The welfare module enables the implementation of different social welfare functions.
| Description | Unit | A | |
|---|---|---|---|
| cm_damage | cm_damage factor for forcing overshoot | x | |
| pm_ies (all_regi) |
intertemporal elasticity of substitution | x | |
| pm_pop (tall, all_regi) |
population data | \(bn people\) | x |
| pm_ts (tall) |
(t_n+1 - t_n-1)/2 for a timestep t_n | x | |
| pm_ttot_val (ttot) |
value of ttot set element | x | |
| sm_giga_2_non | giga to non | x | |
| sm_GJ_2_TWa | multiplicative factor to convert from GJ to TWa | x | |
| vm_cesIO (tall, all_regi, all_in) |
Production factor | x | |
| vm_cons (ttot, all_regi) |
Consumption | x | |
| vm_prodSe (tall, all_regi, all_enty, all_enty, all_te) |
se production. | \(TWa\) | x |
| Description | Unit | |
|---|---|---|
| pm_prtp (all_regi) |
Pure rate of time preference | |
| pm_w (all_regi) |
Negishi weights | |
| pm_welf (tall) |
Weight parameter in the welfare function to avoid jumps with cm_less_TS | |
| vm_forcOs (ttot) |
Forcing overshoot | |
| vm_welfareGlob | Global welfare |
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)
)
)
;Calculation of the inconvenience penalty:
\[\begin{multline*} v02\_inconvPen(t,regi) \geq \cdot ' local air pollution for all entySe production except for coal solids \left(=sesofos\right), which is treated separately \left(see below\right) SUM\left(pe2se(enty,entySe,te)\$\left(NOT sameas(entySe,"sesofos")\right), p02\_inconvpen\_lap(t,regi,te) \cdot vm\_prodSe(t,regi,enty,entySe,te) \right) \end{multline*}\]
\[\begin{multline*} v02\_inconvPenCoalSolids(t,regi) \geq \cdot ' local air pollution for coal: inconvinienve penalty applies only for buildings use \end{multline*}\]
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.
| Description | Unit | A | |
|---|---|---|---|
| p02_inconvpen_lap (ttot, all_regi, all_te) |
Parameter for inconvenience penalty for local air pollution. | \(T\$/TWa at Consumption of 1000\$/cap\) | x |
| q02_inconvPen (ttot, all_regi) |
Calculate the inconvenience penalty v02_inconvPen | x | |
| q02_inconvPenCoalSolids (ttot, all_regi) |
Calculate the inconvenience penalty v02_inconvPen | x | |
| q02_welfare | Regional welfare | x | |
| q02_welfareGlob | Global welfare | x | |
| v02_inconvPen (ttot, all_regi) |
Inconvenience penalty in the welfare function, e.g. for air pollution. Unit: ?Utils? | x | |
| v02_inconvPenCoalSolids (ttot, all_regi) |
Inconvenience penalty in the welfare function, e.g. for air pollution. Unit: ?Utils? | x | |
| v02_sesoInconvPenSlack (ttot, all_regi) |
Slack to avoid negative inconvenience penalty for Coal Solids | x | |
| v02_welfare (all_regi) |
Regional welfare | x |
| description | |
|---|---|
| all_enty | all types of quantities |
| all_in | all inputs and outputs of the CES function |
| all_regi | all regions |
| all_te | all energy technologies, including from modules |
| enty(all_enty) | all types of quantities |
| entySe(all_enty) | secondary energy types |
| in(all_in) | All inputs and outputs of the CES function |
| modules | all the available modules |
| pe2se(all_enty, all_enty, all_te) | map primary energy carriers to secondary |
| regi(all_regi) | all regions used in the solution process |
| t(ttot) | modeling time, usually starting in 2005, but later for fixed delay runs |
| tall | time index |
| te(all_te) | energy technologies |
| ttot(tall) | time index with spin up |
01_macro, 15_climate, 23_capitalMarket, 31_fossil, 45_carbonprice, 51_internalizeDamages, 80_optimization, core