welcome back to our next part of our discussion on perfect competition we uh introduced the
market structure in the previous module and we discussed about where the price comes from
in case of perfect competition where does the price taker take his price from and we
discussed that basically for every individual firm the individual firm faces a horizontal
demand curve at the level of price that is prevalent in the market so we started of with
that and our assumption is the firm is trying to maximize its profit it has taken its price
now the last part of the entire puzzle is the firm has to decide what level of output
to produce . now before we discuss about the level of output
etc and talk about profit maximization lets understand how does the revenue look for uh
revenue look like for a competitive firm so to understanding revenue for a competitive
firm now total revenue is equal to price multiplied by the quantity now here the p is given p
is a p star it is given from the market intersection of demand and supply in the market
so the average revenue is total revenue divided by the amount of output produced so that is
pq divided by q and that is equal to p so average revenue is equal to the price that
is given in the market how much is marginal revenue marginal revenue
is basically uh its differentiation of the total revenue divided by the marginal amount
of outputs basically marginal revenue means that when the firm is selling a additional
unit of output how much additional amount of revenue the firm is receiving that is the
marginal revenue but in case of a perfectly competitive firm
since the price for every individual unit it does not change it is given by the market
and the price remains the same so for the competitive firm marginal revenue that is
del tr divided by del q is equal to the price in the market so this is true for only competitive
firms this is true for only competitive firms because
in other kinds of market structures we are going to see that the price changes with different
levels of output the price changes with different levels of output and we are going to discuss
about them in details later let let me not get into those uh market structures right
away . so this is our understanding of revenue for
a competitive firm and to elaborate this more with an example let me take a very simple
example where we have the price is given so the price is always say 10 rupees so the price
is always say 10 rupees because the firm is facing a horizontal demand curve so no matter
how many units of output it sells or decides to sell the price is always going to be 10
rupees so q is 0 1 2 3 4 or 5 price is always 10 how much is total revenue total revenue
is price multiplied by quantity so it is 0 10 20 30 40 and 50 how much is average revenue
average revenue is always 10 average revenue is always 10 what about marginal revenue marginal
revenue is basically every single so additional amount of output that i am selling the next
marginal unit of output here i am selling 1 unit i am getting 10 rupees another additional
unit i sell i get again 10 rupees another unit i sell again i get 10 rupees so my marginal
revenue in all these situations is 10 so we can see that in case of a perfect competitive
firm average revenue is equal to marginal revenue is equal to price so this holds true
for only a competitive firm so this holds true for only a competitive firm so let me
clean this up okay so moving on . now now that we know what the revenues the
the different forms of the revenue looks like now that we know that price is given we know
about the cost curves of the firms now how does the firm decide the level of output how
does it decide how much output to produce so for this the firm is going to our assumption
is the firm is maximizing profit so as is shown in the slide so pi is our typical
symbol for uh profit which we are going to use during the entire course and pi is equal
to total revenue minus total cost so determining the level of output that will maximize pi
so we would like to determine that level of output which is going to maximize profit and
so that is by the first order condition for maximization it implies that del pi del q
is equal to 0 that is del tr del q minus del tc del q is equal to 0 or marginal revenue
minus marginal cost equals 0 so the firm chooses the level of output q
star that fulfills the condition of marginal revenue equals marginal cost now marginal
revenue equal marginal cost equals marginal cost is the profit maximizes profit maximizing
condition for any firm profit maximization maximizing condition for any firm is that
that the additional revenue that the firm expects to receive from selling the last unit
of output that should be equal to the cost of producing that additional unit of output
now for a perfectly competitive firm lets look at the intuition lets look at the profit
maximizing condition graphically and see how the output is determined .
now we know that price is fixed so p star is given so
so since p star is given what is my total revenue my total revenue is equal to p star
into q so total revenue is p star into q so the total revenue curve will be a straight
line through origin where slope is p star so this is the total revenue curve .
