source consumption:

$$ \begin{array}{ll}{QH}_{r,h,c}=& {\mathit{\mathrm{QCARENE}}}_{r,h,c}\hfill \\ {}& \kern-5.5em +{QCH}_{r," com\_ ene",h}\frac{\beta_{r,c,h}^{\mathit{\mathrm{enec}}}\cdot {\left\{{PQD}_{r,c}\cdot \left(1+{tqd}_{r,c,h}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r,c,h}\cdot {\mathit{\mathrm{efffc}}}_{r,c,h,g}\right\}}^{el_{r,c,h}^{\mathit{\mathrm{enec}}}}}{\sum_{cp}{\beta}_{r, cp,h}^{\mathit{\mathrm{enec}}}\cdot {\left\{\kern-0.05em {PQD}_{r, cp}\cdot \left(1+{tqd}_{r, cp,h}\right)\kern-0.05em ++{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot {\mathit{\mathrm{enur}}}_{r, cp,h}\cdot {\mathit{\mathrm{efffc}}}_{r, cp,h,g},\kern-0.05em \right\}}^{el_{r, cp,h}^{\mathit{\mathrm{enec}}}}},\hfill \\ {}& \kern-5.2em \forall r\in R,h\in H,c\in ENE\kern1em \hfill \end{array} $$

• Household utility (AIDADS):

$$ {Vu}_{r, c h}=\sum_{ch} V{\mu}_{r, c h, h}\cdot \ln \left(\frac{QCH_{r, c h, c}}{poph_{r, h}}-\theta {h}_{r, c h, h}\right)-\left( \ln A+1\right),\kern1em \forall r\in R, h\in H $$

• Household marginal share (AIDADS):

$$ V{\mu}_{r, ch, h}=\frac{\left[\alpha {h}_{r, ch, h}+\beta {h}_{r, ch, h}\cdot {e}^{uh_{r, h}}\right]}{\left[1+{e}^{uh_{r, h}}\right]},\kern1em \forall r\in R, ch\in CH, h\in H $$

• Household consumption spending (AIDADS):

$$ \begin{array}{ll}{QCH}_{r, ch,h}\cdot {PQH}_{r, ch,h}=& \kern-33.5em {\mathit{\mathrm{poph}}}_{r,h}\cdot \hfill \\ {}[\begin{array}{l}\theta {h}_{r, ch,h}\cdot {PQH}_{r, ch,h}+V{\mu}_{r, ch,h}\cdot \\ {}\kern-0.40em \left(\kern-0.40em ,\begin{array}{l}{EH}_h-\sum_{c^{\prime}\in C\_ ENE}\left({PQD}_{r,c\hbox{'}}\cdot {\mathit{\mathrm{dfpq}}}_{r,c\hbox{'},h}\cdot \left(1+{tqd}_{r,c\hbox{'},h}\right)+\sum_{g\in G}{\mathit{\mathrm{PGHG}}}_r\cdot {gwp}_g\cdot {\mathit{\mathrm{efffc}}}_{r,c\hbox{'},h,g}\right)\cdot {\mathit{\mathrm{QCARENE}}}_{r,{c}^{\prime },h}\\ {}-\sum_{chp\in CH}{PQH}_{r, ch p,h}\cdot \theta {h}_{r, ch p,h}\end{array},\kern-0.20em \right)\kern-0.45em \end{array}],\hfill \\ {}\kern1em \forall r\in R, ch\in CH,h\in H\hfill \end{array} $$

• Investment demand:

$$ {QINV}_{r, c}={IADJ}_r\cdot \overline{qinv_{r, c}},\kern1em \forall r\in R, c\in C $$

• Government consumption demand:

$$ {QG}_{r, c}=\overline{GADJ_r}\cdot \overline{qg_{r, c}},\kern1em \forall r\in R, c\in C $$

