Chapter 8
Pure Competition
8.0 Preliminaries
In this chapter we combine the concepts and tools we developed in previous chapters
dealing with demand, production, costs and market structure in order to analyze the
behavior patterns of the market configurations that make up a modern economy. We
ask: what happens (i.e., what are the outcomes) in purely competitive, monopolistically
competitive, oligopolistic and monopolistic industries? We start with pure competition,
which lies at the most competitive end of our scale measuring degrees of
competitiveness. Also, as in Chapters 5 and 6, we ask in each case: Is this a short-run or
a long-run analysis? We usually start with the short run.
REM 8.1:
A purely competitive industry is one with many firms which are
price takers; no single firm is able to determine the market price,
there are no entry barriers, the product is homogeneous and there
is no nonprice competition. Because of these characteristics a firm
in such an industry faces a perfectly elastic demand curve. We
pointed out in Chapter 7 that there are few industries in the United
States and in other developed economies that fit this description.
QUESTION 8.1:
If few industries have the characteristics of pure competition, why
do we devote time and energy to analyzing the behavior of this
market type?
ANSWER 8.1:
There are three main reasons:
(1) Pure competition is the simplest market structure to analyze; it
therefore offers a convenient gateway for the introduction of a
number of crucial economic concepts that apply not only to the
purely competitive case but to the other market structures as well.
(2) Pure competition serves as a kind of “benchmark” in economic
analysis. We show that in a certain (limited) sense pure competition
is the most “efficient” market structure possible; therefore, when
1
we analyze other industry structures, e.g., monopoly, we compare
them to pure competition and ask: in what way does this particular
market type resemble or differ from the purely competitive case?.
(3) There are industries that do not meet the strict requirements of
the definition of pure competition but they approximate those
requirements more or less closely. Then the tools and concepts
developed in this chapter can still be applied in a rough and ready
way to the analysis of such industries.
COMMENT 8.1:
To analyze any market structure we need, in addition to
information about demand, production and costs, at least one
more thing: we need to know what motivates the owners and/or
managers of firms in these industries. We said in Chapter 7 that in
real life such motivations may be highly complex, but the simplest
and also the most realistic assumption is profit maximization: that
is, we assume that the goal of owners and managers is to earn a
profit which is as high as possible given all the circumstances which
they face. We call this a behavioral assumption and we maintain
this assumption throughout most of the rest of our discussion in
this and subsequent chapters. (In the textbox below we use the
capital Greek letter pi (Π) for profit.)
ASSUMPTION 8.1
Firms seek to maximize (economic) profit. In
symbols:
max Π = TR − TC
COMMENT 8.2:
Economists view pure competitors as “hemmed in” from all sides:
They can do nothing about the prices at which they sell their
products (they are price takers); they can do nothing about the
prices which they pay for inputs (they are usually “pure
competitors” on the buyers’ side in input markets) and they are
either too small to influence the technology of their industry or find
no advantage in trying to do so. There is a single decision open to
them: to choose their “profit-maximizing” output level. It is this
choice that we study carefully in this chapter. It may seem like a
relatively insignificant matter, but it turns out that many important
issues emerge from an analysis of this apparently simple choice.
2
8.1 The Profit-Maximizing Output Level in the Short Run: Total
Revenue and Total Cost
We start with the simple accounting definition: Profit = TR − TC. To analyze the logic of
profit maximization and the choice of the profit-maximizing output level we examine
the relationship between total revenue (TR), total cost (TC) and the level of output (Q).
EXAMPLE 8.1:
Consider Table 8.1 below. It represents a standard total cost
structure, with columns (9), (10), and (11) added. These columns
show the price, total revenue and profit at different output levels
(Q). The table summarizes the cost and demand situation facing the
Brockton Corp., a single-product firm in a purely competitive
industry. The information contained in the table was compiled by
the accounting and production departments of the company.
Table 8.1
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9) (10)
Q
0
1
2
3
4
5
6
7
8
9
10
11
TFC TVC TC
AFC AVC ATC
MC P
100
0 100
--------- 71
100 33 133 100.00 33 133.00 33 71
100 56 156 50.00
28
78.00 23 71
100 75 175 33.33
25
58.33 19 71
100 96 196 25.00
24
49.00 21 71
100 125 225 20.00
25
45.00 29 71
100 168 268 16.67
28
44.67 43 71
100 231 331 14.29
33
47.29 63 71
100 320 420 12.50
40
52.50 89 71
100 441 541 11.11
49
60.11 121 71
100 600 700 10.00
60
70.00 159 71
100 803 903 9.09
73
82.09 203 71
(11)
TR Profit
0
-100
71
-62
142 -14
213
38
284
88
355 130
426 158
497 166
568 148
639
98
710
10
781 -122
QUESTION 8.2:
Column (9) in Table 8.1 shows the price ($71) at which Brockton
currently sells its output. Why are the numbers the same
throughout the entire column?
ANSWER 8.2:
Since Brockton is a purely competitive firm, they are price takers.
The price at which they sell their products is determined by
“market forces,” that is, by the forces of supply and demand. But
once that price is set, they can sell any quantity at the marketdetermined price.
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PROBLEM 8.1:
Jim Bitterman is in charge of production planning for Brockton. His
job is to determine the company’s profit maximizing output level
(Q*). How can he do this?
SOLUTION 8.1:
Given the information in Table 8.1 this is easy: Inspect Column (11)
and find the output level at which maximum profit is achieved. This
happens when 7 units are produced and we write: Q* = 7. So if a
large amount of detailed information of the type contained in Table
8.1 is available (and we are dealing with a single-product firm!), the
production decision is simple.
REM 8.2:
When we say that Column (11) in Table 8.1 shows the level of
“profit” we mean economic profit (or loss). The cost items shown in
the table (and in FIG 8.1) include all the relevant opportunity costs
including a normal profit. So profit means a surplus over and above
those costs.
Now consider FIG 8.1below. It reproduces FIG 6.8 (and plots the data from Table 8.1)
with the addition of a total revenue curve. This “curve” is a straight line with a positive
slope starting at the origin since it plots the relationship TR = P x Q. When no production
takes place TR = 0 and so the TR curve starts at the origin. Then, each time production
(and sales) increase by one unit TR increases by the same amount (i.e., the price, $71).
So it is clear that a pure competitor faces a linear total revenue curve.
FIG 8.1
TC
TVC
TR
TFC
4
QUESTION 8.3:
How can you tell just by looking at Table 8.1 and FIG 8.1 that they
involve short-run analysis?
ANSWER 8.3:
Since both the table and the graph differentiate between fixed and
variable costs, we know that they deal with short-run analysis.
PROBLEM 8.2:
How can Jim Bitterman use FIG 8.1 to find the company’s profitmaximizing output level?
SOLUTION 8.2:
Since profit = TR − TC he should search for the output level shown
along the horizontal axis where the vertical distance between the
total revenue curve and the total cost curve is at its maximum. This
happens when Q = 7. (Note the arrow pointing to “7” on the
horizontal axis.) So FIG 8.1 can be used to solve the company’s
production problem graphically.
NOTE 8.1:
Observe that there is a certain “family resemblance” between FIG
8.1 and a diagram which is widely used in break-even analysis. Jim
Bitterman may need to know at what output level the Brockton Co.
“breaks even,” i.e., total revenue is just high enough to cover total
cost, where total cost includes all opportunity costs. This topic is
discussed further below, but note that in FIG 8.1 there are two
break-even points: TR = TC at output levels where the TC curve
crosses the TR curve, and in FIG 8.1 this happens when Q ≈ 2.3 (see
arrow) and when Q equals 10. Also note that if Q < 2.3 and Q > 10
Brockton suffers (economic) losses (TR < TC).
FIG 8.2
5
FIG 8.2, called the “Profit Curve,” plots the profit obtained by the Brockton Corp. at
different output levels. The data come from Column (11) of Table 8.1 or from FIG 8.1. If
Figure 8.1 is used, the graph plots the vertical distances between the TR and TC curves
against the level of output. Logically then the two graphs contain the same information.
PROBLEM 8.3:
How can Bitterman use FIG 8.2 to find Brockton’s profit-maximizing
output level?
SOLUTION 8.3:
Determining the profit-maximizing level of output from this graph is
straightforward: Find the output at which the Profit Curve reaches
its highest level. Clearly FIG 8.1 and FIG 8.2 give the same solution
to Jim Bitterman’s problem, i.e., Q* ≈ 7.
Break-Even Analysis
Imagine that the Brockton Corp. has much less detailed information about its
production process than is available in Table 8.1. This of course is often the case in real
life. In fact, the accounting department is able to provide the production manager with
only two numbers: Fixed costs are $100 and average variable cost is $25 when Q = 5.
