11.2 List of parameters, variables, GAMS names, and parameter values

Table 11.1: Symbolic terms and GAMS names
Symbol Definition GAMS Unit
\(W(clt)\) Aggregated welfare UTILITY unitless
\(w_{t,n}\) Negishi weights w_negishi(t,n) unitless
\(C(t,n)\) Consumption Q(‘CC’,t,n) T$
\(l(t,n)\) Population l(t,n) Million people
\(\beta\) Utility discount factor stpf(t) unitless
\(\eta\) Inverse of IES eta unitless
\(\rho\) Pure rate of time preference srtp(t) unitless
\(\gamma\) Degree or inequality aversion gamma unitless
\(C(t,n)\) Consumption Q(‘CC’,t,n) T$
\(I_{FG}(t,n)\) Investment in final good I(‘FG’,t,n) T$
\(I_j(t,n)\) Investment in energy technologies I_EN(jinv,t,n) T$
\(I_{GRID}(t,n)\) Investment in electric grid I_EN_GRID(t,n) T$
\(I_{OUT,f}(t,n)\) Investment in extraction I_OUT(f,t,n) T$
\(I_{RD,j}(t,n)\) Investment in R&D I_RD(rd,t,n) T$
\(I_{PRADA}(t,n)\) Investment in proactive adaptation I(‘PRADA’,t,n) T$
\(I_{SCAP}(t,n)\) Investment in specific ad. capacity I(‘SCAP’,t,n) T$
\(I_{RADA}(t,n)\) Investment in active adaptation I(‘RADA’,t,n) T$
\(Y(t,n)\) Net Output Q(‘Y’,t,n) T$
\(oem_j(t,n)\) O&M costs in energy technologies oem(j,t,n) $/TW
\(oem\_ex_f\) O&M coefficient in extraction oem_ex(f) $/TWh
\(K_j(t,n)\) Capital in energy tech. K_EN(j,t,n) TW
\(Q_{OUT,f}(t,n)\) Total extraction of fuel \(f\) Q_OUT(f,t,n) TWh
\(tfp0(n)\) Initial level of TFP tfp0(n) unitless
\(C_e(t,n)\) GHG emissions costs COST_EMI(j,t,n) T$
\(C_f(t,n)\) Net cost of Primary Energy Supplies COST_PES(f,t,n) T$
\(C_j(t,n)\) Energy technology penalty costs COST_EN(j,t,n) T$
\(ES(t,n)\) Energy services Q(‘FEN’,t,n) T$
\(K_{FG}(t,n)\) Capital in final good K(‘FG’,t,n) T$
\(Q_E(ghg,t,n)\) Emissions Q_EMI(ghg,t,n) Gt-eqC
\(tfp_y(t,n)\) Total factor productivity tfpy(t,n) unitless
\(l(t,n)\) Population l(t,n) Million people
\(\delta_{FG}\) Yearly depreciation rate of capital delta(‘fg’,t,n) unitless
\(\Delta_{\text{t}}\) Time step duration tstep years
\(EN(t,n)\) Energy aggregate Q(‘en’,t,n) T$
\(HE(t,n)\) R&D Capital in energy efficiency K_RD(‘en’,t,n) T$
\(tfpn(t,n)\) Factor productivity of energy tfpn(t,n) unitless
\(EL(t,n)\) Energy aggregate from the electric sector Q(‘el’,t,n) T$
\(NEL(t,n)\) Energy aggregate from the non-electric sector Q(‘nel’,t,n) T$
\(I_j(t,n)\) Investment in energy tech. I_EN(jinv,t,n) T$
\(K_j(t,n)\) Capital in energy tech. K_EN(j,t,n) TW
\(SC_j(t,n)\) Average investment cost MCOST_INV(j,t,n) T$/TW
\(\delta_j(t,n)\) depreciation rate delta(j,t,n)