• Government revenue:

$$ \begin{array}{ll}{YG}_r=& \sum_{i\in \mathit{\mathrm{INSDNG}}}{\mathit{\mathrm{TINS}}}_{r,i}\cdot {YI}_{r,i}+\sum_{f\in F}{tf}_{r,f}\cdot {YF}_{r,f}\hfill \\ {}& +\sum_{a\in A}{ta}_{r,a}\cdot {PA}_{r,a}\cdot {QA}_{r,a}+\sum_{a\in A}{tva}_{r,a}\cdot {PVA}_{r,a}\cdot {QVA}_{r,a}\hfill \\ {}& +\sum_{c\in CM}{tm}_{r,c}\cdot {PWM}_c\cdot {dis\_ imp}_{r,c}\cdot {QM}_{r,c}\cdot {\overline{EXR}}_r\hfill \\ {}& +\sum_{c\in CE}{te}_{r,c}\cdot {PWE}_c\cdot {dis\_\mathit{\exp}}_{r,c}\cdot {QE}_{r,c}\cdot {\overline{EXR}}_r\hfill \\ {}& +\sum_{c\in C}\sum_{a\in A}{tqd}_{r,c,a}\cdot {\mathit{\mathrm{dfpq}}}_{r,c,a}\cdot {PQD}_{r,c}\cdot {\mathit{\mathrm{QINT}}}_{r,c,a}\hfill \\ {}& +\sum_{c\in C}\sum_{h\in H}{tqd}_{r,c,h}\cdot {\mathit{\mathrm{dfpq}}}_{r,c,h}\cdot {PQD}_{r,c}\cdot {QH}_{r,c,h}\hfill \\ {}& +\sum_{c\in C}{tqd}_{r,c," gov"}\cdot {\mathit{\mathrm{dfpq}}}_{r,c," gov"}\cdot {PQD}_{r,c}\cdot {QG}_{r,c}\hfill \\ {}& +\sum_{c\in C}{tqd}_{r,c,"S-I"}\cdot {\mathit{\mathrm{dfpq}}}_{r,c,"S-I"}\cdot {PQD}_{r,c}\cdot {\mathit{\mathrm{QINV}}}_{r,c}\hfill \\ {}& +\sum_{f\in F}{ YI F}_{r," gov",f}+{\mathit{\mathrm{TRII}}\_\mathit{\mathrm{Resource}}}_{r," gov"}\hfill \\ {}& -{\mathit{\mathrm{TRII}}\_ Use}_{r," gov"}+{\mathit{\mathrm{GHGTCOST}}}_r\cdot {\mathit{\mathrm{shincome}}}_{r," gov"}\hfill \\ {}& +{GHG\_ IMP}_r\cdot {EXR}_r\cdot \left({\mathit{\mathrm{PGHG}}\_ IMP\_ QUO}_r-{\mathit{\mathrm{PGHG}}\_ EXP\_ QUO}_r\right)\hfill \\ {}& +{\mathit{\mathrm{shres}}}_{r," gov"}\cdot \sum_{a\in A}{\mathit{\mathrm{PRES}}}_{r,a}\cdot {\mathit{\mathrm{QRES}}}_{r,a}\kern2em \forall r\in R\hfill \end{array} $$

• Government expenditure:

$$ {EG}_r=\sum_{c\in C}{PQD}_{r, c}\cdot {dfpq}_{r, c," gov"}\cdot \left(1+{tqd}_{r, c," gov"}\right)\cdot {QG}_{r, c}\kern2em \forall r\in R $$

• Transfer use

$$ {TRII\_ Use}_{r, i}={shii\_ use}_{r, i}\cdot \left(1-{MPS}_{r, i}\right)\cdot \left(1-{TINS}_{r, i}\right)\cdot {YI}_{r, i},\kern1.5em \forall r\in R, i\in INSDNG $$

• Government transfer use:

$$ {TRII\_ Use}_{r," gov"}=\overline{{trnsfr\_ CRT}_{r," gov"}}\cdot {CPI}_r\kern2em \forall r\in R $$

• Transfer resource:

$$ \begin{array}{ll}{\mathit{\mathrm{TRII}}\_\mathit{\mathrm{Resource}}}_{r,i}=\kern-1em & :{\mathit{\mathrm{shii}}\_\mathit{\mathrm{resource}}}_{r,i}\cdot \hfill \\ {}& \left({crt\_\mathit{\mathrm{in}}}_r\cdot \overline{EXR_r}-{crt\_\mathit{\mathrm{out}}}_r\cdot \overline{EXR_r}+\sum_{i\hbox{'}}{\mathit{\mathrm{TRII}}\_ Use}_{r,{i}^{\prime }}\right),\hfill \\ {}& \forall r\in R,i\in \mathit{\mathrm{INSD}}\ \hfill \end{array} $$

