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In the last classes, you have learnt that energy has a very special role to play in
this economy. All the other sectors of economy, say transportation, say steel, say plastic,
say all these essentially use some raw materials and produce something that will be either
used in other sectors of economy or directly useful to men; you directly use it. A plastic
bag something that you directly use, but the plastic that goes into making other things,
that goes into another type of industry. The point is that in all these you need energy.
So, energy is a special sector, because in all the other sectors of economy, these things,
say a steel industry needs the things that are made, that is necessary to make steel
and its products are used only in those sectors that needs steel.
Similarly, plastic; the sectors that need plastic produce that and the sectors who do
not need it will not use that. But, energy is a sector, energy is a particular component
of the economy that is used everywhere. No production is possible without energy, right
and it is most important, because whenever you are planning, a planning takes place that
means what does the nation do? Nation plans for certain improvement, certain development
over the next 5 years, next 10 years or so. Now, suppose a country has planned to increase
the residential housing by say 10% over the next 10 years; very logical plan that will
require an increased input of bricks, mortar, stone, cement, steel, everything.
So, the production of steel will have to be increased, production of cement will have
to be increased. Now, the production of steel needs energy, production of cement needs energy.
So, you see, if you make some plan that has a multiplier effect throughout the economy
and many things needs to be changed, right. Most importantly, the energy inputs also need
to be increased. If the nation does not make provision for the necessary amount of energy
to produce the increased amount of steel, the increased amount of cement, the increased
amount of brick, increased amount of so, then the whole planning is completely useless,
right.
This is not true for other sectors of the economy. Suppose you make a plan for increase
of production of steel only, that does not require the increase of plastic, for example;
but, in case of energy, it is not so. Unless the provision for the adequate amount of energy
is made, every planning will be doomed to failure. So, one of the important things that
an energy engineer has to address is questions like supposing I plan to increase the steel
production by 10% in the next 5 years, how much additional provision for electricity
and for petroleum products should I make? Now, this is not a qualitative statement,
qualitative question. One needs a quantitative response, numbers, right. One needs a number;
how much, how big a input and exactly that amounts provisions should be made.
So, what we are now going to address is a quantitative issue, a numerical issue, something
that needs to be computed. The other aspect is that whenever we talk about a product,
for example my pen, it has some bit of steel in it; it has some bit of plastic in it, it
has some bit of ink in it. So, all that had been produced first in order to make this.
Now, when these were produced, obviously these were produced in separate industries. So,
what went into production of this pen? First, somebody mined iron ore. Then, it went to
the steel plant, there the iron was extracted, then from the iron, steel was made. Then,
from the steel these particular components were made and then it came to this - this
particular pen industry where things were assembled. Parallely, in another place, somebody
was either mining petroleum or importing petroleum and it was going to a petroleum, petrochemical
industry and the petrochemical industry was producing the material that goes into making
this plastic and then it went to some plastic industry where the plastic material was made,
then it went to this pen industry where this particular shape was given.
All this went behind making this pen and all these steps needed energy; mining needed energy,
transportation to the factory needed energy, then the factories production of steel needed
energy, so all that components needed energy. So, what we have in our hand is embodied energy,
right. How much? How much energy is embodied in this? Much is not an answer, for at least
technologists; you have to say numbers. How much, how many kilocalories is here. So, we
should also be able to calculate that. It is necessary also in the sense that over the
years how much are we improving that is often quantified by how efficient, energy efficient
are our industries. If say 15 years back this pen would require something like 100 kilocalories
of energy, just for the sake of some numbers, I am not saying that it is something like
100 kilocalories and now it is costing something like 80 kilocalories, then we have a quantification
of the improvement we have done. We are having industries that are now running more energy
efficiently.
So, we need to quantify. Otherwise, everything is fussy; everything is you know, in the air.
