Market allocation factor
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Market allocation factor is a method to balance out market situations when either the demand or supply increase or decrease. To be able to predict this, elasticity, market allocation factor, or other methods need to be used.
Contents
Question
How to predict market balances when either the demand or supply increases or decreases?
Answer
How many per cent does the supply or demand change if the price of the product increases 1 €/product unit?
Obs  Market  Activity  Use  Fuel  Unit  Amount  Description 

1  Fuel wood  Petroleum refineries  Input  Renewables and waste  MWh  1  
2  Fuel wood  CHP plants  Input  Renewables and waste  ton  1  
3  Fuel wood  Heating  Output  Renewables and waste  MWh  1  
4  Fuel wood  Other energy consumption  Output  Renewables and waste  MWh  1  
5  Traffic fuel  Petroleum refineries  Output  Petrochemical products  MWh  1  
6  Traffic fuel  Final energy use  Output  Petrochemical products  MWh  1  
7  Traffic fuel  Petroleum refineries  Output  Petrochemical products  MWh  1  
8  Traffic fuel  Petroleum refineries  Output  Petrochemical products  MWh  1  
9  Global oil  Petroleum refineries  Input  Crude oil  MWh  1  
10  Global oil  CHP plants  Input  Crude oil  ton  1  
11  Peat  CHP plants  Input  Coal and peat  ton  1  
12  District heat  CHP plants  Output  Heat  MWh  1  
13  National electricity  CHP plants  Output  Electricity  MWh  1  
14  Emission trade  CHP plants  Output  CO2e  ton  1  
15  Emission trade  Final energy use  Output  CO2e  ton  1  
16  Cardboard  Other energy consumption  Output  Cardboard products  ton  1 
⇤#: . The input/output column does not make sense. The meaning depends on the part of the energy balance table (supply, transformation, use) where the activity is. Can it be dropped? Jouni 12:09, 24 April 2012 (EEST) (type: truth; paradigms: science: attack)
Rationale
Explanations of the calculations
The logic of the code is the following:
 Energy contains information about the total amounts of energy in a given Activity * Fuel pair per time unit (typically a year). (For example, 54 ktoe/a petrochemical products are used in road transport.)
 Trans contains descriptions of all activities that result in the production or use of energy. (For each ktoe used in road transport, 1 ktoe is imported.
 When these two are merged, we get a table that explains where the energy came from and where the energy went, assuming that all energy flow goes through that activity.
 The ratio of the actual energy stock to the energy stock in the activity table is used as the factor to scale the whole activity (not only the energy). This is done by merging the data.frame with factors again with the activities (tran) and multiplying the factor with the activities. This gives the BAU situation.
 We assume that current energy production and use is distributed in such a way that the cost curves are in balance. If the price changes, both the supply and demand will change according to their cost curves. The new balance can be found from where f_{i} are the cost curves (supply functions producing positive values and demand functions negative values. When p is solved from the equation, values of all supply and demand functions can be solved. If all functions
then individual functions and also the sum of all functions can be expanded and then easily be solved by using the equation for polynomial roots:
Cost curves are parameterised in the way that the current price p = 0 and therefore the current supply or demand is c_{i}.
When a demand or supply changes, a new price p must be calculated based on f_{i}, and then the supplies and demands of other actors can be calculated, resulting in a new balance.
Taxes are complicating this picture. They do not actually change the shape of a cost curve (if it is proportional to energy content) but they shift a supply curve to right (or a demand curve to left if the tax is payed by the buyer and not the seller) by the amount of the tax. In other words, instead of p we solve , i.e.
where t is the amount of tax to the suppliers. With the same formula, it is also easy to calculate particular taxes, where the tax per unit energy is different to different suppliers. Then we simply use t_{i} instead of t.
How to estimate parameters a, b, and c?
Let's start from a simple approach. If the cost curve is linear, then a = 0. If all suppliers or all buyers change their behaviour in the same way (in relative terms) to price changes, then b_{i} are proportional to c_{i}. If we don't care about the absolute values yet, we can simply start from these assumptions and say: a = 0, b = c, c = the current amount of demand or supply, and p = 0.
The curves can be generalised to that they are polynomials with higher degree than just 2. The computations are more laborious, but the computer solves that problems with no additional burden to the user.
#: . We could use a tool that estimates the parameters based on some points that a user gives on a graph about his/her personal cost curve. Jouni 06:53, 2 February 2012 (EET) (type: truth; paradigms: science: comment)
See also
References
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