• Imported commodity:

$$ {QWM}_{r, c}={QM}_{r, c},\kern0.75em \forall r\in R, c\in CM $$

• Exported commodity:

$$ {QWE}_{r, c}={QE}_{r, c},\kern0.75em \forall r\in R, c\in CE $$

• World trade nominal balance:

$$ \begin{array}{c}\sum_{r\in R}\left(1-{tw}_{r, c}\right)\cdot {PWM}_c\cdot {QWM}_{r, c}\cdot dis\_{imp}_{r, c}=\sum_{r\in R}{PWE}_c\cdot {QWE}_{r, c}\cdot {dis\_\mathit{\exp}}_{r, c}\\ {}\kern-10em -\sum_{c\in C\_ TRS}{PTRS}_c\cdot {QTRS}_c,\kern1em \forall c\in \left( CM\cap C E\right)\end{array} $$

• World trade volume balance:

$$ \sum_{r\in R}{QWM}_{r, c}=\left(1-{\lambda}_c^w\right)\cdot \sum_{r\in R}\left({QWE}_{r, c}-{QTRS}_c\right),\kern0.75em \forall c\in \left( CM\cap CE\right) $$

• Transport service demand:

$$ {QTRS}_c={tsh}_c\cdot \sum_r{QWE}_{r, c},\kern2em \forall c\in C\_ TRS $$

• CIF and FOB relationship:

$$ {PTRS}_c\cdot {QTRS}_c=\sum_{r\hbox{'}}{tw}_{r^{\prime }, c}\cdot {PWM}_c\cdot {QWM}_{r^{\prime }, c}\cdot dis\_{imp}_{r^{\prime }, c},\kern1em \forall c\in C\_ TRS $$

• Biomass consumption (household):

$$ {TBH}_{r, h}={poph}_{r, h}\cdot {bioc}_{r, h}\cdot {biod}_{r, h}\kern2em \forall r\in R, h\in H $$

• Biomass consumption (industry):

$$ {TBI}_{r, a}={QA}_{r, a}\cdot {bioc}_{r, a}\cdot {biod}_{r, a}\kern2em \forall r\in R, a\in A $$

• Emissions related to activity level (industrial activity):

$$ \begin{array}{ll}{\mathit{\mathrm{EMALI}}}_{r,a,g}=\kern-0.91em & {QA}_{r,a}\cdot {\mathit{\mathrm{efacl}}}_{r,a,g}\cdot \left(1-{\mathit{\mathrm{NERED}}}_{r,a,g}\right)\cdot \left(1+{\chi}_{r,a,g}\right)\hfill \\ {}& -\sum_{\mathit{\mathrm{emcm}}\in \mathit{\mathrm{EMCM}}}\left(\raisebox{1ex}{${\mathit{\mathrm{QRED}}}_{r,\mathit{\mathrm{emcm}},a}$}\!\left/ \!\raisebox{-1ex}{${\eta}_{\mathit{\mathrm{emcm}},a}$}\right.\right),\kern1em \forall r\in R,a\in A,g\in G\hfill \end{array} $$

• Additional emission reductions related to activity level (industrial activity):

$$ {NERED}_{r, a, g}=1-{\left({PGHG}_r+1\right)}^{-{\sigma}_{r, a, g}^{ghg}},\kern2em \forall r\in R, a\in A, g\in G $$

• Emissions related to activity level (household):

$$ {EMALH}_{r, h, g}={poph}_{r, h}\cdot {efacl}_{r, h, g}\kern2em \forall r\in R, h\in H, g\in G $$

• Emissions related to fossil fuel combustion (industrial activity):

$$ {EMFFI}_{r, c, a, g}={QINT}_{r, c, a}\cdot {enur}_{r, c, a}\cdot {efffc}_{r, c, a, g}\kern2em \forall r\in R, c\in ENE, a\in A, g\in G $$

