Download The Production Decisions of Competitive Firms

The Production Decisions of Competitive Firms
We will consider the production decisions of firms operating in market having different structures.
Alternative market structures:
1. perfect competition
2. monopolistic competition
3. oligopoly
4. monopoly
Crucial elements in distinguishing between the market structures:
 The number of buyers and sellers.
 The degree of homogeneity of the product.
 Knowledge of market prices and product availability.
 Firm’s ease of entry into and exit from the industry.
Consider a market environment in which there is perfect competition.
1. There are large numbers of buyers and sellers.
2. The products are functionally identical or homogeneous; buyers view the products as being perfect
substitutes.
3. There is freedom of entry and exit by firms.
Additional assumptions:
 There is complete information regarding prices, technology and profit opportunities.
 The objective of each firm is to maximize its profits.
Each competitive firm is a “price taker” in that the firm will take the price as being given. Explanation:
 If a firm tries to charge a higher price, buyers will go to other sellers who they know are willing to sell the
same product.
 A firm could sell at a lower price. However, since it can sell all units at the market price, it will not sell at
a lower price as doing so would lower its profits.
Even though all firms together face a downward sloping market demand curve, each individual firm believes
that it can sell any quantity it chooses at the unchanged market price. Each price-taking firm faces a
horizontal demand curve having a height corresponding to the market price.
Example of a firm’s demand curve:
Market
P
S
P0
D
P
individual
firm
P0
50,000
Q
d
100
200
q
Total revenue, TR, is defined to be the firm’s total revenue generated from a given level of output, Q. For
example, if a firm sells 100 units at $20 each and 100 units at $10 each, its total revenue would be
$3000 $20  100  $10  100  .
When a firm sells all units, Q, at the same price, P, its total revenue will be TR  P Q .
Average revenue is the revenue per unit of output; AR 
When all units are sold at the same price, AR 
TR
.
Q
TR P  Q

P
Q
Q
Marginal revenue is the change in revenue per unit change in output; MR 
TR
.
Q
When a good or service’s price per unit does not change as the number of units sold changes, MR will equal P.
This will be the case if and only if the firm’s demand curve is horizontal. MR 
TR P  Q

