We were talking about average cost and marginal
cost.
Immediately I will come to the short run and
long run, but just to look at it how these
two are related we have already studied.
What did we study?
This is what we have studied 
fine or in other word other way to look at
it if MC is greater than AC if marginal cost
is more than average cost it means you are
adding one more unit and the cost of production
is going up by more than the average cost.
So, that will of course, bring the average
cost up.
So, in that case average cost will increase
ok.
Of course, this you can look get from here
too similarly, if marginal cost is less than
average cost what is happening it will drag
down the average cost and average cost will
decrease.
Similarly if marginal cost is equal to average
cost it will remain same just reminder no
change just to remind you.
Further if we look it from the discrete world
let us just let me just write it that MC 1
that is marginal cost to produce the first
unit that is the way I am defining it will
be equal to total cost to produce 1 unit minus
total cost to produce 0 units that is the
way we have defined.
What can we write here what is the total cost
to produce 1 unit total cost we can divide
it into 2 part fixed cost plus variable cost
of producing 1 unit.
And again here also we can do the same thing
fixed cost and variable cost is going to be
0 because there is no output so if this will
get cancelled.
So, marginal cost to produce first unit is
same as the variable cost to produce the first
unit fine.
Let us go little further what happens let
us see what about the marginal cost to produce
the second unit total cost to produce the
second unit minus total cost to produce the
first unit fine.
What we can write again this is equal to FC
plus variable cost to produce 2 units minus
this is going to be again fixed cost plus
variable cost to produce 1 units.
This will get cancelled again fine and VC
2 minus VC 1 and what is VC 1 VC 1 is MC 1
Now, let us proceed little further MC 3 what
is it equal to TC of 3 total cost of producing
3 units minus total cost of producing 2 units.
Again remember I have defined marginal cost
in one particular way one can define it as
marginal cost at level 0 also.
This is just the definition, but roughly it
would the idea would remain the same.
And what we will get here 
and what is this equal to FC, FC will again
get cancelled.
And VC 3 minus what is VC 2?
VC 2 can be given.
If we take this MC 1 in this direction VC
2, is equal to basically MC 2 plus MC 1.
And here from here we can figure out VC 3
is MC 1, plus MC 2 plus MC 3, or in other
word VC Q if we just continue doing this what
we will get VC Q is equal to MC Q plus MC
Q minus 1 until MC 1 fine that is in the discrete
world.
Now, let us look at it the calculus definition.
What is what is MC?
MC at Q this is the rate of change in total
cost with respect to quantity fine or we can
write it the differential change in total
cost is marginal cost as Q multiplied by del
Q.
If we integrate it from 0 to some output Q
naught let us say 0 to some output Q naught.
What we will get here TC Q naught minus TC
0 and what we will get here.
What we will get here the integration of MC
Q [FL] fine ok.
What is this think about it?
What is this no do not look at this side just
explain this.
What is this left-hand side variable cost
of producing Q naught this is variable cost
of producing Q naught.
What is this equal to 0 to Q naught MC Q dq
look at these two definition they are very
similar ah are not they?
Here we are using summation here you are using
integral fine ok.
Now, let us come to short run and long run
marginal cost.
What we have figured out if you remember from
the earlier class this was a digression we
have if you remember from the earlier class.
If we draw the average cost does not matter
whether in the long run or in the short run.
How can we draw the marginal cost curve?
Can we draw the marginal cost curve here passing
through the minimum, minimum of average cost
curve this is average cost this is variable
cost is not it fine.
No this is this is marginal cost sorry this
is marginal cost.
Now, we can bring the earlier graph again
earlier graph again let us say again we have
3 different we can we are fixing capital at
3 different level k 1, k 2, k 3.
So, again this graph may not look the same,
but the attempt is to draw the same thing
things like that a only 3 levels are possible
average cost here we have quantity.
Let us say if we draw short run marginal cost
curve for k 1 level or let us say for k 1
level can you tell me how would it look like;
black color curve passing through the minimum
like this ok.
How about if we draw short-run marginal cost
curve for k 2 level of capital, same for the
blue curve and how about this third it will
be like this is it clear fine.
Now can you tell me if I tell you like ah
the earlier case if I tell you that only 3
levels of capital are possible k 1, k 2, k
3.
How would the long-run marginal cost curve
look like?
Now I am talking about long-run marginal cost
curve minimum.
So, let me tell you to just to help you the
long-run average cost curve will look like
this by green color ah it will be blue think
about it what is happening that if let us
say this is the let me say this is Q 1, this
is Q 2.
So, what is happening in the long run?
If this producer wants to produce Q amount
of output and if Q is less than Q 1 he will
be using this part he will be using in the
long run k 1 bar amount of capital.
If Q is more than Q 1, but less than Q 2 this
producer will be using k 2 bar amount of capital
and similarly if Q is greater than Q 2 then
he will be using k bar 3 amount of capital.
So, look at it very clearly it says that here
this producer in the long run is following
this graph.
So, till this point if I am allowed to extend
like this so till this point till Q 1 the
marginal long-run marginal cost curve is this.
Now of course, I did not draw it so let me
extend it like this.
Let us say this is the same curve from Q 1
level to Q 2 level let me extend it further.
It will be broken in the after in this level
it is going to be like this and beyond this
Q 2 point the long-run marginal cost curve
will be this, fine.
Now, here in this case I restricted the level
of capital at either k 1, k 2, k 3.
Now let us say in the long run this producer
is allowed to vary the amount of capital the
way he wants.
So, of course the better idea would be to
draw all the short run average cost curve
first and then the long-run average cost,
but we know the concepts I am going to do
in the opposite way just because it is easier
to draw ok.
So, let me draw again; this is the minimum,
this is the minimum, and this is the minimum
fine is it clear.
Now this is short run marginal cost 1, short
run marginal cost 2, short run marginal cost
3, here we have quantity here we have average
cost.
So, how would the long-run marginal cost curve
look like first thing you should know that
long run marginal cost curve will pass should
pass through the minimum of long run average
cost curve.
So, let us say this is the minimum so it should
pass through here it comes from below and
its it will be a continuous curve because
here we are allowed to vary capital the way
we want.
But what we know that at this point at this
level of output because remember at this level
of output what is happening what do we have
SRAC is same as LRAC ok fine.
So, at this level the marginal cost will be
the same.
So, what we know here let me draw it then
I will explain something like this.
Why at this point it has to be equal we know
it will pass through this bottom point and
it it is increasing this is the way we have
been drawing fine any question about this.
Before that point why to the straight.
It is not a straight, it is not straight,
it is just my drawing it it will it will be
like this it can be like this again it is
just my poor drawing.
So, all these graphs are going to be replaced
later anyway fine is it clear fine.
So, that brings an into the discussion on
long-run average cost, long-run marginal cost,
short run average cost, short run marginal
cost curve fine ok.