Technologists cannot talk in terms of fussy things. We need to talk in terms of concrete
stuff. So, the problem that I will deal with today is how to concretize it, how to quantify
these things and how to calculate this? So, in that one advantage is that in economics,
a method was developed quite long back in the 50's. This is, this was developed by
the Nobel Laureate economist Wassily Leontief. The method is called input output technique
in economics. That is very widely used in economics, in planning process and we will
make use of that technique to answer the question that I just raised.
So, initially, first I need to introduce the techniques per say and then, we will see how
to apply it for the energy sectors, its basic, specifically. So, what is happening in the
economy? In the economy, just imagine the whole economy, whole economy of this country.
It produces various things. It produces, it has agriculture, it has, you know, fertilizers,
it has say, the tractors are made that go into the agriculture, that then these are
manufacturing industries. There is steel industries, the plastic industries, petrochemical industry,
huge number of industries. Now, all these industries can be sort of clubbed. There may
be 5 petrochemical industries of more or less the same nature. So, they can be clubbed together
as the petrochemical industry of the nation. Similarly, electricity production can be clubbed
together to make one electricity sector of the economy.
Unless you do that, it becomes huge. There are huge numbers of production units and if
you consider each production unit, it becomes massive. So, that is one way of sort of organizing
the information. So, the economy is then divided into a few sectors. The sectors essentially
depend on how minutely you want to divide the economy. Normally for the planning process,
the economy is divided into something like 100 to 130 sectors; then, each sector, say
electricity sector, say steel sector. What does it do? It produces some amount of steel.
Where does the steel go? Where does the steel go? Where does the electricity go?
Some part of the steel goes into other industries. Steel goes into making cars, steel goes into
making pens, steel goes into other sectors of the economy. Electricity goes into producing
electricity, because electrical power plants also need electricity. Electricity goes into
agriculture, irrigation; electricity goes into industries, all industries and also,
electricity goes into the final consumers, who light their bulbs at their homes or fans
in their homes. So, essentially the production of every sector is consumed into two ways
-- one, either it goes to the other sectors of the economy or it goes directly into consumption,
right.
So, if for sector 1, the total production is say capital X 1 or the sector 1 could be
anything; we are just indexing the different sectors of the economy as 1, 2, 3, 4, 5, 6
and all that, so capital X 1 is the total production of the sector 1. Then, this X 1
would be divided into components. Some part of it will be going to another sector, another
sector; So, X 1 is actually small x 11 plus small
x 12 plus small x 13 and all that; means small x is the component of the production that
goes from sector 1 to sector 1, sector 1 to sector 2, sector 1 to sector 3 and all that.
Sector 1 to sector 1 - what does it mean? Say, electricity sector consuming electricity,
steel sector consuming steel, which is obviously possible. It needs energy to produce energy.
So, this x 11 will be there and the component of production that goes from sector 1 to sector
2 is x 12, a component of production that goes from sector 1 to 3 is 13 and all that.
So, it will be x 1n, provided there are n sectors plus there will be a component that
goes to the final demand that is directly consumed by the people. Let that be called
y 1.
Similarly, you have, so X 1 is this; X 2 will be, you can write in the similar way, x 21
plus x 22 plus and all that x 2n plus y 2, so on and so forth and finally you have X
n is equal to x n 1 plus n 1 plus x n 2 plus and all that x nn plus y n, right. You can
write that for the whole economy. Note what these are. You have to carefully keep track
of these quantities. So x ij is, what is x ij? Sales from sector i to ..... Now, ij goes
from 1 to n. This was important, because I am talking about sales, because each one will
be in different units. Steel is produced in say, metric tonnes, electricity is produced
in megawatts, bricks are produced in number of bricks. So, obviously everything has different
units and unless everything is brought into a same, same unit, you cannot really write
equations like this.
So, the same unit means money units. So, all these will be in money units, in terms of
how much monitory worth of the sales goes from sector 1 to sector 2, sector 1 to sector
3 and all that. Similarly, y i is final demand, final demand for the products of sector i in monetary units again and capital
X i is total output sector I, alright.
