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.