Given the known price (P = $71) and a bit of arithmetic, the graph shown in FIG 8.3,
called a break-even diagram, can be plotted. It is based on the assumption that AVC is
constant; hence the TVC curve is linear.
NOTE 8.2:
Elementary geometry indicates that to draw a straight line you
need two points. The TVC curve in FIG 8.3 is drawn through the
origin (TVC = 0) and through the point (Q = 5, TVC = $125).
(The TC curve is obtained in the same way as in FIG 8.1, i.e., by adding the TVC and TFC
curves.) Note again the family resemblance between FIG 8.1 and FIG 8.3.
QUESTION 8.4:
What is the purpose of the break-even diagram (FIG 8.3)?
ANSWER 8.4:
As the name implies, it enables firms to determine their “breakeven” level of output, i.e., the output level at which they are just
able to cover all their costs. At any higher output level they earn
(economic) profits while at lower output levels they suffer
(economic) losses. Note that this occurs at the intersection point
between the TR curve and the TC curve, called the break-even
point. It should be clear that we are discussing the economic breakeven point: When we say the firm is “breaking even” we mean that
they earn zero economic profit but they are earning a normal profit.
6
FIG 8.3
TR
TC
TVC
TFC
PROBLEM 8.4:
The Brockton Corporation’s Jim Bitterman is engaged in production
planning. He assumes that the market price will remain the same
over the next production period but wants to make a “back-of-theenvelope” calculation to determine his minimum input
requirements for that period. How can he do this?
SOLUTION 8.4:
FIG 8.3 provides the answer. Unless Brockton obtains inputs that
are at least sufficient to produce a bit over 2 units, the firm will not
break even.
NOTE 8.3:
We often assume that only “whole” units can be produced, e.g., 3
units but not 3.2 units. Then the answer to PROBLEM 8.4 would be
somewhat different: Brockton must obtain inputs sufficient to
produce at least 3 units.
NOTE 8.4:
Observe that FIG 8.1 can also be thought of as a “break-even”
diagram. But since the cost curves are nonlinear (REM: We derived
them from a production function embodying the law of
“eventually” diminishing returns) there are two break-even points!
(Note the first arrow pointing to the interval between “2” and “3”
and the third arrow pointing a bit to the right of “10.”) Positive
profits are earned at output levels to the right of the first and to the
7
left of the second break-even point. Outside of that interval the
firm incurs (economic) losses.
The Shut-Down Point: TR, TC and TVC
We have examined the problem of finding a firm’s (short-run) profit-maximizing output
level. We now ask a related question: Should the firm produce anything at all, or would
its owners be better off shutting down, i.e., cutting production to zero? We ask this
question from both a short-run and a long-run perspective.
NOTE 8.5:
The price a purely competitive firm receives for its products (and
therefore its total revenue) is determined by the “market,” i.e., by
the forces of supply and demand. But the determinants of supply
and demand may change (REM: Chapter 2) and hence the market
price and the firm’s total revenue may change as well.
FIG 8.4
TR1
TR2
TR3
TR4
Consider FIG 8.4 above. The TC, TVC and TFC curves (unlabeled) are the same as in FIG
8.1. The curve labeled TR1 is the same as the TR curve in FIG 8.1. We now ask: What
happens to the TR curve if there is a change in the market price? Clearly if the price
increases total revenue increases and the TR curve shifts up (while still anchored to the
origin) and if the price decreases the TR curve shifts down. We saw earlier that if the TR
curve lies above the TC curve the firm earns a positive economic profit. So if the market
price increases its profits will increase.
8
REM 8.3:
If a firm’s revenues exceed their economic costs they earn a surplus
called economic or pure (or “above-normal”) profit. (Chapter 6.)
Interesting questions arise if the market price decreases. We show three possibilities in
FIG 8.4:
(1)
The market price decreases (to $44); the TR curve shifts down until it is just
tangent to the TC curve, i.e., it just touches the TC curve at a single point. This is
shown (in red) by TR2. There is one point where TR = TC, that is, there is one
output level where revenues are just enough to cover total costs and the firm
breaks even.
QUESTION 8.5:
From either a short-run or a long-run perspective should the
firm stay in business or should they shut down, i.e., cut
production to zero?
ANSWER 8.5:
Since the firm is breaking even in the economic sense they
are earning a normal profit.
REM 8.4:
Normal profit is defined as the minimum return required to
keep the owners’ (or stockholders’) resources in their
current activity. It is equivalent to the highest return those
resources could earn in any alternative activity.
Since the firm is earning a normal profit they are earning as
high a return in their present business as they could
elsewhere. They therefore would/should stay in their
present line of business both in the short run and the long
run.
(2)
The market price decreases (to $34); the TR curve shifts down until it lies
everywhere below the TC curve but there is an interval in which it lies above the
TVC curve (TVC < TR <TC). This is shown (in blue) by TR3. Revenues are enough to
cover all variable costs and some part of fixed costs but not enough to cover all
costs (including all relevant opportunity costs). In other words, the firm is
suffering an economic loss.
QUESTION 8.6:
What should they do in the short and long run?
ANSWER 8.6:
In the short run they should produce despite an economic
loss but in the long run they should cut production to zero
(and “take their marbles and go elsewhere”).
9
Why should the firm produce in the short run despite an economic loss? The answer is
that ASSUMPTION 8.1 is incomplete: firms seek maximum profits; but if they are unable
to earn a profit they would/should at least try to minimize their losses!
In the short run fixed costs are unavoidable (the firm can do nothing about them), so
logically they should be ignored in making short-run production decisions − only variable
costs should be considered. If the firm were to shut down under these circumstances
their loss would equal their total fixed cost. But if instead they keep on producing,
revenues would be enough to cover total variable cost plus some portion of fixed cost
so their losses would be smaller.
REM 8.5:
The short-run is defined as a time period in which the level of use of at
least one input cannot be changed; we call such an input a fixed input
and the cost of such an input is a fixed cost. So in the short-run firms
are “stuck” with these costs; hence we call them “unavoidable.” But
variable costs are avoidable: If production ceases variable cost no
longer need to be incurred.
We have reached an important conclusion which we will state as a decision rule.
DECISION RULE 8.1: When making (short-run) economic
decisions fixed costs should be
ignored.
NOTE 8.6:
There is an obvious corollary to DECISION RULE 8.1: only
variable costs, i.e., those under the control of the firm’s
management should be considered in making short run
economic decisions.
What about the long run? From a long-run perspective all costs
are variable – there is enough time to change the level of use
of all the inputs employed by the firm; they are not “stuck”
with fixed costs. If revenues are not enough to cover all
(opportunity) costs the owners of the firm can shift their
resources elsewhere. So from a long-run perspective the best
solution is to cut production to zero.
(3)
The market price decreases (to $24); the TR curve shifts down until it is tangent
to the TVC curve, i.e., it just touches the TVC curve at a single point (TR = TVC).
This is shown (in brown) by TR4. Revenues are just enough to cover TVC.
10
(4)
QUESTION 8.7:
What should they do in the short and long run?
ANSWER 8.7:
If TR = TVC the firm is just able to cover its variable costs; so
whether they keep on producing or shut down, their loss
would equal their fixed costs. From a short-run perspective
then they are just on the boundary between producing and
not producing. They can decide which option to choose with
a coin toss. From a long-run perspective the answer remains
as before: Shut down if your revenues are not sufficient to
cover all costs
The market price decreases (to below $24); the TR curve shifts down until it lies
everywhere below the TVC curve (not shown in FIG 8.4). Revenues are not
enough to cover even variable costs.
QUESTION 8.8:
What should they do in the short and long run? Explain.
ANSWER 8.8:
The answer is left as an exercise for the reader.
The conclusions of our discussions in this section are summarized in Table 8.2.
The question mark means that management can decide whether to produce or
not with a coin toss.
Table 8.2
If:
In the Short-Run:
TR>TC
produce
TR = TC
produce
TVC<TR<TC
produce
TR = TVC
produce (?)
TR<TVC
don’t produce
In the Long Run
produce
produce
don’t produce
don’t produce
don’t produce
Fixed Costs, Sunk Costs and Avoidable Costs in Decision-Making
The discussion in the previous section which led us to DECISION RULE 8.1 (“Ignore fixed
costs in short-run decision making”) leads to a broader concept, that of sunk costs,
which plays an important role in the economic analysis of decision-making.
DEF 8.1
Sunk Costs are costs which have been
incurred in the past or for some other
reason cannot be avoided.
11
EXAMPLE 8.2:
The XLC Corp. is in the construction business in the Southwest and
they are putting up an office complex “on speculation,” that is, they
are building it not under contract as is usually the case in the
construction business, but simply in the hope of selling it at a profit
when it is completed. Due to the availability of modern accounting
software they have “real time” information about their expenses.
