Courses

# NCERT Textbook - Chapter 4 - The Theory of the Firm under Perfect Competition, Class 12, Economics Humanities/Arts Notes | EduRev

## UPSC : NCERT Textbook - Chapter 4 - The Theory of the Firm under Perfect Competition, Class 12, Economics Humanities/Arts Notes | EduRev

``` Page 1

Chapter 4
The Theor The Theor The Theor The Theor The Theory of the F y of the F y of the F y of the F y of the Firm irm irm irm irm
under P under P under P under P under Per er er er erfect Competition fect Competition fect Competition fect Competition fect Competition
In the previous chapter, we studied concepts related to a firm’s
production function and cost curves. The focus of this chapter is
different. Here we ask : how does a firm decide how much to
produce? Our answer to this question is by no means simple or
uncontroversial. We base our answer on a critical, if somewhat
unreasonable, assumption about firm behaviour – a firm, we
maintain, is a ruthless profit maximiser. So, the amount that a
firm produces and sells in the market is that which maximises
its profit.
The structure of this chapter is as follows. We first set up and
examine in detail the profit maximisation problem of a firm. This
done, we derive a firm’s supply curve. The supply curve shows
the levels of output that a firm chooses to produce for different
values of the market price. Finally, we study how to aggregate
the supply curves of individual firms and obtain the market
supply curve.
4.1 PERFECT COMPETITION: DEFINING FEATURES
In order to analyse a firm’s profit maximisation problem, we
must first specify the market environment in which the firm
functions. In this chapter, we study a market environment called
perfect competition. A perfectly competitive market has two
defining features
1. The market consists of buyers and sellers (that is, firms). All
firms in the market produce a certain homogeneous (that is,
undifferentiated) good.
2. Each buyer and seller in the market is a price-taker.
Since the first feature of a perfectly competitive market is
easy to understand, we focus on the second feature. From the
viewpoint of a firm, what does price-taking entail? A price-taking
firm believes that should it set a price above the market price, it
will be unable to sell any quantity of the good that it produces.
On the other hand, should the set price be less than or equal to
the market price, the firm can sell as many units of the good as
it wants to sell. From the viewpoint of a buyer, what does price-
taking entail? A buyer would obviously like to buy the good at
the lowest possible price. However, a price-taking buyer believes
that should she ask for a price below the market price, no firm
not to be republished
Page 2

Chapter 4
The Theor The Theor The Theor The Theor The Theory of the F y of the F y of the F y of the F y of the Firm irm irm irm irm
under P under P under P under P under Per er er er erfect Competition fect Competition fect Competition fect Competition fect Competition
In the previous chapter, we studied concepts related to a firm’s
production function and cost curves. The focus of this chapter is
different. Here we ask : how does a firm decide how much to
produce? Our answer to this question is by no means simple or
uncontroversial. We base our answer on a critical, if somewhat
unreasonable, assumption about firm behaviour – a firm, we
maintain, is a ruthless profit maximiser. So, the amount that a
firm produces and sells in the market is that which maximises
its profit.
The structure of this chapter is as follows. We first set up and
examine in detail the profit maximisation problem of a firm. This
done, we derive a firm’s supply curve. The supply curve shows
the levels of output that a firm chooses to produce for different
values of the market price. Finally, we study how to aggregate
the supply curves of individual firms and obtain the market
supply curve.
4.1 PERFECT COMPETITION: DEFINING FEATURES
In order to analyse a firm’s profit maximisation problem, we
must first specify the market environment in which the firm
functions. In this chapter, we study a market environment called
perfect competition. A perfectly competitive market has two
defining features
1. The market consists of buyers and sellers (that is, firms). All
firms in the market produce a certain homogeneous (that is,
undifferentiated) good.
2. Each buyer and seller in the market is a price-taker.
Since the first feature of a perfectly competitive market is
easy to understand, we focus on the second feature. From the
viewpoint of a firm, what does price-taking entail? A price-taking
firm believes that should it set a price above the market price, it
will be unable to sell any quantity of the good that it produces.
On the other hand, should the set price be less than or equal to
the market price, the firm can sell as many units of the good as
it wants to sell. From the viewpoint of a buyer, what does price-
taking entail? A buyer would obviously like to buy the good at
the lowest possible price. However, a price-taking buyer believes
that should she ask for a price below the market price, no firm
not to be republished
will be willing to sell to her. On the other hand, should the price asked be
greater than or equal to the market price, the buyer can obtain as many
units of the good as she desires to buy.
