Welfare (02_welfare)

Description

The welfare module enables the implementation of different social welfare functions.

Interfaces

Input

Output

Realizations

(A) 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 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.

Transformation of coal to liquids/gases/H2 brings local pollution, which is less accepted at higher incomes -> use the inconvenience cost channel

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 $(ttot.val ge 2005),
        pm_welf(ttot) * pm_ts(ttot) * (1 / ( (1 + pm_prtp(regi))**(pm_ttot_val(ttot)-2005) ) )
        *   (  (pm_pop(ttot,regi) 
                *   (
                        ((( (vm_cons(ttot,regi)*(1-cm_damage*vm_forcOs(ttot)*vm_forcOs(ttot)))/pm_pop(ttot,regi))**(1-1/pm_ies(regi))-1)/(1-1/pm_ies(regi)) )$(pm_ies(regi) ne 1)
                       + (log((vm_cons(ttot,regi)*(1-cm_damage*vm_forcOs(ttot)*vm_forcOs(ttot))) / pm_pop(ttot,regi)))$(pm_ies(regi) eq 1)
                    )
                )
$if %cm_INCONV_PENALTY% == "on"  - v02_inconvPen(ttot,regi) - v02_inconvPenCoalSolids(ttot,regi)
$if "%cm_INCONV_PENALTY_FESwitch%" == "on"  - sum((entySe,entyFe,te,sector,emiMkt)$(se2fe(entySe,entyFe,te) AND entyFe2Sector(entyFe,sector) AND sector2emiMkt(sector,emiMkt) AND (entySeBio(entySe) OR entySeSyn(entySe) OR entySeFos(entySe)) ), v02_NegInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt) + v02_PosInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt))/1e3 
            )
        )
;

Calculation of the inconvenience penalty:

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

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

\[\begin{multline*} vm\_demFeSector(ttot,regi,entySe,entyFe,sector,emiMkt) - vm\_demFeSector(ttot-1,regi,entySe,entyFe,sector,emiMkt) + v02\_NegInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt) - v02\_PosInconvPenFeBioSwitch(ttot,regi,entySe,entyFe,sector,emiMkt) = 0 \end{multline*}\]

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.

Limitations There are no known limitations.

Definitions

Objects

Sets

Authors

See Also

01_macro, 15_climate, 23_capitalMarket, 31_fossil, 45_carbonprice, 51_internalizeDamages, 80_optimization, core

References