\(EL(t,n)\) Electric sector aggregate Q(‘el’,t,n) T$
\(EL2(t,n)\) Electric sector aggregate (w/o hydro) Q(‘el2’,t,n) T$
\(EL_{coalwbio}(t,n)\) Coal & wood biomass power plant aggregate Q(‘coalwbio’,t,n) T$
\(EL_{gas}(t,n)\) Gas power plant sector Q(‘gas’,t,n) T$
\(EL_{hydro}(t,n)\) Hydroelectric sector Q(‘ces_elhydro’,t,n) T$
\(EL_{intren}(t,n)\) Intermittent renewable aggregate Q(‘ces_elintren’,t,n) T$
\(EL_{nucback}(t,n)\) Nuclear and backstop aggregate Q(‘ces_elnuclearback’,t,n) T$
\(EL_{oil}(t,n)\) Oil power plant sector Q(‘oil’,t,n) T$
\(ELFF(t,n)\) Fossil-fuel power plants aggregate Q(‘elff’,t,n) T$
\(NEL(t,n)\) Non-electric sector aggregate Q(‘nel’,t,n) T$
\(NEL_{coal}(t,n)\) Energy in Coal sector Q_EN(‘nelcoal’,t,n) TWh
\(NEL_{log}(t,n)\) Other non-electric sector aggregate Q(‘nelog’,t,n) T$
\(NEL_{trbiomass}(t,n)\) Energy in traditional biomass sector Q_EN(‘neltrbiomass’,t,n) TWh
\(NEL_{oilback}(t,n)\) Energy in oil and backstop non-electric Q_EN(‘neloilback’,t,n) TWh
\(NEL_{gas}(t,n)\) Energy in gas sector Q_EN(‘nelgas’,t,n) TWh
\(NEL_{trbiofuel}(t,n)\) Energy in Traditional biofuel Q_EN(‘neltrbiofuel’,t,n) TWh
\(Q_f(t,n)\) Total amount of fuel consumed Q_PES(f,t,n) TWh
\(Q_{j,f}(t,n)\) Total amount of fuel consumed per sector Q_IN(f,jfed,t,n) TWh
\(Q_f(t,n)\) Total amount of fuel consumed Q_PES(f,t,n) TWh
\(X_f(t,n)\) Total amount of fuel extracted Q_OUT(f,t,n) TWh
\(C_f(t,n)\) Primary Energy Supplies cost COST_PES(f,t,n) T$
\(MC_f(t,n)\) Average cost of Primary Energy Supplies MCOST_PES(f,t,n) T$/TWh
\(Q_f(t,n)\) Total amount of fuel consumed Q_PES(f,t,n) TWh
\(X_f(t,n)\) Total amount of fuel extracted Q_OUT(f,t,n) TWh
\(p_f(t,n)\) World market fuel prices FPRICE(f,t) T$/TWh
\(EL_j(t,n)\) Electric production capacity Q_EN(jel,t,n) TWh
\(KEL_j(t,n)\) Capital in electric production K_EN(jel,t,n) TW
\(\mu_j(t,n)\) Capacity factor of maximum production mu(jel,t,n) TWh/TW
\(EL_{elback}(t,n)\) Electric backstop capacity Q_EN(‘elback’,t,n) TWh
\(KEL_j(t,n)\) Total electric capacity Q_EN(‘el’,t,n) TWh
\(Q_j(t,n)\) Production capacity Q_EN(jfed,t,n) TWh
\(Q_{j,f}(t,n)\) Amount of fuel consumed per sector Q_IN(f,jfed,t,n) TWh
\(\xi_{j,f}(t,n)\) Sector efficiency ratio csi(f,jfed,t,n) TWh/TWh
\(Q_j(t,n)\) Production capacity Q_EN(j,t,n) TWh
\(I_{PRADA}(t,n)\) Investment in proactive adaptation I(‘PRADA’,t,n) T$
\(I_{SCAP}(t,n)\) Investment in specific ad. capacity I(‘SCAP’,t,n) T$
\(I_{RADA}(t,n)\) Investment in active adaptation I(‘RADA’,t,n) T$