• Emissions related to fossil fuel combustion (household):

$$ {EMFFH}_{r, c, h, g}={QH}_{r, c, h}\cdot {efffc}_{r, c, h, g}\kern2em \forall r\in R, c\in ENE, h\in H, g\in G $$

• Emissions related to biomass combustion (industrial activity):

$$ {EMBII}_{r, a, g}={TBI}_{r, a}\cdot {efbio}_{r, a, g}\kern2em \forall r\in R, a\in A, g\in G $$

• Emissions related to biomass combustion (household activity):

$$ {EMBIH}_{r, h, g}={TBH}_{r, h}\cdot {efbio}_{r, h, g}\kern2em \forall r\in R, h\in H, g\in G $$

• GHG emission total in a region:

$$ \begin{array}{ll}\kern-0.2em {\mathit{\mathrm{GHGT}}}_r=\kern-0.75em & \sum_{g\in G}{gwp}_g\cdot \hfill \\ {}& \kern-3.9em \left\{\begin{array}{l}\left(\sum_{h\in H}\sum_{c\in C}{QH}_{r,c,h}\cdot {\mathit{\mathrm{enur}}}_{r,c,h}\cdot {\mathit{\mathrm{efffc}}}_{r,c,h,g}+\sum_{a\in A}\sum_{c\in C}{\mathit{\mathrm{QINT}}}_{r,c,a}\cdot {\mathit{\mathrm{enur}}}_{r,c,a}\cdot {\mathit{\mathrm{efffc}}}_{r,c,a,g}\right)\\ {}+\left(\sum_{h\in H}{\mathit{\mathrm{EMALH}}}_{r,h,g}+\sum_{a\in A}{\mathit{\mathrm{EMALI}}}_{r,a,g}\right)\\ {}+\left(\sum_{h\in H}{\mathit{\mathrm{EMBIH}}}_{r,h,g}+\sum_{a\in A}{\mathit{\mathrm{EMBII}}}_{r,a,g}\right)\end{array},\kern-0.45em \right\}\hfill \\ {}& \kern-3.56em \forall r\in R\hfill \end{array} $$

• GHG emission includes emission trading:

$$ {GHGT\_ CT}_r={GHGT}_r-{GHGT\_ IMP}_r\cdot \kern1.5em \forall r\in R $$

• GHG emission importing trading upper limit:

$$ \overline{{ghgt\_ imp\_ cap}_r}-{GHGT\_ IMP}_r\ge 0\kern1em \perp {PGHG\_ IMP\_ QUO}_r\ge 0\kern1.5em \forall r\in R $$

• GHG emission exporting trading upper limit:

$$ {GHGT\_ IMP}_r-\overline{{ghgt\_\mathit{\exp}\_ cap}_r}\ge 0\kern1em \perp {PGHG\_ EXP\_ QUO}_r\ge 0\kern1.5em \forall r\in R $$

• GHG emission price and international price:

$$ {\mathit{\mathrm{PGHG}}}_r={EXR}_r\cdot \left(\mathit{\mathrm{PGHG}}\_G+{\mathit{\mathrm{PGHG}}\_ IMP\_ QUO}_r-{\mathit{\mathrm{PGHG}}\_ EXP\_ QUO}_r\right)\kern1.5em \forall r\in R $$

• GHG emission constraint:

$$ \overline{ghgc_r}-{GHGT\_ CT}_r\ge 0\kern1em \perp {PGHG}_r\ge 0\kern1.5em \forall r\in R $$

• GHG emission cost of nonenergy (industry):

$$ {\mathit{\mathrm{GHGCA}}\_\mathit{\mathrm{NENE}}}_{r,a}={\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot \left({\mathit{\mathrm{EMBII}}}_{r,a,g}+{\mathit{\mathrm{EMALI}}}_{r,a,g}\right)\kern2em \forall r\in R,a\in A $$