Since this chapter deals exclusively with firms, we probe no further into
a reasonable assumption for firms. Price-taking is often thought to be a
reasonable assumption when the market has many firms and buyers have
perfect information about the price prevailing in the market. Why? Let us start
with a situation wherein each firm in the market charges the same (market)
price and sells some amount of the good. Suppose, now, that a certain firm
raises its price above the market price. Observe that since all firms produce
the same good and all buyers are aware of the market price, the firm in question
loses all its buyers. Furthermore, as these buyers switch their purchases to
accommodated when there are many firms in the market. Recall, now, that an
individual firm’s inability to sell any amount of the good at a price exceeding
the market price is precisely what the price-taking assumption stipulates.
4.2 REVENUE
We have indicated that in a perfectly competitive market, a firm believes that
it can sell as many units of the good as it wants by setting a price less than or
equal to the market price. But, if this is the case, surely there is no reason to
set a price lower than the market price. In other words, should the firm desire
to sell some amount of the good, the price that it sets is exactly equal to the
market price.
A firm earns revenue by selling the good that it produces in the market. Let
the market price of a unit of the good be p. Let q be the quantity of the good
produced, and therefore sold, by the firm at price p. Then, total revenue (TR) of
the firm is defined as the market price of the good (p) multiplied by the firm’s
output (q). Hence,
TR = p × q
To make matters concrete, consider the following numerical example. Let
the market for candles be perfectly competitive and let the market price of a
box of candles be Rs 10. For a candle manufacturer, Table 4.1 shows how
total revenue is related to output. Notice that when no box is produced,
TR is equal to zero; if one box of candles is produced, TR is equal to 1 × Rs 10
= Rs 10; if two boxes of candles are produced, TR is equal to 2 × Rs 10
= Rs 20; and so on.
With the example done, let us return to a more general setting. In a perfectly
competitive market, a firm views the market price, p, as given. With the market
price fixed at p, the total revenue curve of a
firm shows the relationship between its total
revenue (y-axis) and its output (x-axis). Figure
4.1 shows the total revenue curve of a firm.
Three observations are relevant here. First,
when the output is zero, the total revenue of
the firm is also zero. Therefore, the TR curve
passes through point O. Second, the total
revenue increases as the output goes up.
Moreover, the equation ‘TR = p  × q’ is that of a
Boxes sold TR (in Rs)
00
110
220
3 30
440
550
Table 4.1: Total Revenue
53
The Theory of the Firm
under P erfect Competition
not to be republished
Page 3

Chapter 4
The Theor The Theor The Theor The Theor The Theory of the F y of the F y of the F y of the F y of the Firm irm irm irm irm
under P under P under P under P under Per er er er erfect Competition fect Competition fect Competition fect Competition fect Competition
In the previous chapter, we studied concepts related to a firm’s
production function and cost curves. The focus of this chapter is
different. Here we ask : how does a firm decide how much to
produce? Our answer to this question is by no means simple or
uncontroversial. We base our answer on a critical, if somewhat
unreasonable, assumption about firm behaviour – a firm, we
maintain, is a ruthless profit maximiser. So, the amount that a
firm produces and sells in the market is that which maximises
its profit.
The structure of this chapter is as follows. We first set up and
examine in detail the profit maximisation problem of a firm. This
done, we derive a firm’s supply curve. The supply curve shows
the levels of output that a firm chooses to produce for different
values of the market price. Finally, we study how to aggregate
the supply curves of individual firms and obtain the market
supply curve.
4.1 PERFECT COMPETITION: DEFINING FEATURES
In order to analyse a firm’s profit maximisation problem, we
must first specify the market environment in which the firm
functions. In this chapter, we study a market environment called
perfect competition. A perfectly competitive market has two
defining features
1. The market consists of buyers and sellers (that is, firms). All
firms in the market produce a certain homogeneous (that is,
undifferentiated) good.
2. Each buyer and seller in the market is a price-taker.
Since the first feature of a perfectly competitive market is
easy to understand, we focus on the second feature. From the
viewpoint of a firm, what does price-taking entail? A price-taking
firm believes that should it set a price above the market price, it
will be unable to sell any quantity of the good that it produces.