\(I_{RADA}(t,n)\) Investment in active adaptation I(‘RADA’,t,n) T$
\(NEL_{nelback}(t,n)\) Non-electric backstop capacity Q_PES(‘backnel’,t,n) TWh
\(Q_{CCS}(t,n)\) CCS emissions Q_EMI(‘ccs’,t,n) GtC-eq
\(M_{CCS}(t)\) CCS cumulated emissions CUM_EMI(‘ccs’,t,n) GtC-eq
\(C_{CCS}(n,t)\) CCS costs MCOST_EMI(‘ccs’,t,n) T$
\(Q_E(\text{ghg},t,n)\) Regional emissions Q_EMI(ghg,t,n) GtC-eq
\(WE(\text{ghg},t)\) World emission W_EMI(ghg,t,n) GtC for CO2/Gt
\(M(\text{ghg},t)\) Concentrations WCUM_EMI(ghg,t,n) GtC for CO2/Gt
\(TRF(t)\) Total radiative forcing TRF(t,n) W/m2
\(RF(\text{ghg},t)\) Gas radiative forcing RF(t,n) W/m2
\(T(t)\) Global temperature increase TEMP(‘atm’,t,n) C
\(T^o(t)\) Ocean temperature increase TEMP(‘low’,t,n) C
\(Q_{CO2}(t,n)\) CO2 emissions Q_EMI(‘co2’,t,n) GtC-eq
\(Q_{CO2ind}(t,n)\) CO2 emissions from fossil-fuel Q_EMI(‘co2ind’,t,n) GtC-eq
\(Q_{CO2lu}(t,n)\) CO2 emissions from land-use change Q_EMI(‘co2lu’,t,n) GtC-eq
\(Q_{redd}(t,n)\) Avoided emissions from REDD Q_EMI(‘redd’,t,n) GtC-eq
\(Q_{CCS}(t,n)\) CCS emissions Q_EMI(‘ccs’,t,n) GtC-eq
\(EX_f(t,n)\) CO2 emissions from extraction Q_EMI_OUT(‘co2’,t,n) GtC-eq
\(Q_{oghg}(t,n)\) other ghg emissions Q_EMI(oghg,t,n) GtC-eq
\(ABAT(oghg,t,n)\) level of abatment ABAT(oghg,t,n) [0-1]
\(Q_{nip}(t,n)\) net import of carbon permits Q_EMI(‘nip’,t,n) GtC-eq
\(C_{CO2}(t,n)\) CO2 costs COST_EMI(‘co2’,t,n) T$
\(Q_{nip}(t,n)\) net import of carbon permits Q_EMI(‘nip’,t,n) GtC-eq
\(p_{nip}(t,n)\) carbon permits price CPRICE(‘nip’,t,n) T$/GtC-eq
\(C_{e}(n,t)\) Non-CO2 emission costs COST_EMI(oghg,t,n) T$
\(ref_e(n,t)\) Baseline emissions emi_baseline(oghg,t,n) GtC-eq
\(\overline{abat}_e(n,t)\) Maximum abatement emi_abat_max(oghg,t,n) [0,1]
\(ABAT_e(n,t)\) Non-CO2 emission abatment ABAT(t,n) [0,1]
\(C_{e}(n,t)\) Emission sink costs COST_EMI(e,t,n) T$
\(Q_{e}(t,n)\) Emission sink Q_EMI(e,t,n) GtC-eq
\(M_{SAV}(t,n)\) Accumulated emission savings CUM_EMI(‘sav’,t,n) GtC-eq
\(Q_{SAV}(t,n)\) Emission savings Q_EMI(‘sav’,t,n) GtC-eq
\(\Omega(t,n)\) Damage coefficient OMEGA(t,n) unitless
\(\omega_{i,n}^-\) coefficients with negative impact comega_neg(n,i) unitless
\(\omega_{i,n}^+\) coefficients with positive impact comega_pos(n,i) unitless
\(T(t,n)\) atmospheric temperature increase from pre-industrial levels TEMP(‘atm’,t,n) C
\(Q(ADA,t,n)\) Adaptation factor Q(‘ADA’,t,n)
\(HE(n,t)\) R&D Capital in energy efficiency K_RD(‘en’,t,n) T$
\(RD_{j}(n,t)\) R&D Capital in backstop technologies K_RD(rd,t,n) T$