• GHG total cost:

$$ \begin{array}{ll}{\mathit{\mathrm{GHGTCOST}}}_r=& \sum_{a\in A}\left({\mathit{\mathrm{QINT}}}_{r,c,a}\cdot {\mathit{\mathrm{enur}}}_{r,c,a}\cdot {\mathit{\mathrm{efffc}}}_{r,c,a,g}\right)\hfill \\ {}& +{\mathit{\mathrm{GHGCA}}\_\mathit{\mathrm{NENE}}}_{r,c,a}+\sum_{h\in H}{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}{gwp}_g\cdot \hfill \\ {}& \left(\sum_{c\in C}{QH}_{r,c,h}\cdot {\mathit{\mathrm{efffc}}}_{r,c,h,g}+{\mathit{\mathrm{EMALH}}}_{r,h,g}+{\mathit{\mathrm{EMBIH}}}_{r,h,g}\right)\hfill \\ {}& \kern0.21em \forall r\in R\hfill \end{array} $$

• Global GHG emission constraint:

$$ \overline{ghgtot\_ c}-\sum_{r\in R}{GHGT\_ CT}_r\ge 0\kern1em \perp PGHG\_ G\ge 0 $$

• Global GHG emission constraint price:

$$ PGHG\_ G={PGHG}_r,\kern2em \forall r\in R $$

• Global GHG emission trading total:

$$ \sum_{r\in R}{GHG\_ IMP}_r=0 $$

• GHG emission related to the international transport:

$$ {EMFFINT}_{tr, g}=\sum_{c\in C}{INTTRSENE}_{tr, c}\cdot efint\_{tr s}_{tr, c, g} $$

(GAS_FROM_FF_INT)

• International transport energy demand:

$$ {\mathit{\mathrm{INTTRSENE}}}_{tr,c}={\mathit{\mathrm{inttrenecoef}}}_{tr,c}\cdot \sum_r{\mathit{\mathrm{QDTRST}}}_{r, tr}\cdot {{\mathit{\mathrm{PGHG}}}_r}^{\mathit{\upsigma \mathrm{ghg}}\_ int} $$

(INTTRSENEDEF)

• Nonenergy related gas emissions:

$$ {EMNEG}_{r, g}={ecfneng}_{r, g}\cdot {GDP}_r $$

• Factor markets:

$$ \sum_{a\in A}{QF}_{r, f, a}={\overline{ QF S}}_{r, f},\kern1.25em \forall r\in R, f\in F $$

• Composite commodity markets:

$$ \begin{array}{c}\kern-11.05em {QQ}_{r,c}-\left( QX{2}_{r,c}+{QM}_{r,c}\right)\cdot {\mathit{\mathrm{loss}}}_{r,c}+\mathit{\mathrm{stch}}{2}_{r,c}\\ {}\kern0.2em =\sum_{a\in A}{\mathit{\mathrm{QINT}}}_{r,c,a}+\sum_{h\in H}{QH}_{r,c,h}+{QG}_{r,c}+{\mathit{\mathrm{QINV}}}_{r,c},\kern1em \forall r\in R,c\in C\end{array} $$

• Current-account balance for the rest of the world, in foreign currency:

$$ \begin{array}{ll}\hfill & \sum_{c\in CM}{PWM}_c\cdot {dis\_ imp}_{r,c}\cdot {QM}_{r,c}+{\mathit{\mathrm{transfr}}\_ crt\_\mathit{\mathrm{out}}}_r\\ {}& +{GHG\_ IMP}_r\cdot {\mathit{\mathrm{PGHG}}}_r+\sum_{f\in F}{\mathit{\mathrm{transfr}}}_{r," ROW",f}=\sum_{c\in CE}{PWE}_c\cdot {dis\_\mathit{\exp}}_{r,c}\cdot {QE}_{r,c}\hfill \\ {}& +{\mathit{\mathrm{transfr}}\_ crt\_\mathit{\mathrm{in}}}_r+\overline{{\mathit{\mathrm{FSAV}}}_r}+\sum_{f\in F}{\mathit{\mathrm{transfr}}\_\kern0.17em f}_{r,\kern0.10em f," ROW"}\hfill \\ {}& \kern0.4em \forall r\in R,f\in F\hfill \end{array} $$

