Welfare (02_welfare)

Description

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

Interfaces

Input

module inputs (A: utilitarian)
	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

Output

module outputs
	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

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.

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:

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

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

Limitations There are no known limitations.

Definitions

Objects

module-internal objects (A: utilitarian)
	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

Sets

sets in use
	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

Model Documentation

| Version 2.1.0

02_welfare