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Own-price elastic supply curve
Dear All,

I would like to ask for your experience and a little help defining supply curve using own-price elasticity rather than different technologies.

The reason we would like to use this (more like a top-down approach) method is that our team is considering to model several industry sectors, however some of those are quite heterogeneous and therefore data intensive. 

Moreover, due to the lack of time we have, we would like to model the supply-side of these sectors by not defining any technologies (and their cost and technology parameters), but rather considering the technological change as a change in the fuel mix for the given sector. Therefore, we would take into account the fuel costs of the relevant energy carriers as building blocks of the short-run supply curve and aggregate these blocks into one final supply curve.  

As quantity "range" (defined by a minimum and a maximum value for an energy carrier as quantity demanded - horizontal axis of the inverse supply curve) for any energy carrier we would provide parameters exogenously (similarly to the own-price elastic demand curve method and based on previous energy balances for Hungary). 

My question would be if any of you have met the same challenge and - if you would be kind to share - what were your solutions? Also, do you find this method possible to insert in TIMES?

I have read Antti's paper from 2010 on "Elastic supply cost curves in TIMES" and the related "Appendix B Damage Cost Functions" part from the "Documentation for the TIMES model - Part II", which I found very useful and thank you for those. However, if it is possible, could you please provide an example from TIMES that you have been worked with before, in order to be able to see how it looks in "real life"? Smile 

Thank you very much for your answer and help in advance! 
Any help is very much appreciated!   

Best regards,
I am not sure what kind of an example you are looking for, but I just tested the example given in the note on Elastic Supply curves, using an exogenously specified Base price (defined by DAM_COST(r,y,c,cur)) and Base quantity (DAM_BQTY(r,c)), and it worked well.  So, at least the example given in that note is a working example, which just has to be supplemented with the Base price and Base quantity when these are exogenous. In VEDA the limitation is that VEDA only supports DAM_BQTY for defining the Base quantity and it has no year index.

It is of course possible to model such supply curves manually, by introducing a process (or a process flow) for each step of the curve. I have a vague feeling that Amit Kanudia (the main VEDA designer) may have done some automation for creating such under VEDA.
Dear Antii,

Thank you very much for your help. Indeed, the note on Elastic Supply curve is very helpful and it seems the we have managed to apply elastic supply curves based on exogenously specified Base Price and Base quantity.

May I have another question that is related to demand functions with constant elasticity of substitution (CES) ?
I have found that in the DemoS examples there are practices about how to define elastic demand curves. Is there maybe an example about how to precisely define elastic demand functions with CES?

The reason why I am asking because after I have read the TIMES Micro note on Elastic Demand Functions I am a bit confused on which parameters should be provided by the user:

1) In the last paragraph of section 2.3 (pp. 5) it is written that the own-price elasticity for the component demand (Ei) /defined by COM_ELAST(r,t,c,s,lim=LO/UP)/ and also for the aggregate demand (Ek) /defined by COM_ELAST(r,t,c,s,lim=FX) for the linear case/ have to be defined along with the substitution elasticities of aggregate demands (sigma k) /defined by COM_ELAST(r,t,c,s,lim=N)/.

2) However, in the paragraph after eq. 22 in section 3.2 (pp.7) it is stated that "As the own price elasticity of the CES component demands are equal with the common ubstitution elasticity (Ei=- sigma k)". Could you please help me how should one understand this? Thank you!

I would also have another question about defining the "substitution elasticity of component demands of the demand aggregation represented by commodity c": COM_ELAST(r,t,c,s,lim=N).
Does it mean that COM_ELAST(r,t,c,s,lim=N) should be defined for each component demand? The reason I am bit confused here is that as far as i understood, a component demand can belong to more aggregate demand: e.g. we are trying to model modal shift in the transport sector, where the component demands are the different modes of transportation (e.g. car, train, bus etc.) and the aggregate demands are represented by a matrix of distance (short-long) and type (person vs. freight), therefore there are 4 different aggregate demands. However a component demand (let's say car) can be allocated to both "long- and short-distance person travelling" aggregate demands. In this case one should define two "car" component demands one for each aggregate demand in order to be able to use two different CES parameter for two the aggregate demands?

I am sorry for the long post and thank you for your help.

Best regards,
I am sorry, I cannot see any reference to COM_ELAST on page 5, and neither should there be any such.

The TIMES user interface is described in Section 4 (pages 9-10), which states that you should use COM_ELAST(r,t,com,ANNUAL,'N'), where com is the aggregate demand, for defining the substitution elasticities for the component demands. It is also said there that the own price elasticities can be defined by COM_ELAST(r,t,com,ANNUAL,bd), where bd=UP/LO/FX. Thus, for a CES demand function you should define:

 • COM_VOC(r,t,c,bd) for the component demands c
 • COM_STEP(r,c,bd) for the component demands c
 • COM_VOC(r,t,com,bd) for the aggregate demand com
 • COM_STEP(r,com,bd) for the aggregate demand com
 • COM_ELAST(r,t,com,'ANNUAL','N') for the aggregate demand com (substitution among components)
 • COM_ELAST(r,t,com,'ANNUAL',bd) for the aggregate demand com (own price elasticity of com)
 • COM_AGG(r,t,c,com) for the aggregation of components c into com

Specifying any COM_ELAST for the component demands of a CES function is discouraged.

I don't think you can feed the same component into several aggregate demands, but you should split "car" into short-distance car travel and long-distance car-travel, because using car in both would clearly seem inconsistent to me. I would say that any such "loops" in the CES structure (which should have a tree topology) are unsupported...
Dear Antti,

Thank you very much for your quick and helpful reply. You made thinks more clear.

May I ask two more questions?
1) In regards to your answer and the example we have mentioned above: does it mean that the component demand c is e.g. short-distance car-travel, while the aggregate demand com is e.g. short-distance travel? And the demand projection /COM_PROJ(r,t,c)/ then should be exogenously provided only for the component demand c (in our example for short-distance car-travel) ?

2) Could you please describe from TIMES Micro note the definition of "dag_k,i (t)" and "alpha_k,i(t)"? Are they related to each other?
Does the aggregation of components c into com /COM_AGG(r,t,c,com)/ describes any of these? Or should one only use /COM_AGG(r,t,c,com)/ to "link" the component demands to the appropriate aggragate demand? If the latter case holds, should we use the parameter "1" (which would indicate in the above example that e.g. 100% of the short-distance car-travel is considered to be allocated to the short-distance travel)?

Thank you again for all your kind help!

Best regards,
1) Yes. All component demand should have baseline demand projections.  Surely one would usually not let the model optimize between short distance/long distance, but their baseline demands are defined exogenously.

2) In a proper CES function, Com_Agg should be set to zero as mentioned in the doc, and the model then internally derives the aggregation parameters according to the price ratios (in the elastic policy runs).

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