On the other hand, should the set price be less than or equal to
the market price, the firm can sell as many units of the good as
it wants to sell. From the viewpoint of a buyer, what does price-
taking entail? A buyer would obviously like to buy the good at
the lowest possible price. However, a price-taking buyer believes
that should she ask for a price below the market price, no firm
not to be republished
will be willing to sell to her. On the other hand, should the price asked be
greater than or equal to the market price, the buyer can obtain as many
units of the good as she desires to buy.
Since this chapter deals exclusively with firms, we probe no further into
a reasonable assumption for firms. Price-taking is often thought to be a
reasonable assumption when the market has many firms and buyers have
perfect information about the price prevailing in the market. Why? Let us start
with a situation wherein each firm in the market charges the same (market)
price and sells some amount of the good. Suppose, now, that a certain firm
raises its price above the market price. Observe that since all firms produce
the same good and all buyers are aware of the market price, the firm in question
loses all its buyers. Furthermore, as these buyers switch their purchases to
accommodated when there are many firms in the market. Recall, now, that an
individual firm’s inability to sell any amount of the good at a price exceeding
the market price is precisely what the price-taking assumption stipulates.
4.2 REVENUE
We have indicated that in a perfectly competitive market, a firm believes that
it can sell as many units of the good as it wants by setting a price less than or
equal to the market price. But, if this is the case, surely there is no reason to
set a price lower than the market price. In other words, should the firm desire
to sell some amount of the good, the price that it sets is exactly equal to the
market price.
A firm earns revenue by selling the good that it produces in the market. Let
the market price of a unit of the good be p. Let q be the quantity of the good
produced, and therefore sold, by the firm at price p. Then, total revenue (TR) of
the firm is defined as the market price of the good (p) multiplied by the firm’s
output (q). Hence,
TR = p × q
To make matters concrete, consider the following numerical example. Let
the market for candles be perfectly competitive and let the market price of a
box of candles be Rs 10. For a candle manufacturer, Table 4.1 shows how
total revenue is related to output. Notice that when no box is produced,
TR is equal to zero; if one box of candles is produced, TR is equal to 1 × Rs 10
= Rs 10; if two boxes of candles are produced, TR is equal to 2 × Rs 10
= Rs 20; and so on.
With the example done, let us return to a more general setting. In a perfectly
competitive market, a firm views the market price, p, as given. With the market
price fixed at p, the total revenue curve of a
firm shows the relationship between its total
revenue (y-axis) and its output (x-axis). Figure
4.1 shows the total revenue curve of a firm.
Three observations are relevant here. First,
when the output is zero, the total revenue of
the firm is also zero. Therefore, the TR curve
passes through point O. Second, the total
revenue increases as the output goes up.
Moreover, the equation ‘TR = p  × q’ is that of a
Boxes sold TR (in Rs)
00
110
220
3 30
440
550
Table 4.1: Total Revenue
53
The Theory of the Firm
under P erfect Competition
not to be republished
54
Introductory Microeconomics
straight line. This means that the
TR curve is an upward rising
straight line. Third, consider the
slope of this straight line. When
the output is one unit (horizontal
distance Oq
1
in Figure 4.1), the
total revenue (vertical height
Aq
1
in Figure 4.1) is p × 1 = p.
Therefore, the slope of the
straight line is Aq
1
/Oq
1
= p.
Now consider Figure 4.2.
Here, we plot the market price
(y-axis) for different values of a
firm’s output (x-axis). Since the
market price is fixed at p, we
obtain a horizontal straight line
that cuts the y-axis at a height
equal to p. This horizontal
straight line is called the price
line. The price line also depicts
the demand curve facing a firm.
Observe that Figure 4.2 shows
that the market price, p, is
independent of a firm’s output.
This means that a firm can sell
as many units of the good as it
wants to sell at price p.
The average revenue ( AR )
of a firm is defined as total
revenue per unit of output.
Recall that if a firm’s output is q
and the market price is p, then
TR equals p × q. Hence
AR =
TR
q
=
pq
q
×
= p
In other words, for a price-taking
firm, average revenue equals the
market price.
The marginal revenue (MR) of a firm is defined as the increase in total revenue
for a unit increase in the firm’s output. Consider a situation where the firm’s
output is increased from q
0
to (q
0
+ 1). Given market price p, notice that
MR = (TR from output (q
0
+ 1)) – (TR from output q
0
)
= (p × (q
0
+ 1)) – (pq
0
) = p
In other words, for a price-taking firm, marginal revenue equals the
market price.