When the project is half-completed they find that up to that point
their expenditures for labor, materials, leased equipment, fuel and
some smaller items add up to $1.7 million. All of these expenses are
sunk costs. Since they have already been incurred there is nothing
XLC can do about them now.
EXAMPLE 8.3:
The management of the King Kong Trading Co. expect to obtain a
number of lucrative contracts from several domestic retailers and
in preparation they sign leases for a large amount of warehouse
space. Unfortunately negotiations for the largest of these contracts
fall through and they end up needing much less warehouse space
than they anticipated. The company’s lawyers tell them that the
leases are tightly written and cannot be broken and that they do
not permit subleasing (that is leasing the space to others). The
lease payments (even though they have not yet occurred) are also
sunk costs.
The contrasting concept is that of avoidable costs. (Some people call them incremental
costs but we use that term somewhat differently later in this chapter.) Like variable
costs, but unlike sunk costs avoidable costs are under the control of management (or
other decision makers.) They can be avoided if a particular choice is not made.
EXAMPLE 8.4:
The Kaycee Corp. is a diversified consumer products company. They
are in the early planning stages of an advertising campaign with an
estimated cost of $17 million. Before the decision is made to
undertake such a campaign, the $17 million is an avoidable cost.
DEF 8.2:
Avoidable costs are costs that can be avoided if
a particular choice or decision is not made.
There is a great deal of overlap between the sunk costs and fixed costs concepts.
Because fixed costs are independent of the firm’s output level and cannot be controlled
by management in the short run they are similar to sunk costs. Sunk costs therefore
play a role similar to fixed costs in economic (and noneconomic!) decision situations.
12
That is, we say that since sunk costs cannot be affected by a particular decision they
should not affect that decision. The point can be summed up in a decision rule:
DECISION RULE 2:
QUESTION 8.9:
Sunk costs should be ignored in making
economic (and many noneconomic)
decisions.
The XLC Corp. (see EXAMPLE 8.2) expected the total cost of the
project to be $3.5 million and to be able to sell the complex for at
least $5 million. Their costs are on track but in the meantime the
market for office space in the region has collapsed and the best
price they can expect to get once the project is completed is $3
million. The top managers of the company are discussing the
question of what to do about it.
Phil Johnson (C.E.O.):
“We cannot bail out in the middle of a
project. We have already spent $1.7
million on it. “
Andy Forrester (C.F.O.): “If we continue the project we will end up
with half a million in losses.”
Who is right, Johnson or Forrester?
ANSWER 8.9:
Neither! The $1.7 million that has already been spent is irrelevant.
It is a sunk cost and should be ignored. The only relevant numbers
are the $1.8 million that still must be spent (an avoidable cost) and
the $3 million for which the completed project can be sold.
8.2 The Profit-Maximizing Output Level in the Short Run:
Marginal Revenue and Marginal Cost
There is an alternative approach to the question we asked in Section 8.1 about a firm’s
profit-maximizing output level. It involves the use of marginal as opposed to total
quantities. The two approaches are logically identical but the marginal approach helps
us gain important insights into both business and nonbusiness decision making.
Consider FIG 8.5. It reproduces FIG 8.2 (and plots the data from Columns (6), (7) and (8)
of Table 8.1) with the addition of the horizontal line labeled P, MR. This line is the
“demand curve” facing the Brockton Corp. It is perfectly elastic and drawn at the level of
the current market price (P = $71; note the arrow along the vertical axis.) So FIG 8.5
13
depicts the demand and cost situation facing the Brockton Corp. expressed on a per unit
basis.
FIG 8.5
MC
ATC
P, MR
AVC
QUESTION 8.10:
Why is the demand curve facing Brockton perfectly elastic?
ANSWER 8.10:
Since Brockton is a firm in a purely competitive industry they are
price takers. At the market-determined price they can sell any
amount they wish but if they attempt to charge a higher price their
sales would drop to zero. They have no reason to charge a lower
price but if they did their sales would grow to “infinity.” The result
is the horizontal, perfectly elastic demand curve we see in FIG 8.5.
To use FIG 8.5 to determine Brockton’s profit-maximizing output level we need a new
concept called marginal revenue (MR).
14
DEF 8.3:
Marginal Revenue (MR) is defined as the change in
total revenue that results from a small (usually a
one-unit) change in production and sales. In
symbols:
MR 
ΔTR
ΔQ
NOTE 8.7:
The MR concept provides an answer to the following question: If
we produce and sell a little bit more, say one more unit, how much
extra revenue would we receive? It is therefore similar to the other
“marginal” concepts we encountered in previous chapters.
NOTE 8.8:
The MR concept is particularly simple for a purely competitive firm:
If they produce and sell one additional unit, the extra revenue they
receive is just the price. (This is not the case in other market
structures!) For firms in purely competitive industries (but only for
such firms!) we can therefore write:
In pure competitors MR = P
It is for this reason that the demand curve in FIG 8.5 is labeled P,
MR so we will sometimes call it the “marginal revenue (MR) curve”
and sometimes the “price line” (and sometimes the “demand
curve”).
We now have the tools to answer the question we stated at the beginning of this
section: What is the Brockton Corp.’s profit-maximizing output level? The answer is
given by the following decision rule:
DECISION RULE 8.3: Produce up to the point where MR = MC
In FIG 8.5 this output level occurs at the intersection between the MR curve and the MC
curve and the answer is again Q* = 7; (note the arrow pointing to “7” on the horizontal
axis). This should come as no surprise since, as we pointed out the two approaches are
logically identical.
15
QUESTION 8.11:
Why is “MR = MC” the proper decision rule?
ANSWER 8.11:
Imagine that Jim Bitterman, the production manager, tries to arrive
at the answer by “trial-and-error.” He writes a small program on his
laptop that tells him for each possible output level, produce
“more,” produce “less” or “stop,” you have found the profitmaximizing output level. He starts with an output below 7, say Q =
5. The marginal revenue of course equals the price (P = $71) and
the marginal cost equals $29. (The numbers come from Table 8.1)
What will his little program tell him? Produce more, since by doing
so you will add more to your revenues than to your costs, so profits
will increase. In other words, as long as MR > MC (the MR line lies
above the MC curve in Figure 8.5), increase production. He next
experiments with an output higher than 7, say Q = 9. MR still equals
$71 but now MC = $121. The program will say produce less, since
by doing so you will lower your costs more than your revenues and
again profits will increase. So when MR < MC (the MR line lies
below the MC curve) reduce production. But when MR = MC there
is no gain from either increasing or decreasing production. It is time
to “stop,” since you have found the profit-maximizing output level.
This analysis is summarized in Table 8.3
Table 8.3
Output Situation
Action
5
MR>MC produce more!
7
MR = MC
stop!
9
MR<MC produce less!
QUESTION 8.12:
Can Jim Bitterman solve the problem of finding the profitmaximizing output level by using the per-unit data in Table 8.1?
ANSWER 8.12:
Yes. He can inspect Columns (8) and (9) which show the marginal
costs and price (marginal revenue) facing the company and find the
output level where MR (=P) = MC. Unfortunately there is no place
in the table where the price is exactly equal to marginal cost. So if
we insist that only whole units (i.e., no fractional units) can be
produced, the rule must be modified:
DECISION RULE 8.3’:
Produce up to the point where MR ≥ MC; (but
make sure that MR and MC are as close as
possible!)
16
Applying this rule we again come up with Q* = 7.
QUESTION 8.13:
To test your understanding of the MR = MC rule ask the following
question: What if Bitterman decides to produce 6 units instead of
7? Why is this a mistake?
ANSWER 8.13:
Because if the company increases its output from Q = 6 to Q = 7 the
added revenue is $71 (i.e., the price or marginal revenue), the
added cost is $63 (the marginal cost) so the added profit is $8 ($72
− $63). By producing only 6 units Brockton Corp. gives up $8 in
potential profit. (The data again come from Table 8.1)
QUESTION 8.14:
What if Bitterman decides to produce 8 units instead of 7? Why is
this a mistake?
ANSWER 8.14:
The answer to this question is left as an exercise for the reader.
QUESTION 8.15:
Bitterman’s assistant, Fred Cook, claims that the profit-maximizing
output level occurs in FIG 8.5 where the ATC curve reaches its
lowest point because this is where the vertical distance between P
and ATC is at its maximum. It is found at the output level where the
MC curve cuts the ATC curve. (Note the arrow pointing to the
interval between “5” and “6” in FIG 8.5.)
REM 8.5:
The MC curve crosses the ATC curve at its minimum point. (Chapter
6).
So Cook’s “decision rule” looks like this:
max (P − ATC)
Why is this incorrect?
