# MIRAGE-e 2 supply side

Production makes use of five factors: capital, skilled labour, unskilled labour, land and natural resources. Factor endowments are assumed to be fully employed.

### Factor supply

Growth rates of factor supply are:

• Natural resources:
• Labor: Exogenous growth based on EconMap, differentiated by skill level
• Land: Endogenous to the model, based on an isoelastic function of the real return to land
• Capital: Endogenous to the model, determined by domestic savings (exogenous share of revenue) and current account (exogenous share of world GDP), both projected by EconMap.

### Factor mobility

#### Capital, natural resources

Installed capital and natural resources are sector-specific, so that their rates of return may vary across sectors and regions.

#### Labour

Labour is region-specific, but perfectly mobile between sectors (agricultural vs. non-agricultural segmentation to be updated).

#### Land

This global factor is distributed across productions based on the assumption that it is a Constant Elasticity of Transformation (CET) function of land demands; this assumption introduces an imperfect mobility of land across uses.

Contrary to previous versions of the MIRAGE-e model, different sectors now have very different production function, mainly due to their different behavior towards non-CO2 emissions. To classify the different sectors and model their production function, MIRAGE-e mainly follows (Robert C Hyman, John M Reilly, Mustafa H Babiker, Ardoin De Masin, Henry D Jacoby, 2003). This results in five potential different production function, that only differ by their top-level nesting (see below):

• Legacy MIRAGE top-tier (used only when aggregation do not follow the requirements for non-CO2 GHGs)
• Fossil production
• Energy-intensive manufacturing
• Agriculture and forest
• Non-energy, non-agriculture production

### Top-level of production function

As pointed ou above, the top-level of production function is different from one sector to the other. The different alternatives are the following:

In this figure, each box corresponds to a MIRAGE-e variable and arrows denote the aggregation relation, most often a CES aggregate. Elasticities of substitution are shown with the different values for $\sigma$ ($\sigma=0$ means the functional form is Leontief).

#### Bundles

• $Y$ is the total production of a given sector
• $VA$ corresponds to the value-added and energy bundle (see below)
• $IC$ corresponds to the intermediate consumption bundle (see below)
• Other bundles, depicted in light gray, are simple CES bundles of the different components

#### Non-CO2 greenhouse gases

Each non-$CO_2$ greenhouse cas ($CH_4$, $N_2O$ and fluorinated gases $FGAS$) enter the production function as a component of production : their value is calibrated at the level of $CO_2$-equivalent emissions their generate and an arbitrary small price.

#### Fossil-specific resource

In fossil energy production, the fuel-specific resource is of two different types:

• This is the natural resource $NatRes$ in case of primary fossil energy production (coal, oil, gas)
• This is crude oil in the case of pretroleum and coal products

#### Value for elasticities

$\sigma_{TOP}$ Standard 0.30 EPPA value (for PFC and SF6 ; 0.15 only for HFC)
Energy-intensive 0.11 EPPA value
Agriculture 0.02 Lowest EPPA value (because EPPA elast. include sector substitutions)
Primary fossil fuel 0.7 Previous MIRAGE-e value. EPPA Value: 0.6
Petroleum 0 Previous MIRAGE-e value (idem EPPA)
$\sigma_{NFGAS}$ Standard 0.11 EPPA value
$\sigma_{NCH4}$ Agriculture 0 Usual CNTER substitution in MIRAGE-e
Energy-intensive 1 EPPA value
$\sigma_{NIC}$ Agriculture 0.02 Lowest EPPA value (idem $\sigma_{TOP}$)
$\sigma_{NN2O}$ Energy-intensive 0.6 EPPA value
$\sigma_{NNR}$ Fossil 0 EPPA Value

Value-added and energy bundle is identical accross sectors in MIRAGE-e, given that energy in value added is toggles (and aggregation meets the requirements of separating the five energy goods) :

#### Emissions from CO2-emitting fuels

For $CO_2$-emitting fuels (coal, oil, gas and refined petroleum), the $CO_2$ emissions are proportional to the volume of fuel demanded:

### Intermediate consumption

Intermediate consumption is identical accross sectors :

The demand for good by origin is presented in the Trade page.

1. ^ a b Robert C Hyman, John M Reilly, Mustafa H Babiker, Ardoin De Masin, Henry D Jacoby, 2003. Modeling non-CO2 greenhouse gas abatement. Environmental Modeling \& Assessment, 8, Springer, pp.175–186.