\(SPILL(n,t)\) Spillover knowledge SPILL(rd,t,n) T$
\(wcum_{j}(t)\) Cumulated Installed Capacity wcum(jrd,t) T$
\(\delta_{RD}\) Depreciation rate for R&D knowledge delta_RD(‘en’)
\(a\) Internal spillover crda(‘en’,t,n)
\(b\) Elasticity w.r.t. R&D Investment crdb(‘en’)
\(c\) Elasticity w.r.t. own past knowledge crdc(‘en’,t,n)
\(d\) Elasticity w.r.t. spillover knowledge crdd(‘en’)
\(lbrrate\) Learning by Searching Coefficient lbr_rate(‘jrd’)
\(lbdrate\) Learning by Doing Coefficient lbd_rate(‘jrd’)
\(kpat0\) knowledge stock in 2005 kpat0
\(pat0\) annual flow of patents in 2005 pat0
\(enintg0\) 5 years decline in energy intensity (2005-2010) enintg0
\(peng0\) 5 years growth in energy price (2005-2010) peng0
\(gdpg0\) 5 years growth in gdp (2005-2010) gdpg0
\(OIL_{cap}(t,n,g)\) Oil extraction capacity (by category) OILCAP(t,n,oilg) TWh
\(\Delta CAP(t,n,g)\) Additional oil capacity (by category) ADDOILCAP(t,n,oilg) TWh
\(I_{OILCAP}(t,n,g)\) Oil investment (by category) I_OIL(t,n,oilg) T$
\(OIL_{capcost}(t,n,g)\) Oil Investment cost (by category) COST_OIL(t,n,oilg) T$/TWh
\(OIL_{prod}(t,n,g)\) Oil production (by category) OILPROD(t,n,oilg) TWh
Cumulative production (by category) CUM_OIL(t,n,oilg) TWh
Total Oil investment (all categories) I_OUT(t,n) T$
Total oil production (all categories) Q_OUT(oil,t,n) TWh
Emissions from oil extraction (all categories) Q_EMI_OUT(t,n) GtC-eq
\(\lambda(g)\) Fixed floor cost component (by categories) data_oilcost(n,oilg) T$/TWh
\(\zeta(n,g)\) Annual Expansion threshold esp_cap(n,oilg) TWh
\(\mu(g)\) Fixed floor cost difference (among categories) cum_param_oil(n,oilg) T$/TWh
\(OIL_{res}(t,n,g)\) Oil resources resmax_oil(n,oilg) TWh
Stoichiometric coefficient for oil extraction emi_st_oil(n,oilg) GtC/TWh
\(K_{EN}(jel,t,n)\) Electric capacity K_EN(jel,t,n) TW
\(Q_{EN}(jel,t,n)\) Electric energy generation Q_EN(jel,t,n) TWh
\(K_{EN}(jel_{solar},t,n)\) Electric capacity K_EN(jel_solar,t,n) TW
\(dens(jel_{solar},n)\) Installation density inst_density(n,jel_solar) MW/km^2
\(area(solar_{distance},n)\) Competition area inst_area(n,solar_distance) km^2
\(SHARE_{EL}(jel,t,n)\) Share in the electricity mix SHARE_EL(jel,t,n) unitless
\(c(n)\) Peak load fraction firm_coeff(n) unitless
\(cf(jel,t,n)\) Capacity factor cap_factor(jel,t,n) unitless
\(cv(SHARE_{EL})\) Capacity value cap_value(jel,t,n) unitless
\(f(jel)\) Flexibility coefficient flex_coeff(jel) unitless
\(K_{EN\_GRID}(t,n)\) Capital of the electrical grid K_EN_GRID(t,n) TW