now what does my total cost curve look like so you may remember that when we were discussing
about costs we developed the cost curve from the production function if you remember this
is the production function that we drew then we flipped the production function and this
is the reason that we flipped the production function to translate it into the cost curve
and see and put the cost curve in this kind of framework to understand the difference
between revenue and cost so this is what we did and our cost curve after including the
fixed cost it looked something like this so this was my cost curve
this is how my total cost curve looked like so if you may remember we had labour here
the variable cost and we had the output here q so we translated the labour into the monetary
units of the wages that is the cost and basically we flipped the curve so that we had cost here
and we had output here so if you can recollect this cost curve then
basically for this firm we are going to draw the cost curve here so this is assuming its
it fixed cost so the cost curve looks something like this so the cost curve looks something
like this total cost curve and so this is the cost curve what do we have over here in
the blue region what do we have in the blue region here and over here
what we have in this blue region is that total cost is more than total revenue in these regions
so total cost being more than total revenue implies that the firm is incurring losses
because its cost is more than its revenue so this is the region where it is incurring
losses and where is it incurring profit its incurring profit in this region the green
region so it is incurring profit in the green region so that basically means that in the
range from q 1 to q 2 the firm is incurring profit and the firm can very well operate
or produce any amount in this range so if the firm produces any amount in this range
it is going to incur a profit but what amount is going to maximize its profit
what amount is going to maximize its profit the amount that is going to maximize its profit
is the region where the distance between the revenue and the cost curve is maximum so this
is the so where total revenue minus total cost is maximum that is where that level of
output should be the profit maximizing output level of the firm so this is so this gap is
maximum where the slope of the cost curve the slope of the cost curve the slope of the
cost curve equals the slope of the revenue curve and that is nothing but the first order
condition of maximization . so when we maximize this our del tr del q
minus del tc del q is equal to 0 or so del tr del q is nothing but the slope of the revenue
curve and del tc del q is nothing but the slope of the cost curve and the slope is called
the marginal revenue minus marginal cost this is equal to 0 so marginal revenue equals marginal
cost is my profit maximizing condition so this is my profit maximizing condition and
this happens at this region so at this region my the difference between the 2 is maximum
and marginal revenue equals marginal cost .
marginal revenue as we saw from the previous slide that this is the definition of marginal
revenue and uh so this is the level at which the firm should basically produce so it is
going to the firm is going to produce the output q star which is going to maximize marginal
revenue and the difference between marginal revenue and marginal cost .
so coming back to the profit maximizing condition so profit maximizing condition is marginal
revenue equals marginal cost or for a perfectly competitive firm profit is maximized at that
level of output where marginal cost equals marginal revenue which is equal to price now
coming back to this graph now what is the slope of the total revenue or what is this
marginal revenue this marginal revenue or del tr del q is nothing but del tr del q is
equal to del pq del q since p is constant at p star so this is p star into del q is
equal to p star so for a perfectly competitive firm the profit
maximizing condition is the price should be equal to the marginal cost this is for only
the perfectly competitive firm so price equals marginal cost now what happens if price is
more than the marginal cost let me uh clean this clean the board and show you a more familiar
diagram that you are going to see in all your text books how profit is determined and how
can we quantify the profit the revenue and the cost i am going to draw that diagram .
so coming back to the this is the market demand and supply this determines the price p star
and the firm is basically so in this diagram we are going to draw all the revenue price
cost all the curves so i am writing here p c r etc so on the x axis you always have the
quantity its rather the small q this if for the firm and since the p is given so we draw
the price line first so we draw the price line first so this is p star and as we have
seen from our understanding of the revenue so p star is equal to average revenue curve
this is also your marginal revenue curve this is not only the price line this is the
demand line that the firm is facing this is the average revenue line of the firm and this
is also the marginal revenue line of the firm now our profit maximizing condition we have
already understood it is clear that profit maximizing condition is marginal revenue equals
marginal cost so lets draw our very familiar marginal cost
curve here now this is the marginal cost curve this is our marginal cost curve so profit
maximizing condition says that the intersection between where the point where mr is equal
to mc that level of output should be profit maximizing so basically the firm is producing
the firm should produce q star q star is going to maximize its profit so does our problem
end there does our problem end there so we have determined price we have determined
quantity and we know about the cost and this is our profit maximizing condition so is it
that our problem ends here no because we need to understand this could be very well our
profit maximizing level of output but is it actually giving me any profit or not that
is important to be understood so lets draw the average cost curve so lets
draw the unless and until i draw the average cost curve here i will not be able to understand
how much cost i am incurring in producing this amount of output so here my revenue is
p into q my total revenue is this rectangle but what is my cost for the cost for understanding
the total cost i need my average cost curve here so in the situation that my average cost
curve is somewhere here if my average cost curve is somewhere here
so this is average total cost so if my average cost curve is somewhere here then at q level
of output my total cost is this is my sorry so this is my average cost so average total
cost so average cost multiplied by output this is my actual cost so the entire rectangle
is my total revenue minus the cost minus the cost minus this cost gives me my profit
so we can very well see that since we can see that since my price line is above my average
total cost so this firm is basically managing to get some profit here so it is basically
getting a profit here and this is the profit so it maximizes its profit and it has a amount
of profit uh has a positive amount of profit .
