Lecture 9: The Competitive Industry
Profit Maximization and the Competitive Firm
A competitive firm is a “price taker”, who

Can sell all it produces at the going market price;

Has no control over the market price
Example: A Kansas wheat farmer
The competitive firm's objective is to set output so as to maximize profits,
given by
 = pq -C(q),
The firm must expand output until price is equal to marginal cost.
If it is producing where MC < P, it can make more profit by expanding output.
If it is producing where MC > P, it can make more profit by contracting output.1
Three Cases of Profit Maximization
1
Profit Maximization
where MC = P
Profit Maximization
where ATC>p>AVC
Profit Maximization
where AVC>P
Economic Profits are > 0.
Economic Profits are < 0
but the firm is covering a
portion of their fixed costs,
i.e. should continue
operating in the short run.
Economic Profits are < 0
and you are not covering
your fixed costs, Shut down
-- Now!
As we all remember from our elementary calculus, profit maximization requires that
‘ = p -C’(q) = 0,
Suppose that a firm has well-behaved costs, traditional average cost and marginal
cost functions.
Data on Cost, Marginal Cost, Average Cost, and
Average Variable Cost
Q
Total
Cost
0
1
2
3
4
5
6
7
8
9
10
11
12
100
115
126
136
148
165
186
217
256
306
360
418
480
Marginal Average Average
Cost
Cost
Variable
Cost
15
11
10
12
17
21
31
39
50
54
58
62
115.0
63.0
45.3
37.0
33.0
31.0
31.0
32.0
34.0
36.0
38.0
40.0
15.0
13.0
12.0
12.0
13.0
14.3
16.7
19.5
22.9
26.0
28.9
31.7

If it cannot get at least $12 for its profit, the firm is better off simply bearing its
fixed costs and producing nothing at all.

If it can get $12-$31, it is best off producing in the short run but attempting to
leave the industry.

It should be willing to stay in the industry only if it can get $31 or more.
Profit Maximizing Production for Different Prices
Price
Output Decision
$0- $11.99
Produce Nothing
$12
4 units
$12.01-$17
5 units
$17.01-$21.00
6 units
$21-$30.99
7 units
If price is $12 to $30.99, the firm will produce only in the S-R
$31- $38.99
8 units
$39-$49.99
9 units
$50-$53.99
10 units
$54-$57.99
11 units
$58-$61.99
12 units
$62
13 units
Some Further Analysis
The U-Shaped Average Cost Curve
The facts dictate an upward sloping cost curve.

An initial section the ATC curve is downward sloping due to economies of scale,
but we don’t see any industry with firms working at infinitesimal size.

If the ATC curve didn't eventually slope upward, a profit maximizing competitive
firm producing at the level where MC = P could not make any profits.
How a Change in Price Affects Output
How a Rise in Market Price
Changes Optimal Output
Since a competitive firm always produces where P=MC, the MC curve (or
at least the portion above the AC curve) is now the firm's supply curve.
When the price is p2, the firm will produce q2; when the price is p1, the
firm will produce q1, etc.
The long –run supply curve is equal to the firm’s marginal cost curve. As long
as the price is above pmin, the minimum of the average cost curve.
The short –run supply curve is equal to the firm’s marginal cost curve. As
long as the price is above the minimum of the average variable cost curve.
It is a fallacy to say “a firm sets price equal to marginal cost.” The correct
way of saying this is to say “a firm sets its level of production where marginal cost
equals price.” Be aware of the difference.
A quick summary
We have now derived a firm’s cost function C(q) and consequently its supply
curves. We know how a competitive firm will act.
The basic rule:

If I can produce a widget at less (marginal) cost than the market price of
widgets, produce it; if I can’t, don’t.
The two qualifications:

If, by obeying the rule, I cannot cover my fixed costs, shut down.

If, by obeying the rule, I can’t cover my variable and fixed costs,
continue producing over the short run at a loss.
Industry Conditions
There are two cases to be considered.

When all firms have the same cost functions and hence the same
marginal cost function, average cost function, and the like.