\(I_{EN\_GRID}(t,n)\) Investments in the electrical grid I_EN_GRID(t,n) T$
\(delta\_grid(t,n)\) Grid depreciation rate grid_delta(t,n) unitless
\(grid\_cost\) Grid specific investment cost grid_cost T$/TW
\(transm\_cost(jel,distance)\) Distance-dependant transmission cost transm_cost(jel,distance) T$/TW
\(tfpy(t,n)\) Total factor productivity tfpy(t,n) unitless
\(tfpn(t,n)\) Factor Productivity of energy tfpn(t,n) unitless
\(Y_{kali}(n,t)\) Calibration GDP ykali(t,n) T$
\(TPES_{kali}(n,t)\) Calibration Energy demand tpes_kali(t,n) EJ
\(\varepsilon_{Y,E}(n,t)\) Investment in extraction income_ela(t,n) unitless
\(r\) Relationship between traditional biomass consumption and GDP trbio_ctr unitless
\(\phi_{n}\) Share of traditional biomass on TPES trbio_ctr(‘phi’,n) percentage
\(Q_{trbiomass,t,n}\) Quantity of primary energy of traditional biomass Q_PES(‘trbiomass’,t,n) EJ
\(ldv\_total(t,n)\) Total number of ldvs ldv_total(t,n) million vehicles
\(ldv\_pthc (t,n)\) Number of ldvs per thousand capita ldv_pthc(t,n) vehicles per thousand capita
\(stfr\_total(t,n)\) Total number of trucks ldv_total(t,n) million vehicles
\(K_{EN}(jveh,t,n)\) Number of ldvs per type K_EN(jveh,t,n) million vehicles
\(Q_{EN}(jveh,t,n)\) Energy used by ldvs Q_EN(jveh,t,n) TWh
\(fuel\_cons(jveh,t,n)\) Fuel consumption per ldv fuel_cons(jveh,t,n) MWh/km
\(fueleff\_rate(t,n)\) Fuel efficiency improvement rate fueleff_rate(t,n) unitless
\(travel\_intensity\_ldv(t,n)\) Travel Intensity LDV travel_intensity_ldv(t,n) km/$
\(km\_d\_ldv(t,n)\) Kilometre demand per LDV km_d_ldv(t,n) km/veh
\(km\_d\_ldv\_tot(t,n)\) Total kilometre demand LDV km_d_ldv_tot(t,n) million km
\(km\_d\_stfr(t,n)\) Kilometre demand per truck km_d_stfr(t,n) km/veh
\(km\_d\_stfr\_tot(t,n)\) Total kilometre demand freight km_d_stfr_tot(t,n) million km
\(load\_factor\_ldv(t,n)\) Load factor LDV load_factor_ldv(t,n) persons/vehicle
\(load\_factor\_stfr(t,n)\) Load factor freight load_factor_stfr(t,n) tons/vehicle
\(s\_d\_ldv(t,n)\) Service demand per LDV s_d_ldv(t,n) pkm/veh
\(s\_d\_ldv\_tot(t,n)\) Total service demand LDV s_d_ldv_tot(t,n) million pkm
\(s\_d\_stfr(t,n)\) Service demand per truck s_d_stfr(t,n) tkm/veh
\(s\_d\_stfr\_tot(t,n)\) Total service demand freight s_d_stfr_tot(t,n) million tkm
\(veh\_cost(jveh,t,n)\) Vehicle cost MCOST_INV(jveh,t,n) T$/million vehicles
\(inv\_cost\_trad\_cars\) Capital cost of traditional cars inv_cost_veh(‘trad_cars’) T$/million vehicles
\(size\_battery(jveh)\) Battery size size_battery(jveh) kWh/veh