Setting the algebra aside, the intuition for this result is quite simple. When
a firm increases its output by one unit, this extra unit is sold at the market
price. Hence, the firm’s increase in total revenue from the one-unit output
expansion – that is, MR – is precisely the market price.
Price Line. The price line shows the relationship
between the market price and a firm’s output level.
The vertical height of the price line is equal to the
market price, p.
Total Revenue curve. The total revenue curve of
a firm shows the relationship between the total
revenue that the firm earns and the output level of
the firm. The slope of the curve, Aq
1
/Oq
1
, is the
market price.
not to be republished
Page 4

Chapter 4
The Theor The Theor The Theor The Theor The Theory of the F y of the F y of the F y of the F y of the Firm irm irm irm irm
under P under P under P under P under Per er er er erfect Competition fect Competition fect Competition fect Competition fect Competition
In the previous chapter, we studied concepts related to a firm’s
production function and cost curves. The focus of this chapter is
different. Here we ask : how does a firm decide how much to
produce? Our answer to this question is by no means simple or
uncontroversial. We base our answer on a critical, if somewhat
unreasonable, assumption about firm behaviour – a firm, we
maintain, is a ruthless profit maximiser. So, the amount that a
firm produces and sells in the market is that which maximises
its profit.
The structure of this chapter is as follows. We first set up and
examine in detail the profit maximisation problem of a firm. This
done, we derive a firm’s supply curve. The supply curve shows
the levels of output that a firm chooses to produce for different
values of the market price. Finally, we study how to aggregate
the supply curves of individual firms and obtain the market
supply curve.
4.1 PERFECT COMPETITION: DEFINING FEATURES
In order to analyse a firm’s profit maximisation problem, we
must first specify the market environment in which the firm
functions. In this chapter, we study a market environment called
perfect competition. A perfectly competitive market has two
defining features
1. The market consists of buyers and sellers (that is, firms). All
firms in the market produce a certain homogeneous (that is,
undifferentiated) good.
2. Each buyer and seller in the market is a price-taker.
Since the first feature of a perfectly competitive market is
easy to understand, we focus on the second feature. From the
viewpoint of a firm, what does price-taking entail? A price-taking
firm believes that should it set a price above the market price, it
will be unable to sell any quantity of the good that it produces.
On the other hand, should the set price be less than or equal to
the market price, the firm can sell as many units of the good as
it wants to sell. From the viewpoint of a buyer, what does price-
taking entail? A buyer would obviously like to buy the good at
the lowest possible price. However, a price-taking buyer believes
that should she ask for a price below the market price, no firm
not to be republished
will be willing to sell to her. On the other hand, should the price asked be
greater than or equal to the market price, the buyer can obtain as many
units of the good as she desires to buy.
Since this chapter deals exclusively with firms, we probe no further into
a reasonable assumption for firms. Price-taking is often thought to be a
reasonable assumption when the market has many firms and buyers have
perfect information about the price prevailing in the market. Why? Let us start
with a situation wherein each firm in the market charges the same (market)
price and sells some amount of the good. Suppose, now, that a certain firm
raises its price above the market price. Observe that since all firms produce
the same good and all buyers are aware of the market price, the firm in question
loses all its buyers. Furthermore, as these buyers switch their purchases to
accommodated when there are many firms in the market. Recall, now, that an
individual firm’s inability to sell any amount of the good at a price exceeding
the market price is precisely what the price-taking assumption stipulates.
4.2 REVENUE
We have indicated that in a perfectly competitive market, a firm believes that
it can sell as many units of the good as it wants by setting a price less than or
equal to the market price. But, if this is the case, surely there is no reason to
set a price lower than the market price. In other words, should the firm desire
to sell some amount of the good, the price that it sets is exactly equal to the
market price.
A firm earns revenue by selling the good that it produces in the market. Let
the market price of a unit of the good be p. Let q be the quantity of the good
produced, and therefore sold, by the firm at price p. Then, total revenue (TR) of
the firm is defined as the market price of the good (p) multiplied by the firm’s
output (q). Hence,
TR = p × q
To make matters concrete, consider the following numerical example. Let
the market for candles be perfectly competitive and let the market price of a
box of candles be Rs 10. For a candle manufacturer, Table 4.1 shows how
total revenue is related to output. Notice that when no box is produced,
TR is equal to zero; if one box of candles is produced, TR is equal to 1 × Rs 10
= Rs 10; if two boxes of candles are produced, TR is equal to 2 × Rs 10
= Rs 20; and so on.