ANSWER 8.15:
Something in fact is maximized at this output level, namely profit
per unit. But ASSUMPTION 8.1 states that firms seek to maximize
total profit. The two are not necessarily the same, as illustrated in
the table below.
17
Table 8.4
Q
P
ATC Profit/Q Total Profit
$5 $71 $45.00
$26.00
$130
6 71 44.67
26.33
158
7 71 47.29
23.71
168
The data are extracted from Table 8.1 with the addition of a column
showing profit per unit (P − ATC). It is clear from this table that if
the company produces 5 or 6 units profit per unit is higher than at
Q = 7 but total profit is lower.
The MR = MC rule is an example of the method called “marginal analysis” which we
mentioned in earlier chapters. We pointed out that this approach is typically used in
economics, especially in microeconomics. So while it is important to be familiar with and
understand this rule, it is even more important to understand the logic behind it. So we
approach the problem from a second, somewhat different perspective.
FIG 8.6
$/Q
MC
c
11
7
3
0
e
a
d
MR
b
1,000
1,800
2,600
Quantity
Consider FIG 8.6. It is a highly simplified version of FIG 8.5. The average cost curves are
omitted and only the upsloping portion of the marginal cost curve is shown. (For
simplicity we also assume that the marginal cost curve is linear.) It depicts the situation
of the Hazelton Company, a large corporate farming operation in the Midwest. (It is
large in absolute terms but small in relation to the markets it operates in.) The graph
shows the wheat-growing part of Hazelton’s business. (The current price of wheat is $7
per bushel.) The company employs an agricultural economist who advises them to plan
18
for an output of 1,800 bushels in the current growing season but the company’s
management ignore her and plan for an output of only 1,000 bushels.
QUESTION 8.16:
Why is the Hazelton Company making a mistake by not listening to
their agricultural economist?
ANSWER 8.16:
Think in marginal terms: Should the company produce 1,001
bushels instead of 1,000? A careful look at FIG 8.6 indicates that the
answer is yes, because if they do they will add $7 to their revenues
and a bit more than $3 to their costs, so their profit would increase
by a bit less than $4. (Why “a bit more” than $3 and a “bit less”
than $4?) Go through the process again: Should they produce 1,002
bushels instead of 1,001? The answer is again yes, because this will
add $7 to their revenues but a bit more than $3 to their costs, so
their profit would again be higher. Continue this process until you
reach an output of 1,800 bushels. Should the company plan to
produce 1,801 bushels? The answer is no, since at this point the MC
curve is above the MR curve: producing 1,801 bushels instead of
1,800 would add more to costs than to revenues, therefore reduce
profits. Hazelton should stop at 1,800.
QUESTION 8.17:
What is the cost of the Hazelton Co.’s mistake?
ANSWER 8.17:
The profit the company loses by not choosing the profit-maximizing
output level is depicted by the area of the triangle bae, shown in
red. Using a bit of elementary geometry the loss can be calculated:
it comes to $1,600.
QUESTION 8.18:
Would the Hazelton Company be making a mistake if they planned
to produce 2,600 bushels instead of 1,800? If it is a mistake
calculate its cost.
ANSWER 8.18:
The answer to this question is left as an exercise for the reader.
19
NOTE 8.9:
We developed the MR = MC rule in the
context of a firm in a purely competitive
industry. But the rule is generally
applicable: Whether the firm is a pure
competitor,
monopolistic
competitor,
oligopolist or pure monopolist, the profitmaximizing output level is found by using
the same decision rule.
QUESTION 8.19:
Can we use FIG 8.5 (the unit-cost-price diagram) to determine total
revenue, total cost and total profit if we know the current market
price?
ANSWER 8.19:
Yes. Consider FIG 8.7 below. It shows the Brockton Corp.’s unit
costs and price (P = $71; note the “P” and the arrow along the
vertical axis.) The price is also shown by the distance QR. As before,
the profit-maximizing output is 7 units (note the “Q” and the arrow
along the horizontal axis). Since TR = P x Q it is shown in the graph
by the area of the rectangle OPRQ (TR = $71 x 7 = $497). Average
total cost when 7 units are produced is shown by the vertical
distance from the horizontal axis to the ATC curve, or the distance
QT. When 7 units are produced ATC = $47.29 (See Table 24.1).
Since TC = ATC x Q, the total cost at the firm’s profit-maximizing
output level is shown by the area of the rectangle OSTQ. (TC =
$47.29 x & = $331.03.) And since profit (Π) = TR − TC, the difference
between these two rectangles shows the firms profit when the
price is $71. (Π = $497 − $331.03 = $165.97.)
20
FIG 8.7
MC
R
P
ATC
T
S
AVC
Q
Incremental Analysis
The marginal approach which we have encountered in several places, but especially in
this chapter with the development of the MR = MC rule, leads naturally to a broader
type of analysis which is applicable to many different decision-making situations.
Imagine a decision-maker (an individual or a group) faced with a problem of choice:
Should we undertake a particular project? Should we engage in a particular activity?
Should we fix the roof on our headquarters building? Should we introduce a new
product? Should the hospital acquire a new MRI machine? Should we raise our prices?
The information that the decision-maker should gather and the analytic tools that
should be employed can get extremely expensive and complicated. But ultimately the
process boils down to two questions: If we do this what will be the incremental
revenue? What will be the incremental cost?
DEF 8.4:
Incremental Revenue (IR) is defined as
the change in revenue that results if a
particular activity is undertaken.
21
EXAMPLE 8.5:
The Baskerville Trucking Co. is considering a job to ship 120 tons of
freight from Philadelphia to Jacksonville, FL at a rate of $140 per
ton. If they accept the job the incremental revenue (IR) would be:
IR = 120 x $140 = $16,800
DEF 8.5:
EXAMPLE 8.6:
Incremental Cost (IC) is defined as the change in cost
that results if a particular activity is undertaken.
The Baskerville firm’s drivers are fully employed so the company
would have to hire 8 temporary drivers at a rate of $170 per day.
(They think the job can be completed in 5 days.) The company has
a sufficient number of idle trucks. The accounting department has
prepared the following table showing the non-labor cost of
transporting 120 tons of freight from Philadelphia to Jacksonville
(a distance of approximately 850 miles).
Cost Item
Amount
Fuel
$2,720
Depreciation (wear-and tear)
1,940
Depreciation (obsolescence)
1,570
License fees
410
Other overhead
1,370
Miscellaneous variable
1,540
Maintenance
775
Total
$10,325
QUESTION 8.20:
What is the incremental cost (IC) of accepting this job? According to
the company’s accountant it is the sum total of the items shown in
the table above and the $6,800 that would have to be paid to the 8
temporary drivers, or $17,125. Is this correct?
ANSWER 8.20:
No! According to DEF 8.5, to calculate incremental cost one must
carefully examine each cost item and decide: Is this cost affected by
the decision to accept the job or not? In other words, is this cost
avoidable? We proceed to do this below:
(1)
Fuel. If the company’s trucks remain idle they will not
use up any fuel. So fuel is clearly an avoidable cost and should be
included in our incremental cost calculation.
22
(2)
Depreciation (wear-and-tear). Presumably the long
journey from Philadelphia to Jacksonville will increase the rate at
which the company’s trucks are “used up,” hence this item should
be included. (The assumption here is that if Baskerville does not
accept the job the trucks will remain idle.)
(3)
Depreciation (obsolescence). Part of what accountants
call depreciation results simply from the passage of time: physical
capital goods become obsolete and must be replaced. This will
happen whether the trucks are in use or not so this item should not
be included.
(4)
License fees. Firms must pay license fees of various sorts
to all levels of government. These fees would have to be paid
whether the job is accepted or not. This item should be excluded.
(5)
Other overhead. Overhead is a term used by accountants
to indicate costs which are not directly related to the level of
production. It is therefore very similar to fixed costs and will not be
affected by the decision to accept the job. Overhead costs should
be excluded.
(6)
Miscellaneous variable costs. The tem “variable” provides
the clue. We can automatically assume that it refers to cost items
which are related to the amount of transportation services
provided by the company, so it clearly should be included as part of
incremental cost.
(7)
Maintenance. Presumably trucks that were on a long trip
need a lot of maintenance but trucks that are idle also require
some maintenance. So there is an ambiguity here. If we had more
information we could come up with a more definitive answer. But
in the absence of such information we will be cautious and assume
that this item should be included in our calculation.
What is the Baskerville Company’s incremental cost if they accept
this particular job? Given the preceding discussion we have:
IC = $6,800 + $2,720 + $1,940 + $1,540 + $775 = $13,775
QUESTION 8.21:
What is the difference between marginal revenue and cost and
incremental revenue and cost?
