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TABLE OF CONTENTS TO COST
1. COSTS .................................................................................................................................................................4
. OPPORTUNITY COST AND OTHER COST VALUATION TECHNIQUES ..........................................................................4
opportunity cost ......................................................................................................................................................... 4
historical cost .............................................................................................................................................................. 4
reproduction cost ....................................................................................................................................................... 4
replacement cost ......................................................................................................................................................... 4
. EXPLICIT AND IMPLICIT COSTS ................................................................................................................................4
Explicit costs............................................................................................................................................................... 4
implicit costs ............................................................................................................................................................... 4
economic profit (see Economist's tool box below). .................................................................................................... 5
. SUNK COSTS ...........................................................................................................................................................5
sunk costs .................................................................................................................................................................... 5
: TECHNOLOGIES FOR LONG DISTANCE TELEPHONE SERVICE ........................................................................ 5
cost............................................................................................................................................................................... 6
ECONOMIST'S TOOL BOX: DEFINING ECONOMIC PROFIT .......................................................................6
measure called accounting profit ................................................................................................................................. 7
2. SHORT RUN DECISIONS ....................................................................................................................................7
COST FUNCTIONS .......................................................................................................................................................7
factors .......................................................................................................................................................................... 7
Variable cost (VC) ...................................................................................................................................................... 8
average total cost (ATC) ............................................................................................................................................ 8
COST SCHEDULES AND COST CURVES........................................................................................................................8
Marginal cost.............................................................................................................................................................. 8
MARGINALISM AND THE SUPPLY CURVE ....................................................................................................................9
PROFIT MAXIMIZING CONDITION: MR = MC ........................................................................................................ 9
PRICE= MC...................................................................................................................................................................... 9
cost curve ..................................................................................................................................................................... 9
supply determinants ................................................................................................................................................... 9
shut down price ........................................................................................................................................................ 10
=================================================================E
EXAMPLE #1: SHORT RUN AVERAGE COST WITH SATELLITE TECHNOLOGY ......................................10
Table 8-1 Short-Run Profit Maximizing Output Using Satellite Technology ................................................................. 11
Figure 8-1. ...................................................................................................................................................................... 11
#2: SHORT RUN AVERAGE COSTS WITH FIBER OPTIC TECHNOLOGY ..................................................12
3. LONG RUN DECISIONS ....................................................................................................................................13
production decision .................................................................................................................................................. 13
the long run .............................................................................................................................................................. 13
investment decision .................................................................................................................................................. 13
revenue (_TR) ............................................................................................................................................................ 13
cost (_TC) .................................................................................................................................................................. 14
. LONG RUN COST SCHEDULE .................................................................................................................................14
B. LONG RUN MARGINAL COST ..............................................................................................................................14
. LONG RUN AVERAGE COST ...................................................................................................................................15
entry .......................................................................................................................................................................... 15
Figure 8-2 ....................................................................................................................................................................... 16
U.S. SPRINT'S CHOICE OF TECHNOLOGY ............................................................................................... 16
8-2 Average Costs for Competing Technologies ........................................................................................................... 17
4. ECONOMIES AND DISECONOMIES OF SCALE .........................................................................................18
8-3. Economies of Scale................................................................................................................................................. 18
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cost elasticity of output, C ....................................................................................................................................... 18
. ECONOMIES OF SCALE ...........................................................................................................................................19
natural monopoly ..................................................................................................................................................... 19
. DISECONOMIES OF SCALE ......................................................................................................................................20
. EXIT, ENTRY, AND EFFICIENCY .............................................................................................................................20
. Minimum Efficient Scale .................................................................................................................................20
minimum efficient scale (MES)................................................................................................................................ 21
8-4 Market Share of Median-Size Plant .......................................................................................................................... 21
. The Survivor Technique ..................................................................................................................................21
survivor technique.................................................................................................................................................... 21
5. ECONOMIES OF SCOPE...................................................................................................................................22
Economies of scope................................................................................................................................................... 22
EXAMPLE: ECONOMIES OF SCOPE AND BREAKING UP AT&T. ....................................................22
6. TECHNOLOGICAL CHANGE AND INVENTION .........................................................................................25
Innovation ................................................................................................................................................................. 25
: INVENTION IN TELECOMMUNICATIONS ..................................................................................................27
8-5. First Demonstration of Transmission Technology ................................................................................................... 27
7. INNOVATION AND THE LEARNING CURVE............................................................................................... 28
learning curve........................................................................................................................................................... 28
experience curve ....................................................................................................................................................... 29
: LOWER AVERAGE COST OF LAYING FIBER OPTIC CABLE ...................................................................29
Table 7-2 Learning Curve Effect..................................................................................................................................... 30
8. DIFFUSION AND THE LOGISTIC CURVE .....................................................................................................31
: ADOPTION OF FIBER OPTIC CABLE. .........................................................................................................34
Figure 8-6........................................................................................................................................................................ 35
9. SUMMARY ............................................................................................................................................................35
DEFINITIONS ...........................................................................................................................................................36
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CHAPTER 8 COST THEORY
On January 1, 1984, American households and firms were allowed to do something they'd
never done before--to choose a firm to provide long distance telephone service. For generations
this service had been provided solely by AT&T, which had been the world's largest corporation.
