Marginal costs and tariffs
How to price energy?
Jakob Rehme
Marginal cost
The change in total cost that comes from making or producing one additional item.
The purpose of analyzing marginal cost is often to determine at what point an organisation can achieve economies of scale. The calculation is most often used among manufacturers as a means of isolating an optimum production level.
The marginal cost shows how much an extra unit of the resource will cost to produce, (or the money saved if the demand can be reduced by one unit.)
Marginal cost – the supply curve
As the price of a produced good is increased, from point 1 to point 2 firms will find that the point at which marginal costs exceed marginal revenue occurs at a higher total production quantity. Firms will increase production to this level of
output, and total units supplied to the marketplace will increase, to point 3 in the figure above.
Similarly, as the price of a produced good is decreased, firms will find that marginal costs exceed marginal revenues at a lower number of output units, firms will decrease output to this level, and the total number of units supplied to the
marketplace will decrease.
We will here talk about marginal cost pricing as being a result of the cost curve, which in turn is based on energy demand
Diminishing marginal utility of consumption results in a negative relationship between the price of a good and the total quantity of that good
demanded from the marketplace.
When the price is PA, the total number of units desired for consumption is QA.
If the price of the good is suddenly increased to PC while we still are consuming QA (depicted by point "B”) - we will conclude that the benefit of the marginal units consumed no longer exceeds the cost of those units.
We will continue to reduce total units demanded until they reach a level at which utility from the marginal units demanded do not exceed the higher price PC.
The new price-quantity combination depicted by point "C" represents another point on the demand curve
Marginal utility – the demand curve
The demand is not only dependent on the price alone, par;cularly for energy -‐ aspects such as how cold or warm it is, the economic ac;vity etc.
Marginal cost
Marginal cost pricing implies that you always pay based on the cost for marginal production.
Consider a district heating plant:
During summer we do not need so much heat and hence we can provide all heat by using garbage as a fuel. This lead to
Marginal cost
Our district heating plant example:
At the autumn the incineration plant cannot provide enough heat. Therefore one has to use other fuels as well:
In this case residuals from demolished wooden buildings. This is also a cheap fuel but more expensive than garbage.
All heat from the district heating plant is now priced as coming from the more expensive source.
Marginal cost
Marginal pricing means that you charge customers with the highest (marginal cost) price for all their demand.
However, in a market this directs customers demand pattern.
If the customers finds the price too high they will therefore reduce their demand.
For our example the district heating plant: this means that garbage should be the marginal source again.
Marginal cost
• When the marginal cost is high the utility can earn money
because only part of their fuel is expensive.
• This surplus can be used for new investments (or better
profitability)
• Economic science tells us that marginal cost pricing is
"optimal" and sends precise signals to customers how to behave.
Marginal cost
• Marginal pricing is not suitable for items that differ in quality.
• For example: one specific brand of MP3 player/or jeans brand does not
have the same prestige/quality as another brand. They can be priced very differently where the market (we as consumers) accepts higher prices than marginal costs for such items.
• Heat, in the form of warm water, or electricity, is likely to be the same
everywhere but you need several providers to compete for the customers.
• This is also the case for other industries, such as paper & pulp, or steel
– but for certain qualities (also cf. different qualities for oil etc.)
• However there are differences where added capacity will be positioned
on the cost curve (paper & pulp lower end of cost curve; steel higher end; energy higher end) – depending on the cost of inputs, the process cost and the capital costs.
Marginal cost
If you connect your building to a district heating grid you normally only have one provider of the heat.
They can therefore charge you with higher prices than the marginal cost. If you do not like their prices you must install other equipment, such as solar panels.
Marginal cost
The utility does not like solar panels because they cannot sell heat during summer.
For instance Tekniska Verken, therefore, has a special summer price of only 0.07 SEK/kWh, while it is five times higher during winter, when solar panels have very little efficiency (almost do not work) .
For a utility company you could even say that the marginal cost for garbage is negative, since the alternative cost for not using garbage as fuel could be regarded as high.
Marginal cost
Sometimes it is
complicated to calculate the marginal cost, since there are many
alternatives/options for energy with various
degrees of connection in-between
Marginal cost
In a CHP plant you manufacture two ”commodities”. • Electricity
• Hot water
The electricity production is dependent of the heat production and vice versa.
