Condition 1 - Economics Video Lecture | Economics Class 11 - Commerce

see first of all we'll have to examine
what output level this firm is going to
produce in order to maximize its profit
okay well you know that the song is is
going to sell some output Q at some
market price P then the total revenue is
given by P into Q okay so just selling
this Q at at market price P so you can
write this that total revenue is a
function of Q which is EQ well of course
in order to produce this Q it must have
incur some cost so you can say this that
total cost
they are the function of Q which is say
whatever C Q C if it is a function of Q
and you know this that economic profits
are are the difference between the
revenues and the cost economic profits
they are the difference between the
revenues and the cost so basically this
would mean that it is the Q minus this
DC which depends upon Q now you have to
understand one thing that this P this is
the market demand function which in
itself is dependent upon Q into Q minus
TC which depends on Q this P is the
market demand function it can have the
form like this just P is equal to a
minus B Q so you can say this that this
P is a function of Q as as it is written
out there okay so these are your
economic profits which is P Q into Q
minus TC which depends on Q now what is
the necessary condition for choosing the
value of Q that maximizes this profit so
necessary condition is necessary and
sufficient condition necessary condition
okay so in maximization your necessary
condition should have been del PI by Del
Q is equal to 0
well the sufficient condition
for maximization should happen til 2 pi
by Del Q 2 is less than equal to 0 right
let us see whether these conditions hold
here or not your what is your profit
function which is P which is a function
of Q into Q minus TC q yeah so in case
if you find it drop the first derivative
this is your del PI by Del Q which is
first function as it is into derivative
of second function which is 1 plus
second function as it is 2 derivative of
first function which is DP by Q minus C
by Del T is equal to 0 okay well you can
write this as this as del PI by Del Q
would be equal to 0 given that T plus Q
del P by Del Q should be equal to del C
by Del Q but this is nothing this is
nothing but this is just the marginal
revenue and this is nothing but the
marginal cost okay this is nothing but
you match with every in marginal cost so
at equilibrium at equilibrium
MC should be equal to M R okay you know
this I'm sure that why it is Emma why
this is marginal revenue because you
know this that marginal revenue is the
change in the total revenue when one
more output is sold in the market okay
so and what is the total revenue
us being 2q okay that is first function
as it is to derivative of second
function which is one the second
function as it is at a derivative of
first function is DV by DT yeah so this
is a marginal revenue only right well
this first function as it is it a second
into derivative the second function is 1
because this you are differentiating Q
with respect to Q okay so it is this so
it's your module revenue should be equal
to marginal cost
well I could have just said it like this
that your DTR your pi is equal to TR
minus T C so D PI by D Q should have
been equal to DTR by DQ minus DTC by DQ
equal to zero so that would have been dt
r by DQ is equal to DT C by DT so you
have your marginal revenue equal to
marginal cost