• Government balance:

$$ {YG}_r={EG}_r+{GSAV}_r\kern2em \forall r\in R $$

• Direct tax rate:

$$ {\mathit{\mathrm{TINS}}}_{r,i}=\overline{{\mathit{\mathrm{tins}}}_{r,i}}\cdot \left(1+\overline{{\mathit{\mathrm{TINS}\mathrm{ADJ}}}_r}\cdot \mathit{\mathrm{tins}}{01}_{r,i}\right)+\overline{{\mathit{\mathrm{DTINS}}}_{r,i}}\cdot \mathit{\mathrm{tins}}{01}_{r,i},\kern1em \forall r\in R,i\in \mathit{\mathrm{INSDNG}} $$

• Institutional savings rates:

$$ {MPS}_{r,i}=\overline{mps_{r,i}}\cdot \left(1+{\overline{\mathit{\mathrm{MPSADJ}}}}_r\cdot mps{01}_{r,i}\right)+{\mathit{\mathrm{DMPS}}}_r\cdot mps{01}_{r,i},\kern1em \forall r\in R,i\in \mathit{\mathrm{INSDNG}} $$

• Savings-investment balance:

$$ \begin{array}{l}\sum_{i\in INSDNG}{MPS}_{r, i}\cdot \left(1-{TINS}_{r, i}\right)\cdot {YI}_{r, i}+{GSAV}_r+\overline{FSAV_r}\cdot \overline{EXR_r}\\ {}=\sum_{c\in C}{PQ}_{r, c}\cdot {dfpq}_{r, c," S- I"}\cdot \left(1+{tq}_{r, c," S- I"}\right)\cdot {QINV}_{r, i}+{WALRAS}_r\kern1.5em \forall r\in R\end{array} $$

• Global investment balance:

$$ \sum_{r\in R}{FSAV}_r=0 $$

• Activity constraint (upper boundary):

$$ \begin{array}{l}{\mathit{\mathrm{renew}}\_ up}_{r,a}-{QA}_{r,a}\cdot {\theta}_{r,a," COM\_ ELY"}\ge 0\kern1.5em {\mathit{\mathrm{VRENCAP}}}_{r,a}\ge 0,\\ {}\kern1em \forall r\in R,a\in A=\left\{{\mathit{\mathrm{renew}}\_ up}_{r,a}>0\right\}\end{array} $$

• Activity constraint (QUOTA for aggregated region and activity):

$$ \begin{array}{ll}{\mathit{\mathrm{quotaqa}}}_{\mathit{\mathrm{ragg}},\mathit{\mathrm{aagg}}}=\kern-0.8em & \sum_{r\in Map\_\mathit{\mathrm{Ragg}}\left(r,\mathit{\mathrm{ragg}}\right)}\sum_{a\in Map\_\mathit{\mathrm{aagg}}\left(a,\mathit{\mathrm{aagg}}\right)}\sum_{c\in C}{QA}_{r,a}\cdot {\theta}_{r,a,c}\ge 0\hfill \\ {}& \perp {\mathit{\mathrm{RQUOQA}}\_ agg}_{\mathit{\mathrm{ragg}},\mathit{\mathrm{aagg}}}\ge 0,\forall \mathit{\mathrm{ragg}}\in \mathit{\mathrm{Ragg}},\mathit{\mathrm{aagg}}\in \mathit{\mathrm{Aagg}}\hfill \end{array} $$

• Activity constraint (QUOTA shadow price):

$$ \begin{array}{c}{\mathit{\mathrm{RQUOQA}}}_{r,a}=\sum_{\mathit{\mathrm{ragg}}\in Map\_\mathit{\mathrm{Ragg}}\left(r,\mathit{\mathrm{ragg}}\right)}\sum_{\mathit{\mathrm{aagg}}\in Map\_\mathit{\mathrm{aagg}}\left(a,\mathit{\mathrm{aagg}}\right)}{\mathit{\mathrm{RQUOQA}}\_ agg}_{\mathit{\mathrm{ragg}},\mathit{\mathrm{aagg}}}\ge 0,\\ {}\kern-14.2em \forall r\in R,a\in A\end{array} $$