Marginal cost
If electricity is sold to the surrounding market and the income covers the production cost for producing the electricity alone
And the heat coming from the process need to be cooled down for the electricity production to work (otherwise you need cooling towers)
The heat coming from this process could therefore be regarded as being very cheap = waste.
Marginal cost
During summer, electricity demand goes down and prices on the electricity market will be comparably low.
The CHP plant cannot compete with prices for ”free water” → only heat is produced but by putting fire to garbage. = ”Almost free”.
Marginal cost
Different fuels are introduced
depending on
demand and cost
Garbage Crushed car tyres Demolished buildings
Marginal cost
First, the cheapest fuel is sufficient
Marginal cost
When demand increases (it
becomes colder), other fuels are needed
Example
• A district heating utility uses 4 boilers.
• 80 MW garbage 0.05 SEK/kWh,
• 120 MW tyres 0.15,
• 100 MW coal 0.4 and
• 100 MW oil 0.6 SEK/kWh.
• The demand is depicted by a triangle with corners in
(0,400) (10000,0) and (0,0). Use hours for a normal year. • Calculate the total cost if marginal costing applies.
Marginal cost
Draw a graph for easier un- derstanding 400MW 100MW 80MW 10,000hours 120MW 100MW 8760hours
Marginal cost
The slope of the line is: 10,000 400 or = 25 M W 400 10,000 h = 0.04 M W h Startwith thisarea 49.6MW 8,000hours 400MW 10,000hours 80MW 120MW 100MW 100MW 8,760hours
Marginal cost
Now calculate the size of the gray area:
760
×
49.6 +
760
×
(80
−
49.6)
= 49, 248
MWh
2
The cost for this area is 0.05 SEK/kWh. The gray area cost/ revenue will be:
Marginal cost
Now calculate the cost/revenue for the new gray area: 5,000hours 8,000hours 200MW 80MW 10,000hours 120MW 0.15SEK/kWh 400MW 100MW 100MW 8760hours
Marginal cost
The most expensive fuel cost is 0.15 SEK/kWh and hence the demand will be: For the square:
[(8, 000 − 5, 000) × 80 = 240,000 MWh
For the triangle:
(8, 000 − 5, 000) × 120
2 ] = 180,000 MWh
And the revenue:
Marginal cost
Corresponding calculations for the next two marginal fuels will give us the total revenue:
2.462 + 63.0 + 250.0 + 525.0 = 840.462 MSEK
Dividing this total revenue with the total amount of energy will give us:
840.462 × 106
Marginal cost
If we just calculated the cost in the ”normal” way we would get: 75.0 + 150.0 + 117.0 + 34.8 = 376.842 M S E K
This corresponds to 0.191 SEK/kWh.
We see that marginal costing gives the utility a surplus which can be used for investments (or profitability).
Marginal cost
Marginal cost pricing calls for several “sources of energy” at different cost levels. If we have only one “source of energy” for the entire energy system – there will be no
surplus value for the energy company/utility and therefore no surplus value/money for new investments.
Then you must use alternative pricing, i.e. take what you can, or in other words what the market can bear.
Think of fees for passing a bridge. You take the bridge as long as the alternative cost (fee + your estimated value of potential time saving) is cheaper than the alternative (the ferry, or driving a detour) – thus setting the price. (District heating compared with the alternative – solar panels – electricity etc.)
In reality – for a district heating plant (in effect a monopoly) political reasons prevent too high prices.
Marginal cost
Marginal costs are difficult to apply in real world because the utility must inform the customers of the price in ”real time”.
If you are not informed of the price you can not act according to economic theory.
Some believe that smart-grids could be a solution for this.
Examples of events/decisions that affect the cost/price for energy: Consider a lake with water.
Water in a hydro power station is almost always free but with marginal cost pricing the value can change, i.e. if you can store water from summer to winter.
During very cold winters the electricity system might not have the capacity to provide everybody with power.
If all peak generators are operating no higher marginal cost is present (no possibility for import).
You then have to add a cost for scarcity, i.e. if you pass a certain level customers have to be disconnected from the grid, and this is a cost that is regarded as very high (blackouts/and grid congestions are costs that are factored in to the
calculation).
Marginal cost
At Nord Pool the system price is set according to marginal cost pricing. This price is not transferred directly to end users, because of taxes
and intermediate power brokers.