With the example done, let us return to a more general setting. In a perfectly
competitive market, a firm views the market price, p, as given. With the market
price fixed at p, the total revenue curve of a
firm shows the relationship between its total
revenue (y-axis) and its output (x-axis). Figure
4.1 shows the total revenue curve of a firm.
Three observations are relevant here. First,
when the output is zero, the total revenue of
the firm is also zero. Therefore, the TR curve
passes through point O. Second, the total
revenue increases as the output goes up.
Moreover, the equation ‘TR = p  × q’ is that of a
Boxes sold TR (in Rs)
00
110
220
3 30
440
550
Table 4.1: Total Revenue
53
The Theory of the Firm
under P erfect Competition
not to be republished
54
Introductory Microeconomics
straight line. This means that the
TR curve is an upward rising
straight line. Third, consider the
slope of this straight line. When
the output is one unit (horizontal
distance Oq
1
in Figure 4.1), the
total revenue (vertical height
Aq
1
in Figure 4.1) is p × 1 = p.
Therefore, the slope of the
straight line is Aq
1
/Oq
1
= p.
Now consider Figure 4.2.
Here, we plot the market price
(y-axis) for different values of a
firm’s output (x-axis). Since the
market price is fixed at p, we
obtain a horizontal straight line
that cuts the y-axis at a height
equal to p. This horizontal
straight line is called the price
line. The price line also depicts
the demand curve facing a firm.
Observe that Figure 4.2 shows
that the market price, p, is
independent of a firm’s output.
This means that a firm can sell
as many units of the good as it
wants to sell at price p.
The average revenue ( AR )
of a firm is defined as total
revenue per unit of output.
Recall that if a firm’s output is q
and the market price is p, then
TR equals p × q. Hence
AR =
TR
q
=
pq
q
×
= p
In other words, for a price-taking
firm, average revenue equals the
market price.
The marginal revenue (MR) of a firm is defined as the increase in total revenue
for a unit increase in the firm’s output. Consider a situation where the firm’s
output is increased from q
0
to (q
0
+ 1). Given market price p, notice that
MR = (TR from output (q
0
+ 1)) – (TR from output q
0
)
= (p × (q
0
+ 1)) – (pq
0
) = p
In other words, for a price-taking firm, marginal revenue equals the
market price.
Setting the algebra aside, the intuition for this result is quite simple. When
a firm increases its output by one unit, this extra unit is sold at the market
price. Hence, the firm’s increase in total revenue from the one-unit output
expansion – that is, MR – is precisely the market price.
Price Line. The price line shows the relationship
between the market price and a firm’s output level.
The vertical height of the price line is equal to the
market price, p.
Total Revenue curve. The total revenue curve of
a firm shows the relationship between the total
revenue that the firm earns and the output level of
the firm. The slope of the curve, Aq
1
/Oq
1
, is the
market price.
not to be republished
55
The Theory of the Firm
under P erfect Competition
4.3 PROFIT MAXIMISATION
A firm produces and sells a certain amount of a good. The firm’s profit, denoted
by p, is defined to be the difference between its total revenue (TR) and its total
cost of production (TC ).
1
In other words
p = TR – TC
Clearly, the gap between TR and TC is the firm’s earnings net of costs.
A firm wishes to maximise its profit. The critical question is: at what output
level is the firm’s profit maximised? Assuming that the firm’s output is perfectly
divisible, we now show that if there is a positive output level, q
0
, at which profit
is maximised, then three conditions must hold:
1. The market price, p, is equal to the marginal cost at q
0
.
2. The marginal cost is non-decreasing at q
0
.
3. In the short run, the market price, p, must be greater than or equal to the
average variable cost at q
0
. In the long run, the market price, p, must be
greater than or equal to the average cost at q
0
.
4.3.1 Condition 1
Consider condition 1. We show that condition 1 is true by arguing that a profit-
maximising firm will not produce at an output level where market price exceeds
marginal cost or marginal cost exceeds market price. We check both the cases.
Case 1: Price greater than MC is ruled out
Consider Figure 4.3 and note that at the output level q
2
, the market price, p,
exceeds the marginal cost. We claim that q
2
cannot be a profit-maximising output
level. Why?
Observe that for all output levels slightly to the right of q
2
, the market price
continues to exceed the marginal cost. So, pick an output level q
3
slightly to the
right of q
2
such that the market price exceeds the marginal cost for all output
levels between q
2
and q
3
.
