Welfare (02_welfare)

Description

The welfare module enables the implementation of different social welfare functions. The ineqLognormal realization includes subregional inequality in the welfare function through a log-normal distribution. Any change in the utilitarian realization needs to be mirrored in the ineqLognormal realization!

Interfaces

Interface plot missing!

Input

Output

Realizations

(A) ineqLognormal

The ineqLognormal realization adds a representation of subregional inequality to the welfare equation. This is determined by the SSP-based Gini projections by Rao et al. and modified by the effects of climate damages and energy expenditure changes due to climate policy. It is also affected by the redistribution of carbon tax revenues, which can be distributed either proportional to income (distributionally neutral) or on an equal-per-capita basis.

The objective of the optimization is to maximize the total discounted intertemporal utility. It is summed over all regions.

\[\begin{multline*} vm\_welfareGlob = \sum_{regi}\left( pm\_w(regi) \cdot v02\_welfare(regi) \right) \end{multline*}\]

Total discounted intertemporal regional welfare calculated from per capita consumption summing over all time steps taking into account the pure time preference rate. Assuming an intertemporal elasticity of substitution of 1, it holds:

q02_welfare(regi) ..
  v02_welfare(regi)
  =e=
    sum(ttot$( ttot.val ge 2005 ),
      pm_welf(ttot)
    * pm_ts(ttot)
    / ((1 + pm_prtp(regi)) ** (pm_ttot_val(ttot) - 2005))
    * ( ( pm_pop(ttot,regi)
        * ( ( ( ( (  vm_cons(ttot,regi)
          * exp(
              -0.5 
            * (1 / pm_ies(regi))
            * v02_distrFinal_sigmaSq_welfare(ttot,regi)
            )
          )
        / pm_pop(ttot,regi)
        )
         ** (1 - 1 / pm_ies(regi))
          - 1
          )
        / (1 - 1/pm_ies(regi)) 
        )$( pm_ies(regi) ne 1 )
      + ( log((vm_cons(ttot,regi)) / pm_pop(ttot,regi))
        - 0.5 * v02_distrFinal_sigmaSq_welfare(ttot,regi)
        )$( pm_ies(regi) eq 1 )
          )
        )
$ifthen %cm_INCONV_PENALTY% == "on"
      - v02_inconvPen(ttot,regi) - v02_inconvPenCoalSolids(ttot,regi)
$endif
$ifthen "%cm_INCONV_PENALTY_FESwitch%" == "on"
      - sum((entySe,entyFe,te,sector,emiMkt)$(
                                    se2fe(entySe,entyFe,te)
                                AND entyFe2Sector(entyFe,sector)
                                AND sector2emiMkt(sector,emiMkt) 
                                AND (entySeBio(entySe) OR  entySeFos(entySe)) ),
          v02_NegInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt)
          + v02_PosInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt)
          )
          / 1e3 
$endif
$ifthen not "%cm_seFeSectorShareDevMethod%" == "off"

        - vm_penSeFeSectorShareDevCost(ttot,regi)
$endif
      )
    )
;

Defining variables which are useful for the inequality module: 1/ Energy Expenditures 2/ Revenues from taxes

\[\begin{multline*} v02\_energyExp(ttot,regi) = \sum_{se2fe(entySe,entyFe,te)}\left( \sum_{sector2emiMkt(sector,emiMkt),entyFe2Sector(entyFe,sector)}\left( vm\_demFeSector(ttot,regi,entySe,entyFe,sector,emiMkt) \cdot pm\_FEPrice(ttot,regi,entyFe,sector,emiMkt)\right) \right) \end{multline*}\]