Now, it is, that is the basic component of the theory of Leontief that we define coefficients
of the, the transaction coefficients, the transection coefficients like we define the
a ij as x ij by capital X j. So, these are the transaction coefficients. What does it
mean physically? Can you, can you see what does it mean? Out of the total production
of sector i, a bit went into sector j. Out of the total production of electricity, a
bit went into the steel industry. So, steel industry consumed a bit of electricity and
in order to produce an unit amount of steel, how much was the electricity needed that is
contained in this. So, essentially these are, a ij if I write in words, it will be input
from sector i, the quantity of input from sector i required to produce one rupee worth
of the product of sector j. That is what is this, clear?
Now, if you can define this way, then you have got this.
These can be reorganized in terms of a ij and x j. So, how will you reorganize? Let
us look at that.
Then it will be, it can be, that particular set of equations can be written as a 11 capital
X 1 plus a 12 capital X 2 plus a 13 capital X 3 to a 1n X n plus y 1 is equal to X 1.
The second line a 21 X 1 plus a 22 X 2 plus a 23 X 3, so on and so forth, a 2n X n plus
y 2 is equal to X 2. Can you write this way, so on and so forth and finally, you have a
n1 X 1 plus a n2 X 2 plus a n3 X 3 to a nn X n plus y n is equal to X n, right. The moment
we have written it in this form you see a matrix in it, right. Can you see the matrix?
Can you see the, it is actually in the form of a matrix equation. The matrix equation
is A X plus Y is equal to X, right, clear? So, let us take stock of the situation. We
have got A X plus Y is equal to X. That is the basic equation we have obtained.
In it, let us write it AX plus Y equal to X; in it, what is what? Capital X matrix is,
what is size of this matrix? n cross 1, vector of sector outputs, right. Y is again n cross
1, vector of final demands and A is n cross n matrix of, these are the technical coefficients, right. Now, notice
the elements of A that we have already seen.
These are the and these essentially tell how efficiently is that particular sector of economy
performing, in terms of that particular input and that is why these are called the technical
coefficients, depends on the status of technology.
So, A matrix is dependent on the status of technology; as technology improves, the A
matrix changes. So, if you follow the evolution of the A matrix over the years in the economy,
you will be able to follow how are we improving in terms of technology, quantitatively; not
those hand waving things that we are doing very well, no, in terms of numbers. So, we
have come to this particular equation and immediately you can see that this can be easily
reorganized, as I need to extract X, right. So, X is equal to what? From here, yes, so
I minus A inverse times Y, fine, while I is a, this is also a n cross n.
Now, what does this equation tell us? Look at it carefully. Suppose what does that the
economic planning do? Economic planning essentially tells that I want to make more of these particular
things available to the people; more house to the people, more say, food to the people,
10% more food grains available to the people. So, essentially we make planning of Y. Y is
set as a policy decision by the planning commission that I want this amount increased and then
the economy needs to know that in order to make that amount available to the people,
how much should be the multiplier effect in the rest of the economy.
In order to make 10% more housing, how much will be the steel needed, how much will be
the cement needed, for that how much sand you have to mine, how much lime stone you
have to mine and how much energy must go into the lime stone industry? So, all this there
will be a multiplier effect immediately and naturally the planning has to take into account
how much should be the increase in the production of each sector and that is here. So, you make
a planning for Y, multiply it by this matrix and that gives, in terms of number how much
should we increase X.
Let us do one example. Unfortunately, the computer here does not have MATLAB, otherwise
I could have done the matrix inversion also; but, that we will leave to you to do. Let
us say a particular country, indeed we need to have a problem that can be solved within
this, you know, sheet of papers. So, I do not really, I cannot really take a big number
of sectors. So, we will take 5 numbers, something that can be written and 5 by 5 matrix, I suppose
you can invert, can you? Hey, you are scratching your head; no, no, you can always do that
by some available routine. MATLAB has readymade routine with which you can do that or XL can
also do that. So, you use whatever you are more conversant with. I am for example, more
conversant with MATLAB. But, in order to do that here I will need to install MATLAB on
to the computer. So, let us leave that.