Even if price is set according to Nord Pool you pay an average for one month, or so.
You cannot avoid the high cost hours because you do not have the information.
Marginal cost
Some companies have predominantly old and very low cost sources of energy.
An example is VaBenfall in Sweden, with their hydro power sta;ons.
With marginal cos;ng they can have substan;al surplus revenues.
However, for the en;re energy system there will eventually be a need for new investments as well as re-‐investments
Marginal cost
The reason for a u;lity to introduce a marginal cost tariff is that the company by this can make the consumers act in an op;mal way.
The cost for the u;lity varies in the same way as the cost for the customer.
When the cost is high for the u;lity the consumer wants to reduce his/her demand.
Marginal cost
If you, as a customer, want to compare a tradi;onal tariff with a one based on marginal cos;ng it is important that both tariffs have the same ”demand level”
This means that they must result in the same average price for iden;cal demand.
Marginal cost
Cheaper district heat during summer makes it harder for solar panels to compete
However note that heat for space/room heating during summer is normally not necessary.
The solar panels might only reduce the demand for domestic hot water heating.
Marginal cost
In Sweden about 50 % of the price for households is tax. Pricing is therefore far from optimal if only the utility is
considered.
However, so called external effects might lead to optimal pricing for the society as a whole.
The level of this optimal pricing is a constant source of
Bio-fuel
In Sweden there is a large potential for using bio-fuel. Such fuel is not aggravating the greenhouse conditions. Bio-fuel can be bio-gas, ethanol, methanol, wood chips, grass, pellets and even olive nuclei.
Bio-fuel in the form of wood logs has a long tradition in Sweden.
Bio-fuel
A very large part of Sweden is
covered by forests.
Bio-fuel
Wood in the form of residuals from saw mills can be used as a fuel. Also logging residues are used (tops and
Bio-fuel
Others want the saw dust, or shavings, as well (paper & pulp for instance). There is a competition for the raw material.
Paper & pulp and other wood industries are worried that wood fuel prices become high – competition for wood resources
For instance in Europe wood panel manufacturers are struggling since energy companies have a higher buying power
Wood as a fuel
Absolutely dry wood contains about 4,500 kcal/kg. This is the same as 5.24 kWh. Such dry wood does not normally exist. We have to use a special expression to reduce the energy amount according to the moisture content u.
Cl = 4, 500 − 600u
1 + u
If we have u=20% Cl will become 3650 kcal or 4.24 kWh.
Wood as a fuel
• Using wood as a fuel is, however, coupled with some
difficulties:
• Automatic furnaces cannot deal with wood logs but need
pellets.
• Such pellets are not very cheap.
• You also get a lot of ash as a residual.
• Smoke from the chimney can also make life hard for
people with lung problems.
• You are normally not allowed to use wood as a heat
Ethanol
• Ethanol is a good replacement for petrol in cars.
• You do not have to change the car very much.
• However, more fuel is used.
• The prices for petrol and ethanol make many people run
on petrol in spite of environment hazards.
• Ethanol is made of corn, cerials et cetera, which people
can eat.
• A large scale ethanol production can aggravate famine
Methanol
• Methanol can be made by gasification of wood while
ethanol is made by fermentation.
• The first process is better in terms of efficiency but more
difficult in large scale processing.
• No factory for methanol from wood exist in Sweden today.
• One famous Swede Björn Gillberg has a project in
Methanol
Some advantages:
• Many newer cars can operate on methanol
• Contains carbon, oxygen and hydrogen, i.e. you can
find it ”everywhere”. • High octane rating
Methanol
There are also drawbacks with methanol:
•
Highly corrosive. Bad fuel for old cars
Highly toxic. If you drink it you will be blind, if
not dead.
Methanol can penetrate your skin and come
into your body
•
Methanol
More drawbacks with methanol:
•
Less energy than in ethanol
Difficult to produce from biomass in a large
scale.
You need energy to produce it.
•
Ethanol
Ethanol is traded on the world market. The CME-group has a contract where one unit is 29,000 U.S. gallons.
Denaturated fuel ethanol, ASTM D4806 + according to California Standards.
Bio-diesel
Manufactured from vegetabilical oil. Made frome rape-seed oil, RME.
Sometimes Methanol added. Statoil sells RME for ≈ 13 SEK/liter. B100 requires special motors.
