# Non-biomass renewables - C3IAM

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C3IAM uses an additional production input called the ‘fixed factor’ to describes the representative capacity building constraint of energy technologies. The fixed factor is used to represent the specialized resources that are required for capacity building such as knowledgeable engineering, specialized manufacturing and services. The price of the fixed factor will therefore affect the rate at which this technology enters the market. If the demand for the technology is high, the fixed factor price representing the limited resources will also be high, thereby limiting the initial rate of expansion of production from new energy technologies and taking into consideration the adjustment costs [1].

The fixed factor also represents innovation in the form of learning-by-doing, which shows that the constraint is less binding as production and experience is gained. The representative agent is endowed with a very small amount of the particular fixed factor resource for each technology in the base year[2], and${\displaystyle FF_{t}}$for the base year is 0.00001 in the model. The amount of fixed factor then is increased as a function of cumulative production of that technology, representing cost reduction as we learn and gain experience. The equation for endowment is based on the forms in McFarland et al. (2004)[3], Jacoby et al. (2005) [2] and Ereira et al. (2010) [1]:

${\displaystyle FF_{t+1}=FF_{t}+({\alpha }{Y_{t}}^{\gamma }+\lambda {Y_{t}}^{\zeta })}$

Where ${\displaystyle Y_{t}}$is the electricity output for a given technology in period t. ${\displaystyle \alpha {Y_{t}}^{\gamma }}$is approximately linear with  ${\displaystyle \gamma =0.8\sim 0.9}$and ${\displaystyle \alpha =0.01}$. This term governs the growth of the fixed factor at low levels of output ${\displaystyle {Y_{t}}^{\gamma }}$as${\displaystyle \alpha >>\lambda }$. The term ${\displaystyle \lambda {Y_{t}}^{\zeta }}$accelerates fixed factor growth at high levels of output as ${\displaystyle \lambda =0.00001}$and${\displaystyle \zeta =2.0\sim 2.2}$[3].

### References

1. Eleanor Charlotte Ereira, 2010. Assessing early investments in low carbon technologies under uncertainty: the case of Carbon Capture and Storage. Massachusetts Institute of Technology.
2. Henry D Jacoby, John M Reilly, James R McFarland, Sergey Paltsev, 2006. Technology and technical change in the MIT EPPA model. Energy Economics 28, 610-631.
3. J.R. McFarland, J.M. Reilly, H.J. Herzog, 2004. Representing energy technologies in top-down economic models using bottom-up information. Energy Economics. 26, 685–707.