Suppose the industry, suppose the economy has five sectors -- agriculture, manufacturing,
manufacturing means that will take into account everything, every, all types of manufacturing,
transport, electricity and other petroleum products. Let that be the division of the
economy, sector wise; very artificial division, but let us take just for the sake of illustrations
of the method.
So, you have agriculture, you have manufacturing. In one side, let me write the whole thing,
otherwise you might forget what it means. It is not a computer menu or so agriculture,
manufacturing, transport, then you have electricity and then finally, have petro products. Suppose,
this is a very artificial division, but nevertheless suffices to illustrate the concept; then,
there I will have to write agri, manufacturing, trans, elect and petro. So, we need to write
down the matrix and we also have the final demand FD, Y vector and the total. Is everything
visible on screen? Yes, okay.
So, suppose the, in million rupees, so all that we will write will be say, in crores
of rupees. So, say 10 goes from agriculture to agriculture. Where does it go from agriculture
to agriculture? Seeds, manure, everything, so organic manure; the agricultural product
going to agricultural product, so it will have some component. 20 - agriculture to manufacture.
Where does it go? Yeah, all the food producing industry; all the achars and chutneys that
you take, these are all food processing products. So, the things that you buy in the supermarket,
they are all coming from here. Transport - agriculture to transport, does anything go? Practically
none, so let us put a zero here. Later, well, when we have ethanol based transport then
there will be some component here. That means the sugarcane or other things that go, that
can produce ethanol that can be used as transport. Well, when that happens there will be component
here.
To electricity - as it is there is practically none. It is possible to have the agricultural
waste generate electricity, so presently put zero. Agriculture petroleum products or other
kinds of energy, there can be of course, because this will have to include also other sources
of energy like biogas and all, so let us put some small number and a large amount of agricultural
products are actually eaten by us. So, there will be a relatively larger component say
55. So, how much is the total? 90. Now you have here manufacture to agriculture. Yes,
all the agricultural implements are manufactured. They go into the fertilizers, so all that
say let us put some number here. Manufacture to manufacture -- yes, there will be large
component say, 30. Manufacture to transport -- yes, reasonably large component. To electricity
- there will be, but not all that big. Petroleum products, yes, there will be, but not all
that big. Manufactured products going to the final demand, obviously there will be a significant
amount say, let that be slightly less than that for the agriculture, so 40. How much
is the total? 130.
Transport to agriculture, yes, of course, agriculture products have to be transported,
so there has to be some component. Transport to manufacture, yes, manufactured product
has to be transported, so there will be some component. Transport to transport, no; transport
to transport - do you transport, transport, no. That that will be, so that will be, that
can be zero. It is possible to transport buses over buses, but let us, yeah, cars are transported
to their, but that is not the transport sector really. When car is transported to the shop,
the car shop, it is essentially the manufacturing sector that goes to the people needs. So,
transport sector means it is a service sector. Transport to electricity, yes, the coal has
to be transported to the power plant, so you have some component. Transport to petroleum
products, they also have to be transported and transport to the final demand, yes, people
have to be transported. So, there will be some larger component. How much is that? 60.
Electricity to agriculture, yes; pumping is done by electricity, so but, that is yet in
India, relatively smaller component, so 10. Electricity to manufacture, a large amount
say 40; electricity to transport, yes, trains and trams and all these things, so let there
be some component here and electricity to electricity, yes, you need to use electricity
in the power plants in order to run the motors and stuff. So, there will some component,
but that is small in comparison to that whole production of electricity, so let us put some
number, but not very large. Electricity to petroleum products, yes; petroleum refineries
do need electricity, but that will be relatively smaller compared to all the other sectors
and electricity goes to people use, yes; reasonably large. How much is the total? 110.