When firms do not have the same cost functions.
Firms with Identical Technologies and Cost Functions
Suppose initially that there are N firms in the industry. Then the supply
curve, holding the number of firms constant, must be N times the supply curve. But
if the price is above pmin, each firm is making money. And that is a signal for entry.
The Common Average Cost and Supply Curve
All firms are assumed to have a common average cost curve and hence
common marginal cost (supply) curves. As long as the price is above pmin,
each firm will make money and others will be induced to enter the
business. If the price drops below pmin, firms will leave the business. At a
price of pmin, each firm will produce qmin widgets. At a price of p1, each
firm produces q1 widgets; at a price of p2, each firm produces q2 widgets.
(from the table above) Suppose that all firms have the same cost function,
then firms will be making a profit if the price is at or above $31. If the price is
below that, firms will eventually leave the business. If the price is above that, they
will enter. Thus the price will be forced to $31, with each firm making seven units.
Consider firm entry into an industry. As the number of firms rises, the
supply curve gets shifted to the right and the price gets driven down to pmin. Over
time, firms will exit and the price will get driven up.
Suppose that at a price of pmin the market demand for widgets is Qo. Then N
= Qo / qmin firms will produce widgets.
A Numerical Illustration (again from the above table)
Suppose the demand curve for the product is
Q = 260 - 5p
The price will be $31, The quantity demanded will be 105, and, since each
firm is willing to supply seven units of output at that price, there will be 105/7 = 15
firms in the industry.
Changes in Factor Prices
Factor prices played a role in determining average cost , C(r,w,q). Two cases
of interest:

Exogenous changes in factor prices and

Endogenous changes in factor prices
Exogenous changes occur when something outside the industry changes the
price of a factor. For example, consider the problems of running a sawmill when gas
prices change.
However, the price of timber, an important input to the lumber business, is
endogenous to the lumber business.
Example:
Suppose the industry is producing Q1 board feet of lumber, and that, given
the price of timber, the average cost curve is Q1, with a minimum of the average cost
curve at p1. Each firm wants to produce q1 board feet of lumber. Equilibrium is at
the price p1 with N1 firms producing q1 = Q1/N1 board feet of lumber.
Now suppose that the industry wants to increase output from Q1 board feet
of lumber to Q2 > Q1 board feet of lumber. The sawmill business is intensively
competitive and have the same cost functions. If we could ignore the impact of
expansion on timber prices, we would expect the industry to expand by "scaling up".
That is, more sawmills would start up, with each firm producing q1 board feet of
lumber, with the lumber selling at a price of p1. The number of firms would grow
from N1 to N2 = Q2/q1.
Alas, we cannot do this. While we could perhaps neglect the impact of the
industry expansion on gasoline prices, we cannot neglect its impact on timber
prices. The higher price of timber will mean that the average cost curve for the
sawmill will shift up to, say, the curve labeled Q2. The new minimum will go up to
p2.
If output is to rise from Q1 to Q2 and then to Q3, the new equilibrium
price in the lumber industry must be rise from p1 to p2 to p3 and the new long
run supply curve is thus upward sloping.
The Supply Curve with Pecuniary Diseconomies
Average Cost Curves at
Different Scales of
Operations
The Long Run Industry
Supply and Demand
Curves
Average cost will rise and fall with
the total level of operation. Each
firm faces a common average cost
curve, but as the scale of industry
rises from Q1 to Q2 to Q3, the price
of timber will rise and hence
average cost will rise.
The
minimum will go from p1 to p2 to p3
and that means an upward sloping
supply curve.
This now gives us the industry
supply curve. Each firm is still
operating at the minimum of its
average cost curve, but the price
rises with industry output.
The impact on the total profits the lumber owners
Supply and Demand for the Scarce Factor of Production
The Demand and Supply of
Timber
Timber is a scarce resource and there is
an upward sloping supply curve
A Shift in the Demand Curve
for Lumber
When the demand curve for lumber
shifts from D to D' there are two effects.
Increasing prices of timber give an
upward sloping supply curve Ss and the
price of lumber rises. As new sawmills
enter, the short run supply curve shifts
to Ss', and the price of lumber falls
partway back to the original level.
In
short,
pecuniary
external
diseconomies can lead to an upward
sloping supply curve SL as illustrated
here.
A Numerical Illustration
Suppose that it takes one board foot of timber to make one board foot of
lumber. Suppose that, right now, the industry is producing 3,000 board feet of
lumber. Timber is selling for $1 a board foot. Given the costs of operation, each
sawmill will produce 3 board feet of lumber, at an average cost of $4 a board foot.
1,000 sawmills will be required to produce the lumber.
Now suppose the industry wants to increase the supply to 4,000 board feet or
5,000 board feet. As production goes up, the cost of timber will rise to (say) $2 a
board foot for 4,000 board feet of timber or $3 a foot for 5,000 board feet of timber.
Cost of Operating A Sawmill at $1 a board foot
for lumber
Board
Cost of
Cost of Average Marginal
Feet
Timber Finishing Total
Cost
Produced
Cost
0
1
2
3
4
5
0
1
2
3
4
5
3
4
6
9
14
20
5
4
4
4.5
5
2
3
4
6
7
As the price rises, each firms average cost curve rises. Since each sawmill
has the same production function and cost function as every other sawmill, they all
operate at the minimum of their average cost curve. But, if industry production is
to rise from 3,000 board feet to 4,000 board feet to 5,000 board feet, the price must
rise from $4 to $5 to $6, to reflect the higher price of timber.
Cost of Operating A Sawmill at $2 a board foot
for lumber
Board
Cost of
Cost of Average Marginal
Feet
Timber Finishing Total
Cost
Produced
Cost
0
1
2
3
4
5
0
2
4
6
8
10
3
4
6
9
14
20
6
5
5
5.5
6
3
4
5
7
8
Cost of Operating A Sawmill at $3 a board foot
for lumber
Board
Cost of
Cost of Average Marginal
Feet
Timber Finishing Total
Cost
Produced
Cost
0
1
2
3
4
5
0
3
6
9
12
15
3
4
6
9
14
20
7
6
6
6.5
7
4
5
6
8
9
The General Case of Firms with Different Technologies
Suppose there are three firms in an industry, A, B, and C, whose average
and marginal cost curves differ. Firm A will supply no widgets when the price is
below p1. At that price, it will supply q1a, and the supply curve for higher prices is
given by its marginal cost curve. To get the supply curve for the industry, we sum
the supply curves of each of the individual firms.
The Supply Curve with Dissimilar Firms
Firm A
Firm B
Average and marginal cost curves
for firm "A"
Average and marginal cost curves
for firm "B"
Firm C
Industry
Average and marginal cost curves for
firm "C"
The industry supply curve is the sum of
the three individual supply curves.
A Numerical Example
Firm A
Firm B
Firm C
Q
C
AC
MC
C
AC
MC
C
AC
MC
0
1
2
3
4
5
6
7
8
16.0
17.0
19.0
22.0
26.0
31.0
37.0
44.0
52.0
17.0
9.5
7.3
6.5
6.2
6.2
6.3
6.5
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
6.0
10.0
15.0
21.0
28.0
36.0
45.0
55.0
66.0
10.0
7.5
7.0
7.0
7.2
7.5
7.9
8.3
4.0
5.0
6.0
7.0
8.0
9.0
10.0
11.0
10.0
11.0
13.0
16.0
20.0
25.0
31.0
38.0
46.0
11.0
6.5
5.3
5.0
5.0
5.2
5.4
7.8
1.0
2.0
3.0
4.0
5.0
6.0
7.0
8.0
A "*" by the number indicates that the firm is still below average cost, and
this constitutes part of the short run supply curve.
Output at Different Price Levels
Price
1
2
3
4
5
6
7
8
Firm A
1*
2*
3*
4*
5*
6*
7
8
Firm B
1*
2*
3*
4
5
Firm C
1*
2*
3*
4*
5
6
7
8
Industry
(LR) =
A+B+C
5
6
18
21
Why Firms earn “profits”
We have now discussed two cases: one case where all firms have an identical
cost function, and another case where there are differences.
To most people it is obvious that firms have different cost functions. But, in
a competitive business with complete information, how can one have anything but a
temporary cost advantage over the other?
Economic Profits versus Accounting Profits
How some competitive firms can earn economic profits?
- firm-specific factors of production; “niche” or “forte”
resource quality, customer good will,
Conclusions
Different firm-specific factors of production can lead to different cost
functions, different average costs functions, and different marginal cost functions.
Clearly these differences may be transitory. But transitions take time and
money, and for many practical purposes it is useful to assume different production
functions.
Government Taxes
Consider the case of government taxes on a product made by a competitive
industry. Assume an increasing cost industry, one with an upward sloping supply
curve. The supply curve is shifted up by $t, but, given the demand curve, part of the
price increase will be mitigated by reduced quantity demanded.
For relatively small tax rates, we can define the percent of the tax passed
along to the consumer in terms of the price elasticities of demand and supply:
Some numerical values
Incidence of Tax
s

1
1
1
0
d
Whatever
-2.0
-1.0
-0.5
Whatever
Percent
100
33
50
67
0
The Effect of a Tax
We have already seen this case. The key point is that the tax falls partly
on the firms in the industry and partly on the consumer.