now what happens if my average cost curve is what happens instead here instead say my
average cost curve is here say this is my average total cost if this is my average total
cost then also i uh also you may have noticed that i am trying to draw the average cost
in such a way that the marginal cost intersects the average cost at its minimum because this
is what we found out when we discussed about the cost curves that the marginal cost intersects
the average cost at its minimum so that is how i am trying to draw and so
when the average cost looks something like this so this is another average cost Say this
is my average cost so here my price is equal to my average cost which means my revenue
is equal to my cost and here my economic profit is equal to 0 so here my profit is equal to
0 so when in case of atc 1 so in case of atc my profit is more than 0 in case of atc 1
my profit is equal to 0 now what happens if my average total cost
is somewhere here it is high up my average cost is higher than my price so my average
cost is higher than my price say it is atc 2 so then what is my cost like so so here
again this is my output so at this output level this is my cost this is my at this output
this is the cost that i am incurring average total cost so average total cost multiplied
by my output this is my total cost and this is my revenue the lower box is my sorry this
is not the revenue this part is the revenue so this is my price line uh marginal cost
and this is my revenue and this is my cost so my so this part is the this part is the
loss that i am incurring so out of this is the so this is the loss that i am incurring
because this part the my cost is more than my price the cost is more than the price that
i can charge in the market so i am incurring a loss over here because the lower part is
my this is my revenue so in case of atc 2 my profit is sorry this is not atc profit
is more than 0 atc 1 profit is equal to 0 atc 2 profit is less than 0
so this is how i determine how much profit i am going to so profit maximizing condition
does not mean if you are able to determine the profit maximizing level of output uh the
problem does not end there because the profit maximizing level of output may very well give
you a loss as we are showing here so we have to find out by using the average cost curve
that actually how much profit or loss the firm is incurring in such a situation now
what happens let me clean the board again .
so so this is my p star equals revenue is equal
to mr is equal to d so everything and this is my marginal cost curve now what happens
if marginal cost is less than price so the produce can make profit by raising output
so what happens if the producer decides that let me produce at a level over here q 1 so
what happens at q 1 now at q 1 marginal cost although it is increasing but still it is
much less than the price so marginal cost is less than the price so
additional unit of output if the firm is to produce it is going to incur a marginal cost
which is much less than the price or the marginal revenue that the firm can expect by selling
that unit of good so it makes sense for the firm to produce that additional unit of output
so here q1 say this is q 1 to q 2 so these are additional units of output it
has to make a decision whether to go to q 2 or not so obviously although its marginal
cost is increasing still it is much less than p so it is going to earn some additional revenue
p is the additional revenue that it is going to get by selling this extra unit of output
so it keeps increasing the output till it reaches q star where its marginal revenue
is equal to its marginal cost now beyond q star what happens again beyond
q star say for example by chance it is operating at this level where it is say q 3 now here
clearly it is incurring a high cost so if it reduces its output by another unit say
here q 4 if it moves this way if it moves this way it is its marginal cost is falling
but it is still above the price that it is going to get
so it keeps on reducing the output till it reaches this point so till it reaches this
point and here it’s the marginal cost that it is going to incur by selling another unit
of output is going to be the marginal revenue that it is going to get by selling that additional
unit of output so this is the optimum point where the firm it makes sense for the firm
to operate so the so if marginal cost is more than p he needs to reduce output to raise
profit and if marginal profit is less than p the producer can make profit by raising
output so that uh so this was our discussion about
profit maximizing condition about how the firm decides what level of output to produce
and will continue this discussion in the next module thank you