Suppose, now, that the firm increases its output level from q
2
to q
3
. The
increase in the total revenue of the firm from this output expansion is just
the market price multiplied by the change in quantity; that is, the area of the
rectangle q
2
q
3
CB. On the other hand, the increase in total cost associated
with this output expansion is just the area under the marginal cost curve
between output levels q
2
and q
3
; that is, the area of the region q
2
q
3
XW. But, a
comparison of the two areas shows that the firm’s profit is higher when its
output level is q
3
rather than q
2
. But, if this is the case, q
2
cannot be a profit-
maximising output level.
Case 2: Price less than MC is ruled out
Consider Figure 4.3 and note that at the output level q
5
, the market price, p, is
less than the marginal cost. We claim that q
5
cannot be a profit-maximising
output level. Why?
Observe that for all output levels slightly to the left of q
5
, the market price
remains lower than the marginal cost. So, pick an output level q
4
slightly to the
left of q
5
such that the market price is less than the marginal cost for all output
levels between q
4
and q
5
.
Suppose, now, that the firm cuts its output level from q
5
to q
4
. The decrease
in the total revenue of the firm from this output contraction is just the market
1
It is a convention in economics to denote profit with the Greek letter p.
not to be republished
Page 5

Chapter 4
The Theor The Theor The Theor The Theor The Theory of the F y of the F y of the F y of the F y of the Firm irm irm irm irm
under P under P under P under P under Per er er er erfect Competition fect Competition fect Competition fect Competition fect Competition
In the previous chapter, we studied concepts related to a firm’s
production function and cost curves. The focus of this chapter is
different. Here we ask : how does a firm decide how much to
produce? Our answer to this question is by no means simple or
uncontroversial. We base our answer on a critical, if somewhat
unreasonable, assumption about firm behaviour – a firm, we
maintain, is a ruthless profit maximiser. So, the amount that a
firm produces and sells in the market is that which maximises
its profit.
The structure of this chapter is as follows. We first set up and
examine in detail the profit maximisation problem of a firm. This
done, we derive a firm’s supply curve. The supply curve shows
the levels of output that a firm chooses to produce for different
values of the market price. Finally, we study how to aggregate
the supply curves of individual firms and obtain the market
supply curve.
4.1 PERFECT COMPETITION: DEFINING FEATURES
In order to analyse a firm’s profit maximisation problem, we
must first specify the market environment in which the firm
functions. In this chapter, we study a market environment called
perfect competition. A perfectly competitive market has two
defining features
1. The market consists of buyers and sellers (that is, firms). All
firms in the market produce a certain homogeneous (that is,
undifferentiated) good.
2. Each buyer and seller in the market is a price-taker.
Since the first feature of a perfectly competitive market is
easy to understand, we focus on the second feature. From the
viewpoint of a firm, what does price-taking entail? A price-taking
firm believes that should it set a price above the market price, it
will be unable to sell any quantity of the good that it produces.
On the other hand, should the set price be less than or equal to
the market price, the firm can sell as many units of the good as
it wants to sell. From the viewpoint of a buyer, what does price-
taking entail? A buyer would obviously like to buy the good at
the lowest possible price. However, a price-taking buyer believes
that should she ask for a price below the market price, no firm
not to be republished
will be willing to sell to her. On the other hand, should the price asked be
greater than or equal to the market price, the buyer can obtain as many
units of the good as she desires to buy.
Since this chapter deals exclusively with firms, we probe no further into
a reasonable assumption for firms. Price-taking is often thought to be a
reasonable assumption when the market has many firms and buyers have
perfect information about the price prevailing in the market. Why? Let us start
with a situation wherein each firm in the market charges the same (market)
price and sells some amount of the good. Suppose, now, that a certain firm
raises its price above the market price. Observe that since all firms produce
the same good and all buyers are aware of the market price, the firm in question
loses all its buyers. Furthermore, as these buyers switch their purchases to
accommodated when there are many firms in the market. Recall, now, that an
individual firm’s inability to sell any amount of the good at a price exceeding
the market price is precisely what the price-taking assumption stipulates.
4.2 REVENUE
We have indicated that in a perfectly competitive market, a firm believes that
it can sell as many units of the good as it wants by setting a price less than or
equal to the market price. But, if this is the case, surely there is no reason to
set a price lower than the market price. In other words, should the firm desire
to sell some amount of the good, the price that it sets is exactly equal to the
market price.