Then, petroleum products to agriculture, yes. All the shallow pumps are now run with petroleum
products that means, so you have 20. Petroleum products to manufacture, obviously a reasonably
large amount, 20. Petroleum products to transport - transport actually runs on petroleum products,
so .... Petroleum products to electricity, small amount is needed really; as I told you
I will, I will tell where it is, later when we discuss the electricity production in detail,
but let us put some number. Petroleum products to petroleum products -- let us put some
number. So, what do you have here and petroleum product going to directly to people use; well,
people use means the transportation sector, public transportation sector is already taken
care of, so individual use that is relatively smaller. Add them up, 90 so that is the matrix
that we have sort of cooked up. From there we need to construct the A matrix.
Now, construct the A matrix, your job. Build the first one, 10, here is 10. So, x ii, x
11 divided by X 1, 90. Second one is 20 divided by, wrong; yes; because; yes; that is the
point. It is not 90, not here; but, it is this, going to the manufacturing industry;
how much agricultural product going to manufacturing industry divided by the total product of manufacturing
industry, here. That is the technical intensity of the manufacturing sector. The other two,
next two are 0, 0, therefore if you divide by something it will still remain zero. 5
by, 5 is going to petroleum products; petroleum products final production is 90, so by 90.
Second here 20 divided by 90, 30 divided by 130, 20 divided by 60, 10 divided by 110,
40 divided by 90; am I writing right?
Sir, 10.
Oh, 10, sorry, sorry; here 10 divided by 90, I have just moved one .... So, third one,
transport, 10 divided by first sector -- agriculture, whose production, total production is 90;
10 by 90. Second one, 10 by 130, 0, 10 by 110, 10 by 90. Please keep a check. We have
come to the thing, fourth line; 10 by 90, 40 by 130, 20 by 60, 5 by 110, again 5 by
90. You have 20 by 90, 20 by 130, 30 by 60, 5 by 110, again 5 by 90. So, this is how you
construct the A matrix, clear? Then what will you do? Yes, then you will have to obtain
I minus A, this matrix, invert it, multiply it by Y; you can do that, okay. That gives
you X.
What does it tell you then? What does it tell you? Say, X will have, Y will have, Y 1, Y
2, Y 3, Y 4, Y 5 and you have obtained X 1, X 2, X 3, X 4, X 5. Now, if I ask you about
the manufacturing sector, I am asking you about the meaning of terms now.
We have Y 1, Y 2, Y 3, Y 4, Y 5. Tell me what is the meaning of Y 2 physically? Yes, how
much is the final demand of sector 2, which is manufacturing sector. So, for that, if
you obtain this, you have obtained X 1, X 2, X 3, X 4, X 5. If I ask you what the meaning
of X 4 is, total output of the electric sector that is necessary to meet all these. Now,
suppose the nation plans to increase manufacturing by say 20% in the next 10 years, what will
you do? You have got this, this matrix already in hand. A component, a particular element
of Y matrix will change, because of that.
With that changed Y matrix, you can again multiply by this matrix and obtain the changed
X matrix. You will find that it will change many places and as a result the changed, this
X vector will tell you how much increased amount of petroleum products you need to meet
that, how much increased amount of electricity you need to meet that, even how much increased
amount of agricultural products you need there, which is not immediately clear. From logic
it is not immediately clear, but then because of the interdependence of various sectors
of the economy, things that are not immediately intuitively clear that becomes clear only
when you compute these matrices, clear.
So, this is how in the classical way, the energy sector or the economic planning is
done in any country, including ours and that is why for all countries, either some kind
of government agency keeps track of these numbers and publishes it. In India also these
are published, but unfortunately the published matrix, it is published, available on the
net, but you cannot download it, because you need to be a member. It is central statistical
organization; you have to be a member of the site and the membership fee is more than 20,000
rupees and so, obviously very few people will be really, very few students will be able
to become members of that. But, on the net you will find available the input output matrices
of many countries.