• End-use device stock:

$$ {END\_ STK}_{r, ac,l}=\left(\left(1-1/{\tau}_l\right)\cdot {\mathit{\mathrm{stka}}\_ pre}_{r, ac,l}\cdot \left(1-\sum_{i\in LI\left(l,i\right)}{END\_\mathit{\mathrm{QEOR}}}_{r, ac,i}\right)+{END\_ QR}_{r, ac,l}\right) $$

• End-use device stock operation:

$$ \left(1+{\lambda}_{r, ac, l}^d\right)\cdot {END\_ STK}_{r, ac, l}={END\_ QXD}_{r, ac, l} $$

• End-use device service supply:

$$ \left(1+{\varphi}_{r, ac, i}\right)\cdot \sum_{l\in LI\left( l, i\right)}\left({ad}_{r, ac, l, i}\cdot END\_{QXD}_{r, ac, l}\right)={QSD}_{r, ac, i} $$

• Industry service demand:

$$ {QSD}_{r,a,i}={sd\_\mathit{\mathrm{base}}}_{r,a,i}\cdot {\left(\frac{QA_{r,a}}{{QA\_\mathit{\mathrm{base}}}_{r,a}}\right)}^{{\mathit{\mathrm{indserincel}}}_{r,a}}\kern0.84em \forall a\notin A\_ TRS $$

• Residential service demand:

$$ {QSD}_{r, h, i}={sd\_ base}_{r, h, i}\cdot {\left(\frac{EH_{r, h}}{{EH\_ base}_{r, h}}\cdot \frac{{CPI\_ base}_r}{CPI_r}\right)}^{{r esserincel}_{r, h}} $$

• Transport service demand:

$$ {QSD}_{r, a, i}={sd\_ base}_{r, a, i}\cdot \frac{\sum_{tr\in MTR\left( tr, i\right)}{QDTRST}_{r, tr}}{\sum_{tr\in MTR\left( tr, i\right)} QDTRST\_{base}_{r, tr}}\kern0.96em \forall a\in A\_ TRS $$

• End-use device new investment selection:

$$ \begin{array}{l}\sum_{i\in LI\left( l, i\right)}\left(\left(1+{\varphi}_{r, ac, i}\right)\cdot {ad}_{r, ac, l, i}\cdot \left(1+{\lambda}_{r, ac, l}^d\right)\cdot END\_{QR}_{r, ac, l}\right)\\ {}\kern1em =\sum_{i\in LI\left( l, i\right)}\left(\frac{\mu_{r, ac, l}\cdot {\left({END\_ PCOST}_{r, ac, l}\right)}^{\eta_{r, ac, l}^{end}}}{\sum_{ll\in LI\left( l l, i\right)}\left({\mu}_{r, ac, l l}\cdot {\left({END\_ PCOST}_{r, ac, l l}\right)}^{\eta_{r, ac, l l}^{end}}\right)}\cdot END\_{QR T}_{r, ac, i}\;\right)\end{array} $$

• End-use device price:

$$ {END\_\mathit{\mathrm{PCOST}}}_{r, ac,l}={\mathit{\mathrm{invc}}}_{r, ac,l}+({\mathit{\mathrm{oped}}}_{r, ac,l}+\sum_{K\_ END}({ied}_{r, ac,l,K\_ END}\cdot ({END\_ PED}_{r,K\_ END, ac}+(1-\sum_{i\in LI\left(l,i\right)}{\mathit{\mathrm{BFRATIO}}}_{r, ac,i})\cdot {\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}\left({gwp}_{r,g}\cdot {\mathit{\mathrm{emcoef}}\_ end}_{r, ac,K\_ END,g}\right)))\;)\cdot \left(1+{\lambda}_{r, ac,l}^d\right) $$

• End-use total new investment for service:

$$ {END\_ QRT}_{r, ac, i}\ge 0\kern1em \perp \kern1em {END\_ QEOR}_{r, ac, i}\ge 0 $$

• End-use energy price:

$$ {END\_ PED}_{r, K\_ END, ac}={end\_ ped\_ base}_{r, K\_ END, ac}\cdot \sum_{c\in ENEENDMAP\left( c, K\_ END\right)}\left(\frac{PQD_{r, c}}{{PQD\_ base}_{r, c}}\right) $$

