Macro-economy - WITCH

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Model Documentation - WITCH

Corresponding documentation
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Model information
Model link
Institution European Institute on Economics and the Environment (RFF-CMCC EIEE), Italy,
Solution concept General equilibrium (closed economy)
Solution method Optimization

Production function

The production side of the economy is very aggregated. Each region produces one single commodity that can be used for consumption or investments. The final good is produced using
capital, labour and energy services. In the first place capital and labor are aggregated using a Cobb-Douglas production function. This nest is then aggregated with energy services with a Constant Elasticity of Substitution production function (CES), see Figure 2.3.1 .

The optimal path of consumption is determined by optimising the intertemporal social welfare function, which is defined as the an isoelastic utility function of per capita consumption, weighted by regional population. The pure rate of time is set at 1% per year.

Energy services, in turn, are given by a combination of the physical energy input and a stock of energy efficiency knowledge. This way of modelling energy services allows for endogenous improvements in energy efficiency. Energy efficiency increases with investments in dedicated energy R&D, which build up the stock of knowledge. The stock of knowledge can then replace (or substitute) physical energy in the production of energy services.

Energy used in final production is a combination of electric and non electric energy. Electric energy can be generated using a set of different technology options and non electric energy also entails different fuels. Each region will choose the optimal intertemporal mix of technologies and R&D investments in a strategic way

Figure 2.3.1 The nested production function
WITCH CES Production Function.png