But a "consent decree" with the Justice Department ended AT&T's monopoly over long distance
telephone service.
On January 31, 2005, American households woke up to the news that AT&T was to be
bought by SBC communications. SBC was one of the “baby bells” that had been spun off by
AT&T in 1984. In an attempt to avoid regulation, to milk the profits of long distance service,
and to position itself to enter the computer industry, AT&T eliminated its ownership of its local
telephone monopolies. Unfortunately it continued to act like a monopoly which would cripple its
ability to survive in competitive markets; it would not be aggressive enough in using its own
inventions and it squandered its cash by buying into markets that it would then have to leave.
During the next 21 years it would downsize as it failed to survive in the computer market and as
the long distance market dwindled.
In discussing how AT&T lost its monopoly, how new firms entered the
telecommunications market, how the major long distance producers lost their profitability (and
MCI went bankrupt) this chapter shows how costs are important in both long run and short run
managerial decisions and how technological change influences the market in which those
decisions are made.
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SECTION 1. COSTS
Should a firm expand? Should it cut back? Regardless of the choice, the decision
involves an increment of business- units of output, an aggregation of units of output, a division of
a firm, a subsidiary, a location, or the firm itself. For that increment, revenues should exceed
costs if the decision is to be profitable. An evaluation of the economic costs of an increment of
business should be based on the opportunity costs of the resources which are used, should
include implicit as well as explicit cost, and should ignore costs which remain unchanged with or
without the increment of business.
A. Opportunity Cost and Other Cost Valuation Techniques.
The opportunity cost of a resource is its value in its best alternative use. While
opportunity cost is the best way for a decision maker to value resources, some firms hold goods
in inventory, or on their balance sheet, according to historical cost which reflects the price(s) at
which the resources were originally purchased. Other firms may value resources on the basis of
how much it would cost to buy the identical resources at current market prices, but if such
resources are out-of-date and difficult to find, this reproduction cost would overstate resource
value. Firms like utilities often try to find the replacement cost of the resource--the least cost to
buy the resource or a close, up-to-date substitute on the market. If markets are competitive and
work efficiently, the current market price of the resource should be both the resource's
opportunity cost and replacement value.
B. Explicit and Implicit Costs.
The commonly used accounting definition of profit ignores many opportunity costs. A
firm must cover two kinds of costs; those which are explicit and those which are implicit.
Explicit costs are those for which arms-length payments are actually made to owners of
resources. Explicit costs include but are not limited to:
(a)
Interest payments on borrowed money,
(b)
Depreciation which represents wearing out of plant and equipment,
(c)
Maintenance and operating costs associated with the use of capital,
(d)
Raw material which must be purchased from vendors in the market place, and
(e)
Labor which must be paid wages or salaries.
While these costs must be included on a firm's income statement, there are implicit costs for
which payments are not actually made. Implicit costs are associated with the use of resources but
for which no compensation is provided. Some examples include:
(a)
Use of funds. For purchasers of a firm's stock, the highest rate of interest which could
have been earned elsewhere is the implicit (opportunity) cost of buying the stock.
