MIRAGE-VA supply side

Substitutions in the production chain

Contrary to previous versions of the MIRAGE-e model, different sectors now have very different production functions, mainly due to their different behavior towards non-CO\(_2\) emissions. To classify the different sectors and model their production function, MIRAGE-VA mainly follows Hyman et al. (2003). This results in five potentially different production functions, that only differ by their top-level nesting (see below):

  • Legacy MIRAGE top-tier
  • Fossil production
  • Energy-intensive manufacturing
  • Agriculture and forest
  • Non-energy, non-agriculture production

Top-level of production function

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

Each box corresponds to a MIRAGE-VA variable in this figure, 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-CO\(_2\) greenhouse gases

Each non-CO\(_2\) greenhouse gas (CH\(_4\), N\(_2\)O, and fluorinated gases \(FGAS\)) enters the production function as a component of production: their value is calibrated at the level of CO\(_2\)-equivalent emissions they generate, and an arbitrary small price.

The elasticity of substitution is chosen following Hyman et al. (2003) and represents the different abatement costs corresponding to the greenhouse gas.

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 petroleum 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. includes 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 across sectors in MIRAGE-VA:

Emissions from CO\(_2\)-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 across sectors :

The Trade page presents the demand for goods by origin.


Hyman, Robert C., John M. Reilly, Mustafa H. Babiker, Ardoin De Masin, and Henry D. Jacoby. 2003. “Modeling Non-CO2 Greenhouse Gas Abatement.” Environmental Modeling and Assessment 8 (3): 175–86. https://doi.org/10.1023/a:1025576926029.