A firm earns revenue by selling the good that it produces in the market. Let
the market price of a unit of the good be p. Let q be the quantity of the good
produced, and therefore sold, by the firm at price p. Then, total revenue (TR) of
the firm is defined as the market price of the good (p) multiplied by the firm’s
output (q). Hence,
TR = p × q
To make matters concrete, consider the following numerical example. Let
the market for candles be perfectly competitive and let the market price of a
box of candles be Rs 10. For a candle manufacturer, Table 4.1 shows how
total revenue is related to output. Notice that when no box is produced,
TR is equal to zero; if one box of candles is produced, TR is equal to 1 × Rs 10
= Rs 10; if two boxes of candles are produced, TR is equal to 2 × Rs 10
= Rs 20; and so on.
With the example done, let us return to a more general setting. In a perfectly
competitive market, a firm views the market price, p, as given. With the market
price fixed at p, the total revenue curve of a
firm shows the relationship between its total
revenue (y-axis) and its output (x-axis). Figure
4.1 shows the total revenue curve of a firm.
Three observations are relevant here. First,
when the output is zero, the total revenue of
the firm is also zero. Therefore, the TR curve
passes through point O. Second, the total
revenue increases as the output goes up.
Moreover, the equation ‘TR = p  × q’ is that of a
Boxes sold TR (in Rs)
00
110
220
3 30
440
550
Table 4.1: Total Revenue
53
The Theory of the Firm
under P erfect Competition
not to be republished
54
Introductory Microeconomics
straight line. This means that the
TR curve is an upward rising
straight line. Third, consider the
slope of this straight line. When
the output is one unit (horizontal
distance Oq
1
in Figure 4.1), the
total revenue (vertical height
Aq
1
in Figure 4.1) is p × 1 = p.
Therefore, the slope of the
straight line is Aq
1
/Oq
1
= p.
Now consider Figure 4.2.
Here, we plot the market price
(y-axis) for different values of a
firm’s output (x-axis). Since the
market price is fixed at p, we
obtain a horizontal straight line
that cuts the y-axis at a height
equal to p. This horizontal
straight line is called the price
line. The price line also depicts
the demand curve facing a firm.
Observe that Figure 4.2 shows
that the market price, p, is
independent of a firm’s output.
This means that a firm can sell
as many units of the good as it
wants to sell at price p.
The average revenue ( AR )
of a firm is defined as total
revenue per unit of output.
Recall that if a firm’s output is q
and the market price is p, then
TR equals p × q. Hence
AR =
TR
q
=
pq
q
×
= p
In other words, for a price-taking
firm, average revenue equals the
market price.
The marginal revenue (MR) of a firm is defined as the increase in total revenue
for a unit increase in the firm’s output. Consider a situation where the firm’s
output is increased from q
0
to (q
0
+ 1). Given market price p, notice that
MR = (TR from output (q
0
+ 1)) – (TR from output q
0
)
= (p × (q
0
+ 1)) – (pq
0
) = p
In other words, for a price-taking firm, marginal revenue equals the
market price.
Setting the algebra aside, the intuition for this result is quite simple. When
a firm increases its output by one unit, this extra unit is sold at the market
price. Hence, the firm’s increase in total revenue from the one-unit output
expansion – that is, MR – is precisely the market price.
Price Line. The price line shows the relationship
between the market price and a firm’s output level.
The vertical height of the price line is equal to the
market price, p.
Total Revenue curve. The total revenue curve of
a firm shows the relationship between the total
revenue that the firm earns and the output level of
the firm. The slope of the curve, Aq
1
/Oq
1
, is the
market price.
not to be republished
55
The Theory of the Firm
under P erfect Competition
4.3 PROFIT MAXIMISATION
A firm produces and sells a certain amount of a good. The firm’s profit, denoted
by p, is defined to be the difference between its total revenue (TR) and its total
cost of production (TC ).
1
In other words
p = TR – TC
Clearly, the gap between TR and TC is the firm’s earnings net of costs.
A firm wishes to maximise its profit. The critical question is: at what output
level is the firm’s profit maximised? Assuming that the firm’s output is perfectly
divisible, we now show that if there is a positive output level, q
0
, at which profit
is maximised, then three conditions must hold:
1. The market price, p, is equal to the marginal cost at q
0
.
2. The marginal cost is non-decreasing at q
0
.
3. In the short run, the market price, p, must be greater than or equal to the
average variable cost at q
0
. In the long run, the market price, p, must be
greater than or equal to the average cost at q
0
.