(b)
Use of owner's time. While the owner of a firm may receive a salary, the payment may
not reflect the owner's true opportunity cost. For example, Bill McGowan, the executive
who made MCI a big player in the long distance market turned down many other lucrative
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(c)
opportunities to go with MCI. His opportunity cost was equal to the amount he could
have earned in his best alternative opportunity.
Use of owner's real resources. Sometimes the owner of a firm brings real resources to the
firm in the form of buildings, land, or equipment, and the firm does not pay for them.
Since there are opportunities to rent or lease these inputs, the owners incur an opportunity
cost equal to their highest return from alternative employment of these resources.
Implicit costs are also incurred from lost future opportunities of using resources. The value of
land, for example, may be diminished by one use (say strip-mining) and may be less valuable in
future uses. Even the goodwill of a firm may be damaged by the decision to take on an
additional increment of business. For example, Maytag's high quality image suffered when that
company took on a low-end appliance line. However, none of these implicit costs appear in an
income statement. The distinction between implicit and explicit cost has an important impact in
defining a firm's objective. Economists subtract both implicit and explicit costs from total
revenue to calculate economic profit (see Economist's tool box below).
C. Sunk Costs
A firm should not base a decision on any costs that remain unchanged, regardless of the
choices that are made. For example, once a firm has paid for inputs, the costs of those inputs are
considered sunk costs. Any cost which remains unchanged, regardless of the outcome of a
decision, should not be considered in the decision. This truism greatly simplifies the problem of
determining what costs to consider in managerial choices.
====================================================================
EXAMPLE: TECHNOLOGIES FOR LONG DISTANCE TELEPHONE SERVICE
New technologies for transmitting voice signals threatened the long distance monopoly of
American Telephone and Telegraph (AT&T). Each technology forced a "go, no go" decision on
AT&T. The technology of fiber optics was just such a decision.
Fiber optic cable sends light signals through a fiber optic cable which has proved less
expensive than the copper cable used in AT&T's old network. However, AT&T's copper cable
was already in place and paid for. In 1989 Business Week reported about AT&T's initial
reluctance to switch to fiber optics:
Last year, it [AT&T] wrote down $6.7 billion in aging equipment. And it is spending $6
billion to modernize its network over the next two years. Without Sprint [a major
competitor] on its heels, AT&T might have stretched out those expenditures.1
For the sake of simplicity, let's say that the $6.7 billion was the original cost of AT&T's copper
cable network and the $6.0 billion was the cost of installing the new fiber optic cable network.
Should AT&T have made the incremental choice to go to a fiber optic network earlier? Let's
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look at the costs:
(1)
Sunk costs of $6.7 billion. AT&T's decision to go, or not to go, with fiber optics would
not change this historical cost.
(2)
Opportunity cost of copper cable. When fiber optic cable first became viable, no one
would want to buy, dig up or maintain the old obsolescent copper cable network. Since
the market value sank toward nothing, AT&T had to write it off. AT&T's decision to go,
or not to go, with fiber optics would not change this either.
(3)
Opportunity loss of using old technology. If it had continued to use the copper cable,
AT&T would still have had to reproduce more of the cable as it replaced worn segments
of its network.
The reproduction cost of this cable at current market prices would have been
much higher than the historical market value of $6.7 billion.
The explicit replacement cost of simply installing an entirely new fiber optic
system was only $6.0 billion.
The difference in reproduction and replacement value was at least $.7 billion
($6.7-$6.0) and probably much more.
The $0.7 billion-plus opportunity loss would be a very real cost of staying with the copper
network and would therefore have to be considered in AT&T's incremental decision.
Opportunity cost of $600 million per year. If $6.0 billion could have earned a 10% rate of
return in some other venture with similar risk, it would have had an opportunity cost cost
of $600 million per year, representing:
an implicit cost cost if the money were raised by selling stock in the company;
stockholders would not have received an explicit payment for owning shares in
the firm.
an explicit cost if $6 billion were borrowed at an interest rate of 10%; an explicit
interest payment would be required by lenders.
Either way, the $600 million per year would have to be considered as an economic cost of
going with fiber optics and should be considered in AT&T's decision.