ANSWER 8.21:
Here we use the term marginal for small changes (often a one
“unit” change) and the term incremental for any change. So if the
KLS Corp. is considering building a new plant at a cost of $300
23
million, we say that the incremental cost of this project is $300
million (not small change!)
QUESTION 8.22:
Should the Baskerville Trucking Co. accept the job?
ANSWER 8.22:
Since the incremental revenue is $16,800 and the incremental cost
is $13,775, accepting the job would add $3,025 to the company’s
profits, so the job should be accepted, assuming that the company
has no reason to expect that a more profitable job may appear over
the horizon!
ANSWER 8.22 has an important implication: a decision rule which is at the heart of
incremental analysis and is based on the same logic we used in developing the MR = MC
rule.
Table 8.5
DECISION RULE 8.4
If:
Should I do it?
IR > IC
Yes
IR = IC
?
IR < IC
No
In Table 8.5 “Should I do it?” means: Should I undertake the particular project I am
considering? Should we build the new factory? Should we introduce the new product?
And so on. (The question mark in the table means that the decision maker is indifferent:
If IR = IC they would be as well off whether they “do it” or not.)
There is a slightly different way to express this decision rule which requires a new
definition.
DEF 8.6:
Incremental Profit (IP) is defined as the additional profit (or the
change in profit) that results from undertaking a particular
activity. In symbols:
IP = IR − IC
This decision rule is shown in the table below.
24
Table 8.6
DECISION RULE 8.4’
If:
Should I do it?
IP > 0
Yes
IP = 0
?
IP< 0
No
DECISION RULES 8.4 and 8.4’ are logically identical and the answer to a decision problem
should obviously be the same. So in the case of the Baskerville Trucking Co. we have IR =
$16,800, IC = $13,775 so IP = $3,025 > 0 and the answer is the same as before: Accept
the job.
NOTE 8.10:
There is a close connection between incremental
analysis and our earlier discussion of sunk and
avoidable costs. REM: sunk costs are unavoidable so
they cannot be affected by any particular decision.
Therefore they should not be included in any
calculation of incremental costs. In fact, the most
common error in the application of incremental
analysis is the inclusion of sunk costs as part of
incremental cost.
25
APPLICATION 8.1
The Plymouth Co.
The Plymouth Co. is a small East Coast Manufacturer of work shirts. The
following cost data have been assembled by Margaret Rutherford, Plymouth’s
accountant. Monthly overhead is $104,800. The materials that go into each
shirt cost $1.70. Labor cost per shirt is $1.65 for skilled labor and $1.10 for
unskilled labor. Both kinds of labor are required in the manufacturing process
but skilled workers are never required to do unskilled work. Miscellaneous
variable costs per shirt come to $0.65. Ms. Rutherford has calculated “fully
allocated cost per unit” (equivalent to the economist’s average total cost or
ATC) to be $6.41.The standard production volume is 80,000 shirts per month.
The usual manufacturer’s price is $7.45 per shirt.
The following additional information may be relevant: The summer months
are usually slow and production volume falls to 20,000 shirts per month. In
order not to incur extra search and training costs the company keeps its
entire skilled work force (but not its unskilled work force) on the payroll in the
summer months. If there is not enough work for them to do they engage in
training activities and in additional maintenance work. (We assume for
simplicity that average variable cost is constant in the relevant range.)
The company receives an order for 50,000 shirts to be produced in July and to
be sold under a private label on the West Coast, far from Plymouth’s usual
market. The offered price is $4.42 per shirt.
PROBLEM:
Should the order be accepted or rejected? (Note: Assume that
all the unit costs calculated by Ms. Rutherford are constant
over the relevant output range.)
SOLUTION:
(1) Calculate Plymouth’s incremental revenue (IR) if the order
is accepted:
IR = 50,000 x $4.42 = $221,000
(2) Calculate Plymouth’s incremental cost (IC) if the order is
accepted:
26
APPLICATION 8.1, continued
We assume overhead costs to be fixed and should therefore be
ignored. The company has a policy of keeping its skilled
workers on the payroll in the summer months even if there is
not enough work for them to do, which apparently is the case
in the summer. So skilled labor is in effect available “for free”
and should not be counted as part of incremental cost. Clearly
the remaining three cost items are relevant, so we have:
IC = 50,000 x ($1.70 + $1.10 + $0.65) = 50,000 x $3.45 = $172,500
IR = $221,000 > IC = $172,500
The order should be accepted.
(Alternatively, IP = IR − IC = $221,000 − $172,500 = $48,500 > 0
and the order should be accepted.)
APPLICATION 8.2
Globe Air Lines
Globe Air is an expanding regional airline serving mainly the Midwest. The
company is committed to flying the Des Moines- Sarasota route three times a
week for at least the next two years regardless of economic conditions. They
use the Boeing 737, which seats 180 passengers as their standard equipment.
Usually 90% of the seats are occupied and based on this “load factor” the
accounting department has calculated the cost of flying one passenger one
way on this route as shown in the table below.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
Labor
$17.45
Fuel
8.90
Food Service
5.45
Depreciation
7.25
Other Overhead 14.50
Ground Service
7.90
Maintenance
4.85
Total
66.30
27
APPLICATION 8.2, continued
The usual one-way fare is $99. In the summer months travel from the
Midwest to Florida declines sharply and Globe’s load factor drops to 30%.
Fred Cox, the marketing V.P. submits a proposal that the fare be lowered to
$49 in July and August on the basis of a forecast that this would lead to a
significant increase in summer travel with a projected load factor of 75%.
Assumptions: (1)
(2)
(3)
(4)
(5)
(5)
(6)
All forecasts and estimates are accurate.
The labor item refers to flight crew; the size of the crew
is determined by F.A.A regulations and is independent
of the number of passengers.
The amount of fuel used is independent of the number
of passengers. (Aeronautical engineers may disagree!)
Ground service is purchased from an outside vendor
and the cost is proportional to the number of
passengers.
Maintenance is performed on a regular schedule to
conform to F.A.A regulations and is independent of the
number of passengers.
Globe is a “single-fare” carrier: they charge the same
price for every seat.
Globe is the only carrier on this route and does not
have to consider competitors’ reactions to its short-run
pricing decisions.
PROBLEM:
Should the proposal be accepted or rejected?
SOLUTION:
(1)
Calculate Globe Air’s incremental revenue for each
flight.
IR = 0.75 x 180 x $49 − 0.30 x 180 x $99 = $6,615 −
$5,346 = $1,269
(2)
Calculate Globe Air’s incremental cost for each flight.
A careful look at the cost items in the table and the
assumptions listed above show that only items (3) and
(6) should be included as incremental costs. That is only
food service and ground service vary with the number
28
APPLICATION 8.2, continued
of passengers and are therefore affected by the
decision to lower or not to lower the fare. Hence:
IC = 45 x ($5.45 + $7.90) = $600.75
(Where does the number 45 in this calculation come
from?)
Since IR > IC, the proposal to lower the fare to $49
should be accepted.
The Shut-Down Point: Price, ATC and AVC
It is useful to discuss the question of the shut-down point using the framework of the
unit cost-price diagram, which we do below.
NOTE 8.11
It should be clear from all our preceding discussions that everything
we can do using FIG 8.1 (the Total Revenue-Total Cost diagram) we
can also do using FIG 8.5 (the Price-Unit Cost diagram). For
example, we can observe the same break-even points in both
diagrams: In FIG 8.5 the break-even points occur where P = ATC.
(Note the arrows pointing to the interval between “2” and “3,” the
first break-even point and a bit to the right of “10,” the second
break-even point.) When P = ATC the firm’s revenues are just
enough to cover all their costs (including all relevant opportunity
costs) and as before, we say that the firm “breaks even.” The firm
earns positive profits in the interval between the two break-even
points and suffers economic losses in the range to the left of the
first and to the right of the second break-even point.
29
FIG 8.8
MC
ATC
a
(1)
b
(2)
(3)
c
d
(4)
(5)
AVC
e
Consider FIG 8.8. It reproduces the unit cost curves from FIG 8.5. It also contains the
same demand-marginal revenue “curve” we used previously (with P = $71). Notice the
arrow labeled (2) along the vertical axis; it points to the $71 price. This line intersects
the MC curve at point b, i.e., an output of 7 and we conclude once again that the profitmaximizing output level for the Brockton Corp. is 7 units. The $71 price line lies above
the ATC curve (P > ATC) so we know that TR exceeds TC and Brockton is earning a
positive economic profit. But we said in Section 8.1 that since Brockton is a firm in a
purely competitive industry the price is determined by “market forces,” i.e., supply and
demand. We know that the determinants of supply and demand may change and as a
result the market price may change. If the market price increases the demand-MR curve
will shift up and Brockton will earn higher profits. But once again interesting questions
arise if the market price decreases. (The discussion here will be brief since we covered
the essential logic in Section 8.1) We show 3 possibilities:
(1)
The price drops to $44. The arrow marked (3) points to the new price line. It is
just tangent to the ATC curve; that is, there is a single output level at which P =
ATC and the firm breaks even. Since “breaking even” means that they receive a
30
return as high as they could obtain in any alternative activity they will produce
both in the long run and the short run.