4.3.1 Condition 1
Consider condition 1. We show that condition 1 is true by arguing that a profit-
maximising firm will not produce at an output level where market price exceeds
marginal cost or marginal cost exceeds market price. We check both the cases.
Case 1: Price greater than MC is ruled out
Consider Figure 4.3 and note that at the output level q
2
, the market price, p,
exceeds the marginal cost. We claim that q
2
cannot be a profit-maximising output
level. Why?
Observe that for all output levels slightly to the right of q
2
, the market price
continues to exceed the marginal cost. So, pick an output level q
3
slightly to the
right of q
2
such that the market price exceeds the marginal cost for all output
levels between q
2
and q
3
.
Suppose, now, that the firm increases its output level from q
2
to q
3
. The
increase in the total revenue of the firm from this output expansion is just
the market price multiplied by the change in quantity; that is, the area of the
rectangle q
2
q
3
CB. On the other hand, the increase in total cost associated
with this output expansion is just the area under the marginal cost curve
between output levels q
2
and q
3
; that is, the area of the region q
2
q
3
XW. But, a
comparison of the two areas shows that the firm’s profit is higher when its
output level is q
3
rather than q
2
. But, if this is the case, q
2
cannot be a profit-
maximising output level.
Case 2: Price less than MC is ruled out
Consider Figure 4.3 and note that at the output level q
5
, the market price, p, is
less than the marginal cost. We claim that q
5
cannot be a profit-maximising
output level. Why?
Observe that for all output levels slightly to the left of q
5
, the market price
remains lower than the marginal cost. So, pick an output level q
4
slightly to the
left of q
5
such that the market price is less than the marginal cost for all output
levels between q
4
and q
5
.
Suppose, now, that the firm cuts its output level from q
5
to q
4
. The decrease
in the total revenue of the firm from this output contraction is just the market
1
It is a convention in economics to denote profit with the Greek letter p.
not to be republished
56
Introductory Microeconomics
price multiplied by the change in quantity; that is, the area of the rectangle
q
4
q
5
EF. On the other hand, the decrease in total cost brought about by this
output contraction is the area under the marginal cost curve between output
levels q
4
and q
5
; that is, the area of the region q
4
q
5
ZY. But, a comparison of the
two areas shows that the firm’s profit is higher when its output level is q
4
rather
than q
5
. But, if this is the case, q
5
cannot be a profit-maximising output level.
4.3.2 Condition 2
Consider the second condition
that must hold when the profit-
maximising output level is
positive. Why is it the case that
the marginal cost curve cannot
slope downwards at the profit-
maximising output level? To
again to Figure 4.3. Note that at
the output level q
1
, the market
price is equal to the marginal cost;
however, the marginal cost curve
is downward sloping. We claim
that q
1
cannot be a profit-
maximising output level. Why?
Observe that for all output
levels slightly to the left of q
1
,
the market price is lower than
the marginal cost. But, the
argument outlined in case 2 of section 3.1 immediately implies that the firm’s
profit at an output level slightly smaller than q
1
exceeds that corresponding to the
output level q
1
. This being the
case, q
1
cannot be a profit-
maximising output level.
4.3.3 Condition 3
Consider the third condition that
must hold when the profit-
maximising output level is
positive. Notice that the third
condition has two parts: one part
applies in the short run while the
other applies in the long run.
Case 1: Price must be greater
than or equal to AVC in the
short run
We will show that the statement of
Case 1 (see above) is true by
arguing that a profit-maximising
firm, in the short run, will not
produce at an output level wherein
the market price is lower than
the AVC.
Conditions 1 and 2 for profit maximisation.
The figure is used to demonstrate that when the
market price is p, the output level of a profit-
maximising firm cannot be q
1
(marginal cost
curve, MC, is downward sloping), q
2
(market
price exceeds marginal cost), or q
5
(marginal cost
exceeds market price).
Price-AVC Relationship with Profit
Maximisation (Short Run).  The figure is used
to demonstrate that a profit-maximising firm
produces zero output in the short run when the
market price, p, is less than the minimum of its
average variable cost (AVC). If the firm’s output
level is q
1
, the firm’s total variable cost exceeds
its revenue by an amount equal to the area of
rectangle pEBA.
not to be republished
```
Offer running on EduRev: Apply code STAYHOME200 to get INR 200 off on our premium plan EduRev Infinity!

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

,

;