(4)
For determining if AT&T should go to fiber optics, some information (sunk costs) is irrelevant
and some (incremental revenues and opportunity costs) is not provided by Business Week. But
Business Week does tell us implicitly that incremental revenues exceeded the incremental costs
of going to fiber optics; AT&T made the decision to go to fiber, and they had been pushed into
this incremental decision by their competitors.
===============================================================
ECONOMIST'S TOOL BOX: DEFINING ECONOMIC PROFIT
A firm's goal is generally assumed to be profit maximization. Profits are found by
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subtracting costs from revenues (sales). However, accountants generally subtract only explicit
costs from total revenue to obtain a measure called accounting profitmeasure called accounting
profit. The fact that a firm has a positive accounting profit does not mean it can survive; there
may be substantial implicit costs for which an accounting has not been made. Here's a way to
remember the difference between accounting profit and economic profit using EXCEL.
Total Revenue
minus Explicit Cost
Accounting Profit
minus Implicit cost
Economic profit
Revenue,Costs
$
100.00
$
60.00
Difference
$ 40.00
$
50.00
-$10.00
Here a total revenue of $100 and an explicit cost of $60 means accounting profit is $40. But
after taking out $50 of implicit costs economic profit is only -$10. In other words there is a
positive accounting profit and an economic loss. Since implicit costs can never be less than zero,
accounting profit will always be at least equal to economic profit.
When economic profit is zero the accounting profits are considered normal profit. All
economic costs are covered, the resources have earned a return equal to that which they could
have earned in their best alternative employment, and the firm can survive. Losses on an
economic basis should lead to the firm's demise.
===========================================================
SECTION 2. SHORT RUN DECISIONS
Stockholders want managers to maximize profits. In short run decisions, a manager
decides how much output to produce in order to maximize the difference between revenues and
costs. As in the case of revenues, there are three ways to express the relationship between cost
and output; (a) as a cost function, which shows the algebraic relationship between cost and
output, (b) in a cost schedule which can be calculated from the cost function for different levels
of output, and (c) as a cost curve which is a graph of the relationship between cost (Y-axis) and
output per unit of time (X-axis).
A. Cost Functions.
In short run decision making, a manager must determine which
factors can be changed, and those which cannot. Fixed factors are those which do not vary with
output while variable factors do change with output. A list of typical fixed factors would
include, but not be limited to, plant, equipment, insurance, and utilities. To change output a firm
can usually vary overtime hours, the amount of materials, and other easily changed inputs.
However, recently in Japan, where workers have generally not been laid off when business
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declines, workers become the equivalent of fixed factors.2 Factors are fixed or variable
according to the nature of the specific decision, and the institutional setting in which those
decisions are made.
With sufficient information about which factors are variable and which are fixed, a cost
function can be defined. Fixed cost (FC) is that part of total cost that remains the same
regardless of the rate at which output is produced, and is incurred even when output is zero.
Variable cost (VC) changes as output changes. The following total cost (TC) function can be
defined for the short run:
(8-1) TC = FC
+
VC
If each side of this equation is divided by quantity (Q), the resulting equation defines average
total cost (ATC) as the sum of average fixed cost (AFC), and average variable cost (AVC):
(8-2) ATC = AFC
+ AVC
Since fixed costs remain constant, average fixed cost falls as output rises; this always happens.
While total variable cost rises with output, average variable cost may fall, rise, or remain
constant. When average variable cost is constant at all levels of output (Q), then a linear total
cost equation can be defined:
(8-3) TC = FC
+
(AVC)*(Q)
In your accounting class breakeven analysis is illustrated using this basic formulation of costs.