(2)
The price drops to $34. The arrow marked (4) points to the new price line. It lies
below the ATC curve but there is an interval in which it lies above the AVC curve.
That is, AVC < P <ATC. Since the price is more than enough to cover AVC but not
enough to cover ATC they will produce in the short run but shut down (cut
production to zero) in the long run.
(3)
The price drops to $24. The arrow marked (5) points to the new MR line. It is just
tangent to the AVC curve; that is, there is a single output level at which P = AVC
and the firm is just able to cover its variable costs. They are on the boundary
between producing and shutting down so they can decide what they should do
with a coin toss.
(4)
The price drops below $24. The price line (not shown) falls below the AVC curve.
The price is not enough to cover even variable costs. What will/should the firm
do? The answer to this question is left as an exercise for the reader.
This discussion can be summarized in Table 8.7.
Table 8.7
If:
In the Short-Run:
P>ATC
produce
P = ATC
produce
AVC<P<ATC
produce
P = AVC
produce (?)
P<AVC
don’t produce
In the Long Run
produce
produce
don’t produce
don’t produce
don’t produce
The Marginal Cost Curve and the Supply Curve
In Chapter 2 we introduced the concept of supply and the supply curve. We also
discussed the determinants of supply and pointed out that the major determinants are
production costs. We are now in a position to make this idea more precise.
Consider FIG 8.7 again, which depicts the cost and demand situation facing the Brockton
Corp. There are 5 horizontal demand (or marginal revenue) lines based on 5 possible
market prices, ranging from $24 to $100. Each of these lines crosses the marginal cost
curve at a different point. When P = $100 the MR line crosses the MC curve at point a
and using the MR = MC rule we can read off the horizontal axis that the resulting profitmaximizing output is almost 8 units (7.9 units to be precise). When P = $71 the MR line
crosses the MC curve at point b and again we can read off the horizontal axis that the
resulting profit-maximizing output is 7 units. We can do this several more times with the
31
results shown in the table below. In other words, we have a curve, called the “marginal
cost curve” that traces out for us the quantities that the Brockton Corp. is willing and
able to supply at different possible market prices, i.e., what we have called the
“quantities supplied.”
a
b
c
d
e
Price
$100
71
44
34
24
Qs
7.9
7.0
5.6
5.0
4.0
QUESTION 8.23:
Starting in Chapter 2 what did we call a curve or line that tells us
what a firm’s “quantity supplied” is at different possible market
prices?
ANSWER 8.23:
We called it a supply curve.
NOTE 8.12:
It is not entirely correct to say that the firm’s marginal cost curve is
its (short-run) supply curve since, as we saw earlier in our
discussion of the shutdown point, if the market price is below
average variable cost the firm cuts it output to zero. (It “shuts
down.”) A more correct statement is made in the following
definition:
DEF 8.7:
The portion of a purely competitive firm’s marginal cost
curve which lies above the average variable cost curve
constitutes the firm’s (short-run) supply curve.
To get from an individual firm’s supply curve to the market supply curve consider the
two panels of FIG 8.9 below.
NOTE 8.13:
In the two panels the vertical axes have the same scale but the
horizontal axes have different scales. So in Panel B on the horizontal
axis one inch might represent one unit but in Panel A it might
represent 100 or 1,000 units.
Panel A shows Brockton’s marginal cost curve as wells as their average variable cost
curve. The part of the MC curve which lies above the AVC curve (above point m) depicts
their supply curve. Assume Brockton is a typical firm in its industry and there are many
more like it, with similarly-shaped MC curves. We add these curves “horizontally” and
we end up (in Panel B) with the sum of all the MC curves (labeled S = ΣMC), which
32
constitutes the industry (or market) supply curve. Insert a (market) demand curve
which is obtained by adding up all the individual demand curves of potential buyers in
this market and we have (in Panel B) the standard market supply-and-demand diagram
which we introduced in Chapter 2.
In FIG 8.9(B) the equilibrium price is $100. This price is then “transmitted” to all the
individual firms making up this (purely competitive) industry and, since they are price
takers, this is the price they will receive (and accept) for their product. So Brockton’s
demand curve is drawn at a price of $100 but at this price they can sell any output they
decide to produce (and we know, based on the MR = MC rule that at the $100 price they
will produce and sell a little less than 8 units.)
FIG 8.9 (A)
MC = S
P = MR
AVC
m
Pure Competition in the Long Run
To discuss pure competition from a long run point of view we need new definitions of
the short run and the long run from an industry perspective as opposed to an individual
firm perspective.
DEF 8.8:
The short run is defined as a period so short
that there is not enough time for new firms to
enter an industry (or for old firms to exit).
33
FIG 8.9(B)
S = ΣMC
D
DEF 8.9:
The long run is defined as a period long enough
so that there is enough time for new firms to
enter an industry (or for old firms to exit).
To enter (or leave) an industry is time-consuming. To enter the garment industry may
take months. To enter the electric power industry may take years. But in either case
entry (or exit) are not instantaneous. So just like in DEF 5.1 (Chapter 5) “short run “ and
“long run” are not calendar concepts but differ across industries depending on a variety
of factors such as the industry’s technology, market size, availability of financing, etc.
Consider FIG 8.10(A). It is a standard market supply-and-demand diagram. FIG 8.10(B)
represents a unit cost and price diagram depicting, once again, the situation of the
Brockton Corp, a “typical” firm in this (purely competitive) industry. The average cost
curve is labeled AC because for this long-run analysis there is no need to differentiate
between fixed and variable costs.
Assume initially that demand is given by D and supply by S1.Then the equilibrium price is
$75. This price is “transmitted” to each firm in the industry. Brockton’s demand-(MR)
line lies above its AC line and we conclude that Brockton is earning a “pure” or economic
profit.
34
FIG 8.10 (A)
S1
S2
S3
Demand (D)
FIG 8.10 (B)
MC
AC
QUESTION 8.24:
One of the important characteristics of pure competition is that
there are no barriers to entry. What do you predict will happen in
an industry in which there are no entry barriers and in which the
35
“typical” firm is earning above-normal profits, that is profits higher
than they could earn in other industries with similar
characteristics?
ANSWER 8.24:
Obviously the above-normal profits will attract new firms into the
industry. Since “number of producers or sellers” is one of the
determinants of supply, supply will increase and the supply curve
will shift to the right.
QUESTION 8.25:
How long will “entry” continue?
ANSWER 8.25:
In principle, as long as there are above-normal profits. (In reality
people make mistakes and entry may continue beyond that point.)
But sooner or later entry will stop and the above-normal profits will
disappear. (We say that they have been “competed away.”) In FIG
8.10 this happens when the supply curve is S2. Then the equilibrium
price is approximately $63 (see the arrow in FIG 8.10(B)) and for
Brockton and the other firms the horizontal price line is just
tangent to their AC curves. The firms in the industry are “breaking
even” but we know that this means that they are earning a normal
profit.
QUESTION 8.26:
We arbitrarily assumed that the initial equilibrium price in the
industry is such that the typical firm is earning an above-normal
profit. But we could just as easily have started with the
assumption that the typical firm is earning a below-normal profit
(that is, suffering an economic loss). This is shown in FIG 8.10(A)
by D and S3. What do you predict would happen then?
ANSWER 8.26:
The answer to this question is left as an exercise for the reader.
We have arrived at an important point in our discussion which requires us to define a
new equilibrium concept called long-run equilibrium.
DEF 8.10:
An industry is in long-run equilibrium if there is no
tendency for firms either to enter or to leave the
industry.
36
NOTE 8.14:
What our previous discussion has revealed is that firms
in a purely competitive industry in long-run equilibrium
earn just a normal profit (or saying the same thing, zero
economic profit).
Since the typical firm in the industry is breaking even, (i.e., just earning a normal profit)
we know that for such a firm P = AC. But more specifically the price line is tangent to the
AC curve so we can write P = min AC, that is P = AC at the lowest point of the AC curve.
We also know that firms maximize profits when they follow the MR = MC rule and for a
firm in a purely competitive industry MR = P. We can therefore define what is called the
long-run equilibrium condition for a purely competitive industry as follows:
DEF 8.11:
A purely competitive industry is in long-run equilibrium when:
P = MC = min AC
This is significant because we will show below that when an industry satisfies the
condition contained in DEF 8.11 it is “efficient” and in a world of scarcity (REM: Chapter
1) efficiency is a desirable goal to achieve.