\[\begin{multline*} v02\_emitaxredistr(ttot,regi) = \sum_{emiMkt}\left( vm\_emiTeMkt(ttot,regi,"co2",emiMkt)+vm\_emiCdr(ttot,regi,"co2")\$sameas(emiMkt,"ETS") + sm\_tgn\_2\_pgc \cdot \left(vm\_emiTeMkt \left(ttot,regi,"n2o",emiMkt\right)+vm\_emiCdr(ttot,regi,"n2o")\$sameas(emiMkt,"ETS")\right) + sm\_tgch4\_2\_pgc \cdot \left(vm\_emiTeMkt \left(ttot,regi,"ch4",emiMkt\right)+vm\_emiCdr(ttot,regi,"ch4")\$sameas(emiMkt,"ETS")\right) \right) + vm\_emiMacSector(ttot,regi,"co2cement\_process") + sm\_tgch4\_2\_pgc \cdot \left(vm\_emiMacSector(ttot,regi,"ch4coal")+vm\_emiMacSector(ttot,regi,"ch4gas")+vm\_emiMacSector(ttot,regi,"ch4oil")\right) + sm\_tgn\_2\_pgc \cdot \left(vm\_emiMacSector(ttot,regi,"n2otrans")+vm\_emiMacSector(ttot,regi,"n2oadac")+vm\_emiMacSector(ttot,regi,"n2onitac")\right) \end{multline*}\]

Limitations There are no known limitations.

(B) utilitarian

The utilitarian realization loads the utilitarian aka. Benthamite social welfare function, in which social welfare is equal to the discounted intertemporal sum of utility, which itself is a function of per capita consumption.

The objective of the optimization is to maximize the total discounted intertemporal utility. It is summed over all regions.

\[\begin{multline*} vm\_welfareGlob = \sum_{regi}\left( pm\_w(regi) \cdot v02\_welfare(regi) \right) \end{multline*}\]

Total discounted intertemporal regional welfare calculated from per capita consumption summing over all time steps taking into account the pure time preference rate. Assuming an intertemporal elasticity of substitution of 1, it holds:

q02_welfare(regi) ..
  v02_welfare(regi) 
  =e=
    sum(ttot$( ttot.val ge 2005 ),
      pm_welf(ttot)
    * pm_ts(ttot)
    / ((1 + pm_prtp(regi)) ** (pm_ttot_val(ttot) - 2005))
    * ( ( pm_pop(ttot,regi) 
        * ( ( ( ( vm_cons(ttot,regi)
            / pm_pop(ttot,regi)
        )
         ** (1 - 1 / pm_ies(regi))
          - 1
          )
        / (1 - 1 / pm_ies(regi))
        )$( pm_ies(regi) ne 1 )
      + log(vm_cons(ttot,regi) / pm_pop(ttot,regi))$( pm_ies(regi) eq 1 )
          )
        )
$ifthen %cm_INCONV_PENALTY% == "on"
      - v02_inconvPen(ttot,regi)
      - v02_inconvPenCoalSolids(ttot,regi)
$endif
$ifthen "%cm_INCONV_PENALTY_FESwitch%" == "on"



      - sum((entySe,entyFe,te,sector,emiMkt)$(
                                    se2fe(entySe,entyFe,te)
                                AND entyFe2Sector(entyFe,sector) 
                                AND sector2emiMkt(sector,emiMkt) 
                                AND (entySeBio(entySe) OR  entySeFos(entySe)) ),
          v02_NegInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt)
          + v02_PosInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt)
          )
          / 1e3 
$endif
$ifthen not "%cm_seFeSectorShareDevMethod%" == "off"

        - vm_penSeFeSectorShareDevCost(ttot,regi)
$endif
      )
    )
;

Calculation of the inconvenience penalty:

\[\begin{multline*} v02\_inconvPen(t,regi) \geq \cdot ' local air pollution for all entySe production except for coal solids \left(=sesofos\right), which is treated separately \left(see below\right) SUM\left(pe2se(enty,entySe,te)\$\left(NOT sameas(entySe,"sesofos")\right), p02\_inconvpen\_lap(t,regi,te) \cdot vm\_prodSe(t,regi,enty,entySe,te) \right) \end{multline*}\]

\[\begin{multline*} v02\_inconvPenCoalSolids(t,regi) \geq \cdot ' local air pollution for coal: inconvinience penalty applies only for buildings use \end{multline*}\]

Limitations There are no known limitations.

Definitions

Objects

Sets

See Also

01_macro, 23_capitalMarket, 31_fossil, 45_carbonprice, 50_damages, 51_internalizeDamages, 80_optimization, core

References