P
Q
Q
Summary: In cases where a firm is a price-taker (i.e., the firm faces a horizontal demand), P = MR = AR.
The above relationships are illustrated using the following example.
Q
units
0
1
2
3
P
$/unit
2
2
2
2
TR
$
0
2
4
6
MR
$/unit
2
2
2
AR
$/unit
2
2
2
Output decision of a competitive firm
The assumption of profit maximizing behavior implies that the firm will make output decisions so as to
maximize profits,   TR  TC . (Remember that TC includes both explicit and implicit costs.)
The choices faced by a firm in the short-run will differ from those in the long-run. Therefore, the decisions
could differ.
Decisions made by a firm:
Short-run decisions:
Long-run decisions:
 Quantity of output
 quantity of output
 quantity of each variable input
 quantity of each and every input
 shutdown decision
 entry and exit decision
What about the choice of price?
The Short-Run
Consider the short-run output and shutdown decisions of a competitive firm.
Example: Consider a perfectly competitive firm operating in a market where the equilibrium price is $13. Given the
cost structure shown below, what level of output would the firm choose?
Q
units
0
1
2
3
4
5
6
7
TVC
$
0
10
16
24
34
46
60
77
TC
$
10
20
26
34
44
56
70
87
AVC
$/unit
10
8
8
8.5
9.2
10
11
AC
$/unit
20
13
11.33
11
11.2
11.67
12.43
MC
$/unit
10
6
8
10
12
14
17
P = MR
$/unit
13
13
13
13
13
13
13
13
TR
$
0
13
26
39
52
65
78
91
Profits
$
-10
-7
0
5
8
9
8
4
Profits are largest at 5 units of output. Furthermore, since the price is greater than the average total cost at 5 units of
output, profits are positive. Note that the total profit, $9, is equal to (P - ATC)  Q  ($13 - $11.2)  5  $1.80  5  $9.00 .
P - ATC is the average profit per unit of output. With a total of Q units sold, it follows that (P - ATC)  Q is the total
profit.
The profit maximizing level of output can be identified using marginal analysis. For the units of output up to
the 5th, MR > MC; each of these units contributes more to revenue (MR) than to cost (MC). It follows that
the production and sale of each of these units leads to higher profits. Beyond the 5th unit, MR < MC. Thus,
production of units beyond the 5th would result in lower profits.
Exercise:
 Graph TR, TC and show graphically the level of output that reflects the largest level of profits. How is
that level of profits shown in the graph?
 Graph MR, MC, ATC and AVC. Show the level of output that corresponds to the largest level of profits.
Suppose that the cost structure were unchanged but that the market price were 10? What would be the profit
maximizing level of output?
Q
units
0
1
2
3
4
5
6
7
TVC
$
0
10
16
24
34
46
60
77
TC
$
10
20
26
34
44
56
70
87
AVC
$/unit
10
8
8
8.5
9.2
10
11
AC
$/unit
20
13
11.33
11
11.2
11.67
12.43
MC
$/unit
10
6
8
10
12
14
17
P = MR
$/unit
10
10
10
10
10
10
10
TR
$
0
10
20
30
40
50
60
70
Profits
$
-10
-10
-6
-4
-4
-6
-10
-17
With P = $10, MC equals MR when output is 4 units. Note that at this profit maximizing level of output the firm would
have negative profits. (This can be seen in the last column, as well as from the fact that the average cost at Q=4, $11, is
greater the price received per unit; P - ATC < 0.) Even so, the firm would be maximize its profits – here minimize its
losses – by producing four units. This follows from the fact that the revenues of $40 will cover all variable costs ($34),
as well as a portion of the fixed costs. Even though all the fixed costs are not covered, the firm would do better by
producing the 4 units. If the firm shut down it would have no revenues to cover even a portion of the fixed costs. If the
firm shutdown, it profits would be -$10.
What if P=6?
Q
units
0
1
2
3
4
5
6
7
TVC
$
0
10
16
24
34
46
60
77
TC
$
10
20
26
34
44
56
70
87
AVC
$/unit
10
8
8
8.5
9.2
10
11
AC
$/unit
20
13
11.33
11
11.2
11.67
12.43
MC
$/unit
10
6
8
10
12
14
17
P = MR
$/unit
6
6
6
6
6
6
6
6
TR
$
0
6
12
18
24
30
36
42
Profits
$
-10
-14
-14
-16
-20
-26
-34
-45
With P = $6, MC equals MR when output is 2 units. However, the average variable cost at Q=2 exceeds the price
received per unit. In this case, the revenue generated from selling the two units of output will not even cover variable
costs, resulting in a loss of $14. If the firm shutdown, its loss would only be $10. Thus, the firm would make larger
profits (here have a smaller loss) shutting down and not producing any output.
The graphs for these three examples are shown below.
Example 1
25
dollars per unit
20
15
10
5
0
1
2
3
4
5
6
7
output
Example 2
Example 3
20
20
AC
16
16
14
14
12
P = MR
10
8
AC
18
MC
dollars per unit
dollars per unit
18
AVC
6
12
10
8
AVC
6
4
4
2
2
0
MC
P = MR
0
1
2
3
4
output
5
6
7
1
2
3
4
output
5
6
7
Digression: Make sure that you can show/measure profits and fixed costs graphically. To do so, you need to
understand the following two relationships.
  TR  TC
 Q  P  Q  ATC
FC  Q  AFC .
 Q  ( P  ATC )
Consider graphical representations of profits and fixed costs in the following two cases. In figure 1 the market
price is $2.00 and 50 units are sold. In figure 2, the market price is $1.00 and 30 units are sold. (It is
explained below why these are the quantities the firm would produce.)
Figure 1
2.50
Figure 2
P=$2
=$2$2.00
MC
P 2.50
2.00
MC
2.00
ATC
1.50
1.50
1.30
1.00
AVC
.50
1.20
0.70
10
20
30
40
AC
P =$1
$1.00
1.00
AVC
.50
50
Q = 50
10
20
30
40
TR = P  Q = $2  50 = $100
TR = P  Q = $1  30 = $30
TC = Q  AC = 50  $1.30 = $65
TC = Q  AC = 30  $1.20 = $36
 = TR – TC = $100 - $65 = $35
 = TR – TC = $30 - $36 = - $6
50
Q
NOTE:  = TR – TC = Q  P – Q  AC = Q  (P – AC)
 = Q  (P – AC) = 50  ($2 - $1.30) = $35
 = Q  (P – AC) = 30  ($1 - $1.20) = - $6
NOTE: FC = Q  AFC = Q  (AC – AVC)
FC = Q  (AC – AVC) = 50  ($1.30 - $1.00) = $15
FC = Q(AC – AVC) = 30($1.20 - $0.70) = $15
Be sure that you can show how the dollar values of TR, TC,  and FC can be represented as areas in the above
diagrams.
End of digression.
The above three examples (tables and graphs) illustrate the following general rule for profit maximization in
the short run.
Condition for profit maximization in the short-run: The firm will produce the level of output where
MR = MC as long as it is not more profitable for the firm to shut down (i.e., not produce any output).
When would it be more profitable to not produce at all (i.e., shut down) rather than produce at a loss?
 o TR TC

Short-run profits if the firm shuts down:
(TR  VC ) FC
(0  0)  FC
  FC
1 TRTC

Short-run profits if the firm produces:
(TR VC ) FC
(Q  P  Q  AVC )  FC
Q ( P AVC ) FC
It will be more profitable for the firm to produce in the short-run (rather than shut down) only if 1   0 or,
equivalently, TR  VC . When all units are sold at the same price, an equivalent expressions is P AVC .
Conversely, it will be more profitable for the firm to shut down (rather than produce) if TR < VC. An
equivalent condition is P < AVC.
These conditions can be illustrated using the following graph.
MC
$ per
unit
P1
AC
P2
AVC
P3
P4
P5
AFC
q5
q4 q3 q2
q1
q
The firm will not produce any output if the market price is below the average variable cost corresponding to
the intersection of MC and AVC (i.e., the minimum AVC).
Restatement of profit maximizing firm’s short-run output decision rule:
The firm will choose to shut down if P is less than the minimum AVC. Otherwise, the firm will produce the
output for which the associated marginal cost is equal to marginal revenue, which equals price for a
competitive firm.
Basic insights:
1. Fixed costs are irrelevant in the short-run shutdown decision, as well as in the decision of how many units
to produce.
2. The firm’s MC curve above AVC is its short-run supply curve.
The second insight helps us understand what factors affect a competitive firm’s supply curve (e.g., cause a
change in supply). For some variable to affect supply, the variable must affect MC or the minimum AVC.
(This follows from the fact that the MC curve above the minimum AVC is the supply curve.) Such factors
would include the prices of variable inputs and the marginal productivity of variable inputs.
The market supply curve representing the total quantity that all firms are willing and able to supply is the
horizontal summation of the individual firms’ supply curves. It follows that the market supply curve will
depend upon the prices and marginal products of variable inputs as well as the number of firms.