Pure Competition and Efficiency
There is an important sense in which pure competition is “efficient” from society’s point
of view and therefore serves as a kind of “benchmark” that is used to evaluate other
industry types. (REM: Section 8.0)
The following is a rather abstract definition of efficiency as used in economics:
DEF 8.12:
A situation is efficient if there is no
possible way it can be improved.
From this perspective there are two types of efficiency: technical and economic or
allocative efficiency.
37
Technical Efficiency
DEF 8.13:
Technical
efficiency
(sometimes
called
production efficiency) exists in any productive
activity if: (a) more of one good (good X) cannot
be produced without producing less of another
(good Y), or (b) the same quantity of a good
(good X) cannot be produced by using less of
one input (input A) and no more of any other
(inputs B, C, D,…).
REM 8.6:
In Chapter 1 we discussed the production-possibilities set and its
boundary, the production-possibilities frontier (or PPF). Any
output bundle in the production-possibilities set but off the PPF
represents technical inefficiency because given available resources
and technical knowledge more of one good can be produced
without producing less of another.
EXAMPLE 8.7:
The Terra Co. lays pipe for municipal water and sewage systems.
For several years they have employed standard seven-member
crews on most of their jobs. Recently they hired a consultant who
informed them that current “best-practice” in the industry
requires only five-member crews. They responded by reducing the
size of their crews accordingly. Before they made the change,
Terra was operating in a technically inefficient manner.
COMMENT 8.3:
What DEF 8.13 comes down to is that a productive activity is
technically efficient if its output is produced at the lowest possible
cost given current technology and resource prices.
Firms in purely competitive industries in long-run equilibrium are compelled to be
technically efficient. Why?
Consider FIG 8.11 below. It shows the Average Cost curve of a typical firm in a purely
competitive industry. We assume that the typical firm engages in “best-practice”
production, that is, it is technically efficient. Its AC curve therefore shows the lowest
possible unit cost of producing any given level of output. For example, the vertical
broken line from “8” on the horizontal axis to point a on the AC curve shows the lowest
possible cost of producing 8 units, given current technology and input prices.
38
FIG 8.11
AC’
AC
a
REM 8.7:
In our discussion of production functions (Chapter 5) and the cost
curves derived from them (this chapter) we implicitly assumed that
there is technical efficiency in production.
Now assume that there are some firms in the industry that are badly managed. Top
managers are lazy and hire their nephews to be in charge of production and marketing.
This shows up in Figure 8.11 as an AC curve which lies above the technically-efficient AC
curve of the typical firm. It is shown by the broken line marked AC’. In other words, the
badly-managed firm has higher unit costs of production than the typical (well-managed)
firm.
Assume the industry is not in long-run equilibrium (The market price is $45; note the
arrow pointing to “45” along the vertical axis.)
QUESTION 8.27:
Can the badly-managed firms survive under these circumstances?
ANSWER 8.27:
Yes. As long as the market price in some interval lies above the
firm’s AC curve (which presumably includes a normal profit!) the
firm is able to survive.
39
QUESTION 8.28:
Can the badly-managed firms survive if the industry is in long-run
equilibrium?
ANSWER 8.28:
In a purely competitive industry in long-run equilibrium P = min AC.
“Market forces” drive the price down to the point where the typical
firm just “breaks even,” i.e., they earn a normal profit. (This
happens in FIG 8.11 when P = $24; note the arrow pointing to “24”
along the horizontal axis.) The market price is too low for the badly
managed firm to cover all their costs and they are unable to
survive.
CONCLUSION 8.1:
Firms in purely competitive industries in
long-run equilibrium are compelled to be
technically efficient.
Allocative Efficiency
We have said several times in previous chapters, starting in Chapter 1, that we live in a
world of scarcity. Hence a central theme in economics is the desirability of an “efficient”
or “proper” or “optimal” allocation of resources. Scarce productive resources are
allocated efficiently over different goods, activities or actions from a social point of view
if the allocation conforms to the preferences of the individuals making up the society.
We start the discussion with the following abstract definition of allocative efficiency:
DEF 8.14:
NOTE 8.15:
A situation is allocatively efficient if no
individual can be made better off without
making any one else worse off.
An obvious addition to DEF 8.14 is that if a situation exists in which
at least one individual can be made better off without making
anyone worse off the situation is not allocatively efficient.
One of the three major problems confronting every economic system is to decide what
to produce (REM: Chapter 1). We now ask: Is this decision made in a way which is
allocatively efficient or not?
EXAMPLE 8.8:
Coruna is an island nation in the Mediterranean. Its people prefer
black shoes but its economy is run in such a way that warehouses
are full of brown shoes that no one wants. Coruna’s economy is not
allocatively efficient. A reallocation of productive resources from
40
brown shoes to black shoes would increase the well-being of the
people of Coruna.
FIG 8.12
$/Q
S = MC
28
a
22
c
e
16
10
b
d
D = MB
0
80
160
240
Quantity (Q)
How can we determine if the particular output bundle chosen by an economy is
allocatively efficient? Consider Figure 8.12 above. It is a standard supply-and-demand
diagram depicting the market for good X. But the demand curve has the additional label
“MB” for marginal benefit and the supply curve has the additional label “MC” for
marginal cost. In this (purely competitive) market the equilibrium price is $16 and the
equilibrium quantity is 160 units.
We now make the following claims: (a) If the equilibrium price and quantity
prevail, this represents a situation of allocative efficiency and (b) purely
competitive industries achieve allocative efficiency “automatically.” We sum
up this claim in a “rule.”
RULE 8.1:
NOTE 8.16:
Allocative efficiency exists in an industry if: P = MC
We do not call this a “decision rule” since in many cases there is no
“decision maker” who can see to it that “P = MC.”
41
NOTE 8.17:
There are situations, which we will discuss in later chapters,
especially in Chapter 12, where a decision-maker (for example a
regulatory agency) is able to influence the price of a good or service
in such a way that the end result may be P= MC. If such a pricing
rule is followed it is called marginal-cost pricing.
Why is an industry allocatively efficient if P = MC?
REM 8.8:
In Chapter 2 we pointed out that a demand curve can also be
thought of as a “marginal benefit” or “willingness-to-pay” curve.
Why? In FIG 8.12 we can read off the demand curve that at a price
of a bit less than $28 (say $27.97) there is one individual who would
buy one unit of this good. Why is this individual willing to pay this
price? Presumably because that is what good X is “worth” to him: it
is the “marginal benefit” he receives (or expects to receive) from
one unit of the good. Assume for simplicity that each individual in
this market buys just one unit. Then there is a second individual
who is willing to pay a bit less than the first (say $27.94) for one
unit. We ask the same question again and come up with the same
answer: The second individual is willing to pay the $27.94 price
because that is what good X is worth to her. The price she is willing
to pay represents her evaluation of the (marginal) benefit she
receives (or expects to receive) from this good. We proceed in the
same way until we reach the 160th individual: Given the $16
equilibrium price she is just on the boundary between buying and
not buying. Assume that she buys. Then we can say that the
marginal benefit of good X for the 160 individuals who buy the
good at the $16 equilibrium price is at least $16. And since for any
quantity shown on the horizontal axis we can read off the curve
what the marginal benefit obtained by the “last” buyer is, we can
also think of the demand curve as representing a “marginal
benefit” curve.
REM 8.9
In this chapter we discovered that the market supply curve is
constructed by adding up the marginal cost curves of the individual
firms making up the industry. So if we pick an arbitrary quantity on
the horizontal axis in FIG 8.12 we can read off the supply curve
what the corresponding marginal cost is. For example, the MC of
the 240th unit of good X is $22. (Can you see why?) But “cost” in
economics means opportunity cost. So when we say that the MC of
the 240th unit is $22 we mean that the highest-valued alternative
good that could be produced with the same bundle of resources is
worth $22 to someone in this society.
42
So according to the claim we are making, the market depicted in FIG 8.12 is allocatively
efficient if the price charged is $16 and the quantity bought and sold is 160 units. But
why?
Assume that the market for good X is interfered with in some way: A government
agency insists that a price higher (or lower) than $16 be charged; a monopoly takes over
the industry, or whatever.
QUESTION 8.29:
Say the price ends up at P = $22 and people buy 80 units of god X.
Why does this represent a situation of allocative inefficiency, or
expressed differently, a misallocation of resources?