If you simply do a Google search it will show up. For example, one of the first one that
comes is Scotland's input output matrix. Take a look at that. That will sort of tell
you what are the entries, how the sector is divided, the sector wise production is divided.
For example, in most countries as I told you, this, the total number of sectors would be
something like between 100 to 130; that is the average number in which people divide
the sectors. In the next class, I will bring some of those matrices, so that on the computer
I can show you what the sectoral divisions are.
But, I have noticed one thing that in this, when we wrote it this way and wrote it as a matrix like this or finally we transform
into the form here, some of these rows are energy rows.
For example, in the example that we have taken the last two rows are energy rows. This row
belongs to electricity sector and this row belongs to the other petroleum sectors, right.
So, these two are energy rows and so the information necessary in order to infer the energy requirement
for the production are all ingrained here, but often people do some further manipulation
of these matrices, so that these energy impact of the industry, energy efficiency of the
industry, energy efficiency of particular products these are silently clear.
So, that manipulation of these matrices will come to ..... Let us start today; we will
continue in the next class, because we do not have as much time to complete that part.
So, we have a matrix something like this from which we start, in order to extract the information
regarding the energy, because when you actually look at the total matrix for a country, there
will be some rows scattered here and there that are actually belonging to energy rows,
right and you need to extract that information. So, there has to be some consistent methodology
to extract that information about the energy rows. That is what we will do now.
So, for the energy rows, if E i is the total output of energy sector i, E ik be the intersectoral
transaction from energy sector i to another sector, any other sector, sector k. Apart from that there
will be the finally demand. So, E iy is the sale of .....; it is the sale of energy of
type i to final demand. Then, we can write that as in the form E i is summation of k
is equal to 1 to n of E ik plus the final demand of component. So, that is the equation
for energy sector i. Now, remember when we talk about the energy sectors, there are various
ways of representing this.
In what unit do you, do you represent this energy? You can represent that in terms of
the kilowatt equivalent or energy, energy not kilowatt, kilowatt hour equivalent. You
can also represent these in terms of British thermal unit. Also, you can represent these
in terms of, because all these are energy sectors, petroleum products, how much is the
heat content of that, you can express in that term. So, that will be British thermal unit
or if you consider its electricity equivalent, then it will be kilowatt hour equivalent.
Also, it is possible to express this in terms of monitory units.
Now, in literature we will find all these in practice. In some literature we will find
they are expressed in terms of the BTU's, in some literature you will find they are
expressed in the kilowatt, KLOE - kiloliters of oil equivalent, you can express in that
form. Coal, its heat content can be equivalent to the equivalent amount of oil or it can
also be expressed in terms of the monitory value; monitory value fluctuates, the coal
is there. So, there is a disadvantage of using the monitory value though. The advantage is
that if you use this in terms of the monitory value, then that can be simply read from the
published tables that are, as I told you, the whole A matrix is published you can simply
read the values from there. So, here you have the basic equation for the energy sector,
which can be expressed in various units. Remember, do not be confused if you see in literature
that this is expressed in terms of the kiloliters of oil equivalent, KLOE; do not be confused.
We will, however, since I would like you to use the input output matrices published, I
would continue with the monitory terms. In the next class, when we continue, we will
continue with the monitory terms, fine. So, as I told you, the assignment for the next
week is to obtain the best fit curve, the parameters for the best fit curve for the
world production of oil, whose graph I have given you. Unfortunately, right now the eni.in
is down. Therefore, you will not be able to access it; it is down, we cannot help it,
but you will able to, where do give, where, how do I give you?
......
Yeah, it is there; it is there. I downloaded it from there, therefore it is there. So,
all you need to do is to find the particular article in which the graph is there and if
you go to the site map and go to the articles that are in the repository you will find it.
You can do that, else after the eni.in comes, you will have it. So, fine, that is all; by
the next week it should be in. In the mean time, I will put it in my web page, but you
may not be able to access it, there is a problem. Till the eni.in machine comes back, its hard
disk has crashed, so it is only a transient problem.
Thank you very much.