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


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.

See land section for details

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).


  • $Y$ 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

Elasticity Sectors Value Comments
$\sigma_{TOP}$ 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

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.