ANSWER 8.29:
Again, think in marginal terms. Would “society” be better off if 81
units of good X were produced instead of 80? The answer is yes,
since the value of the 81st unit (the marginal benefit, or MB) to
someone in this society is a bit less than $22 whereas the value of
the alternative good that could be produced with the same bundle
of resources (the marginal cost, or MC) is a bit more than $10. So
switching resources from elsewhere in the economy to producing
an additional unit of good X would create a net benefit of a bit less
than $12. Would society be better off if 82 units of good X were
produced instead of 81? The answer is again yes. We continue
along this line until we reach an output of 160 units. We now ask
again: Would society be better off if 161 units were produced
instead of 160? The answer is no since the MB of the 161st unit is a
bit less than $16 while the MC is a bit more than $16, so there is a
small net loss from producing the 161st unit. So as long as MB > MC
there is a net gain to society if production is increased and as long
as MB < MC there is a net gain to society if production is reduced.
We conclude that when MB = MC the “optimal” quantity is
produced (from society’s point of view). It represents a situation of
allocative efficiency. But MB is identical to price and so we end up
with the P = MC rule.
QUESTION 8.30:
What is the cost to society of underproducing good X, for example
by producing 80 units instead of 160 units?
ANSWER 8.30:
The cost is shown by the area of the triangle bae
shown in red.
A bit of elementary geometry reveals that this amounts to $480.
QUESTION 8.31:
What is the cost to society of overproducing good X, for example by
producing 240 units instead of 160 units?
ANSWER 8.31:
The answer to this question is left as an exercise for the reader.
43
QUESTION 8.32:
How does the P= MC rule relate to DEF 8.14 and its addition (If a
situation exists in which at least one individual can be made better
off without making anyone worse off the situation is not
allocatively efficient)?
ANSWER 8.32:
Consider FIG 8.12 again. Assume that 80 units of good X are being
produced. The fact that MB > MC constitutes a signal: There are
some people in this society who would prefer that more of good X
be produced rather than its highest-valued alternative, good Y.
They go to those who are currently consuming good Y and they
make an offer: Allow us to reallocate some of the resources from
their current activity (producing good Y) to producing a little more
(say one unit more) of good X. We will pay you $16 for those
resources. (The amount has to lie somewhere between $16 and
$22. Can you see why?) An agreement is reached and the transfer
of resources takes place. Both sides benefit and no one is hurt.
Why? Because the people who prefer good X were willing to pay a
little bit less than$22 for an additional unit, yet they got it for $16.
The people who prefer good Y value the unit they “gave up” at a bit
over $10, yet they got $16. (They would rather have $16 than a unit
of good Y.) Both parties benefited from the bargain and no one was
hurt, so the initial situation could not have been allocatively
efficient.
NOTE 8.18:
It is important to understand that we are not making the claim that
a purely competitive industry is always and everywhere allocatively
efficient. There are numerous instances, called market failures,
which we will discuss in several places, especially in Chapter X in
which a purely competitive industry simply fails to “register” all the
costs and/ or benefits associated with a productive activity and
therefore may underproduce (or overproduce) a good or service
when viewed from a social point of view, even though the P = MC
condition is satisfied.
NOTE 8.19:
Because of our conclusion that a purely competitive industry in
long-run equilibrium is both technically and allocatively efficient we
shall use it as a “benchmark” to evaluate other industry types in
subsequent chapters.
44
PROBLEMS:
Q TFC TVC TC AFC AVC ATC MC
0
------- --1
17
2
34
3
14
4
9
10
5
100
6
85
7
151
8
20
9
56
(1)
Consider the table above. It describes the cost structure of the
Jericho Co., a single-product firm in a purely competitive industry.
(Assume that only “whole” units can be produced; i.e., 3 units but
not 3.4 units.)
(a)
(b)
(c)
(d)
(e)
(2)
Fill in all the blank cells.
If the market price is $37, what is Jericho’s profitmaximizing output (Q*) in the long run? The short-run?
Calculate Jericho’s profit at Q*, Q* − 1 and Q* + 1. Do the
results of these calculations support the MR (=P) = MC rule?
Explain.
If the market price drops to $17, what is Jericho’s profitmaximizing output in the long run? The short-run? Explain.
If the market price drops to $11, what is Jericho’s profitmaximizing output in the long run? The short-run? Explain.
Consider the diagram below. It represents the cost situation of the
Ramsey Co., a small metal-grinding firm located in Pittsburgh.
Ramsey’s management view all their costs as variable, hence no
distinction is made between average variable and average total
cost. Assume the industry is purely competitive.
(a)
If the market price is $30, what is Ramsey’s profitmaximizing output (Q*)?
45
40
MC
30
$/Q
AC
20
10
0
0
40
80
120
160
200
240
280
Quantity (Q)
(b)
(c)
(d)
(e)
(3)
At Q* what is Ramsey’s total revenue (TR), total cost (TC),
and total profit (Π)?
If the market price is $20, what is Ramsey’s profitmaximizing output (Q**)? At Q** what is TR, TC and Π?
Construct a table showing Ramsey profit-maximizing output
at market prices ranging from 0 to $40 at $5 intervals (i.e.,
$5, $10,…).
Explain why the resulting table represents Ramsey’s supply
schedule.
Mollyplast, Inc. is a medium-size manufacturer of plastic cups and
similar commodities produced by injection molding. Their “normal”
output is 275,000 gross per month. They have a relatively steady
customer base on the East coast but in recent months their market
has “softened” and they are experiencing excess capacity: their
output has shrunk to 200,000 gross per month. The usual price for
the cups is $5.45 per gross. They have recently received an order
from a supermarket chain located in the Midwest for 70,000 gross
of this product but the offered price is $4.65. Jim Dine, Mollyplast’s
CEO, must decide whether to accept or reject the order. The table
below shows the accounting department’s estimate of the firm’s
costs, calculated at a normal output level, i.e., at Q = 275,000.
[Assume average variable costs and their components are constant
throughout.]
46
Total
Per Unit
Materials
$290,000
$1.05
Direct Labor
715,000
2.60
Administrative and sales
88,000
0.32
Utilities
17,000
0.06
Other variable costs
151,000
0.55
Other fixed costs
34,000
0.12
Total
$1,295,000
$4.71
Should the order be accepted or rejected? Explain, using incremental
analysis.
(4)
The diagram below represents a drastically simplified picture of the
cost situation facing the Bryce Co., a firm in a purely competitive
industry. (Only its MC curve is shown.) The market price is $15.
According to the MR (=P) = MC rule for pure competitors, to
maximize profits they should produce 1,000 units. Explain the
reasoning behind the rule.
Hint: Assume that Bryce initially is not following the rule, that is,
they are producing more, (say 50% more), or less, (say half as
much) as the rule requires. Explain how their profits would
change if they were to reduce (or increase) their production
level by one (hundred) units, then by another hundred units
and and so on.
30
25
MC
$/Q
20
15
10
5
0
0
200
400
600
800
1000
Quantity (Q)
47
1200
1400
1600
1800
2000
(5)
Horn of Plenty is a large buffet-style restaurant located on the New
Jersey shore, a popular summer resort area on the East coast. They
offer dinners at a single price of $29. Their dining room and kitchen
can accommodate 10,000 diners a week and during the summer
months they usually serve that number. In the fall they suffer a
sharp drop in patronage serving only about 2,000 customers a
week. The restaurant’s practice has been to maintain the $29 price
during the slow fall season. John Dean, the Assistant Manger, has
approached the owners with a proposal to lower the price in the
fall to $19.95. He estimates that this would increase patronage to
9,000 per week.
The restaurant’s accountant has prepared the following cost
estimates, based on the assumption that 10,000 meals per week
are being served
Total Per meal
Food
$44,500
$4.45
Labor
67,500
6.75
Management and supervision 19,500
1.95
Other variable costs
41,500
4.15
Other fixed costs
28,500
2.85
Total
201,500
20.15
Make the following additional assumptions:



Dean’s estimates are reliable.
Managers are kept on the payroll throughout the year.
Average variable cost and its component are constant
throughout.
Should the price be lowered in the fall or not? Explain, using
incremental analysis.
48
(6)
Consider the graph below. It shows the cost situation facing the
Rutherford Co., a purely competitive producer of widgets. (Assume
that Rutherford is a “typical” firm in the widget industry.) For the
purpose of this question there is no need to differentiate between
average total and average variable costs so we just use the label
“AC.” The current market price of widgets is $145.
(a)
(b)
(c)
(d)
(e)
What is Rutherford’s profit-maximizing output?
Is the Rutherford Co. earning a “pure” (or “economic” or
“above-normal”) profit or just a normal profit? Explain.
Is the widget industry in long-run equilibrium? Explain.
If not, what is the industry’s long-run equilibrium price?
What would be Rutherford’s output at that price? Explain.
Describe the process by which the widget industry would
move toward long-run equilibrium if it is not there already.
160
155
MC
$/Q
150
145
AC
140
135
0
2
4
6
8
Quantity (Q)
49
10
12
14
16