• Energy use of service i in end-use energy:

$$ {END\_ ENE}_{r, ac, i, K\_ END}=\sum_{l\in LI\left( l, i\right)}{ied}_{r, ac, l, K\_ END}\cdot {END\_ QXD}_{r, ac, l} $$

• Energy use of service i in CGE energy:

$$ \begin{array}{ll}\hfill & {\mathit{\mathrm{QEND}}\_ ENE}_{r,c, ac,i}\\ {}& =\sum_{\begin{array}{l}\mathit{\mathrm{KAGG}}\_ END\in MK\_\mathit{\mathrm{AGGC}}\left(\mathit{\mathrm{KAGG}}\_ END,c\right)\end{array}}\left(\sum_{\begin{array}{l}K\_ END\in MK\_\mathit{\mathrm{AGGEND}}\\ {}\left(\mathit{\mathrm{KAGG}}\_ END,K\_ END\right)\end{array}},\left({END\_ ENE}_{r, ac,i,K\_ END}\right),\cdot \right.\left.\frac{\mu_{r,c, ac,i}^{ea}\cdot {\left({\mathit{\mathrm{dfpq}}}_{r,c, ac}\cdot {PQD}_{r,c}\cdot \left(1+{tqd}_{r,c, ac}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}\left({gwp}_{r,g}\cdot {\mathit{\mathrm{enur}}}_{r,c, ac}\cdot {\mathit{\mathrm{efffc}}}_{r,c, ac,g}\right)\right)}^{\eta_{r,c, ac}^{ea}}}{\kern0.36em \sum_{\begin{array}{l} cp\in \mathit{\mathrm{MKAGGC}}\\ {}\left(\mathit{\mathrm{KAGG}}\_ END, CP\right)\end{array}}\left({\mu}_{r, cp, ac,i}^{ea}\cdot {\left({\mathit{\mathrm{dfpq}}}_{r, cp, ac}\cdot {PQD}_{r, cp}\cdot \left(1+{tqd}_{r, cp, ac}\right)+{\mathit{\mathrm{PGHG}}}_r\cdot \sum_{g\in G}\left({gwp}_{r,g}\cdot {\mathit{\mathrm{enur}}}_{r, cp, ac}\cdot {\mathit{\mathrm{efffc}}}_{r, cp, ac,g}\right)\right)}^{\eta_{r, cp, ac}^{ea}}\right)}\right)\;\hfill \end{array} $$

• Industry end-use energy mapping:

$$ {QINT}_{r, c, a}=\sum_i\kern0.24em {QEND\_ ENE}_{r, c, a, i} $$

• Industry end-use energy total:

$$ {QENE}_{r, a}=\sum_{c\in C\_ ENE(c)}\kern0.24em {QINT}_{r, c, a} $$

• Transport end-use energy mapping:

$$ {TRS\_ ENE\_ FL}_{r, tr, c}=\sum_{i\in MTR\_ I\left( tr, i\right)}\kern0.24em {QEND\_ ENE}_{r, c," TRS", i}\kern1.12em \forall tr\in TR $$

• Transport end-use energy total:

$$ {TRS\_ ENE}_{r, tr}=\sum_c{TRS\_ ENE\_ FL}_{r, tr, c} $$

• Residential end-use energy mapping:

$$ {QH}_{r, c, h}-{QCARENE}_{r, h, c}=\sum_i\kern0.24em {QEND\_ ENE}_{r, c, h, i} $$

• Residential car end-use energy mapping:

$$ {QCARENE}_{r, h, c}=\sum_{i\in MTR\_ I\left(" PC", i\right)}\kern0.24em {QEND\_ ENE}_{r, c," TRS", i} $$

• Residential car end-use energy total:

$$ { QCARENE T}_{r, h}=\sum_c\kern0.24em {QCARENE}_{r, h, c} $$

• End-use biofuel ratio:

$$ {BFRATIO}_{r, ac, i}\cdot \sum_{c\in MKaggc\left(" OIL", c\right)}\kern-0.24em {QEND\_ ENE}_{r, c, ac, i}=\kern0.36em {QEND\_ ENE}_{r," COM\_ BIO", ac, i} $$