B. Cost Schedules and Cost Curves.
Using a cost function, a planner can "cost out" different "scenarios." The data for
different scenarios can be arranged in a cost schedule--often in a spreadsheet--to show the costs
that would be incurred at different rates of output. The cost schedule can be used to calculate
marginal cost. Marginal cost is the change in total cost incurred from producing an additional
unit of output. Suppose a firm's first scenario involves a total cost (TC1) at an output of Q1 and a
second scenario might involve a total cost (TC2) at an output of Q2. Marginal cost can be
estimated by:
TC2-TC1
(8-4) MC = --------Q2-Q1
For example, suppose a business produces 10 items at $100 in total cost, but it doubles its
production to 20 items and experiences total costs of only $175. In Excel the method of
calculating marginal cost might look as follows:
8
Cost
1
2
3
A
Output
10
20
B
Total
Costs
C
Marginal
Costs
100
175
7.5
The marginal cost is found in cell C3 by placing the formula “=(B3-B2)/(A3-A2)”. Notice that
the marginal cost is placed by convention at the higher output level and nothing is placed at the
lower output level.
Several other useful cost-categories--average total cost, average variable cost, average
fixed cost and marginal cost--can be calculated as well. Measuring output along the X-axis, and
dollar cost per unit on the Y-axis allows us to graph all of these on the same set of axes.
C. Marginalism and the Supply Curve
The manager's job is to choose among all possible output scenarios the one scenario that
maximizes profit. Maximization problems should be solved using an incremental approach or
"marginalism". Marginalism requires that each additional unit of output make a positive
contribution to profit. This means that the additional revenue associated with the sale of the unit
must exceed the additional cost of producing it. A firm should continue to expand production as
long as marginal revenue exceeds marginal cost, which means that each additional unit produced
makes a positive contribution to profit. The maximum profit is achieved when marginal revenue
equals marginal cost:
(8-5) GENERAL PROFIT MAXIMIZING CONDITION: MR = MC
As long as a firm has no market power, price is equal to marginal revenue and the profit
maximizing condition becomes:
(8-6) PRICE= MC
This means that the curve relating marginal cost and output (the marginal cost curve) indicates
the output a firm is willing and able to provide at any given price. A supply curve also is defined
as the set of outputs that a firm is willing and able to provide at different prices during a given
period of time, ceteris paribus. The supply curve consists of the same points as a marginal cost
curve, with two exceptions that will be noted below.
Since the marginal cost curve and the supply curve consist of the same points both will
shift in response to changes in the same influences. Anything that shifts the variable cost curve
will also shift the supply curve. These factors are often referred to as supply determinants. The
supply determinants are the prices of resources, technology, the opportunity cost of using
resources for other purposes, taxes, or seller's expectations about the future state of the market.
9
Cost
Because the supply curve shows what happens to the quantity supplied at different prices, prices
are not considered a determinant of supply; they DEFINE the supply curve itself.
However, there are two important conditions under which the marginal cost curve is not
the supply curve:
(a)
(b)
When the firm has market power. A firm facing a downward sloping demand curve (in
other words, it has the market power to control prices) does not maximize profit where
marginal cost is equal to price.
When marginal cost falls below the minimum of average variable cost. If the marginal
cost curve is below the minimum of the short run average variable cost curve it is no
longer the supply curve.
If a firm stops producing, it still has to pay for its fixed factors. All contributions towards these
fixed costs help to reduce the size of its losses. As long as the output can be sold for a price
which is above the minimum of the average variable cost curve, some of the firms' fixed costs are
defrayed by continuing to produce. The shut down price occurs at the minimum average
variable cost. At any price below the minimum average variable cost the firm cannot even pay
for the full variable cost, not to mention being able to defray any fixed cost. A firm would rather
shut down (produce no output) than take greater losses by providing output at a price below
average variable cost.
=================================================================
EXAMPLE #1: SHORT RUN AVERAGE COST WITH SATELLITE TECHNOLOGY
U.S Sprint was one of the new entrants into the long distance telephone market. As
reported by The New York Times the firm experienced rough going initially:
Analysts attributed the losses at U.S. Sprint in part to higher operating costs that
have resulted from an increase in new customers.
Last year, U.S. Sprint had to lease extra telephone lines to accommodate the two
million new customers it added to its network.3
The article suggests that Sprint took on more business than it could handle and that it was
incurring losses as a result. Why didn't Sprint shut down?
Sprint has a short run problem; how to handle its expanding customer base given its fixed
short-run capacity. Suppose that it leases satellite capacity with the hypothetical costs shown in
Table 8-1. A unit of output for the telecommunications market is measured in "voice channels"
which permit two way transmission of a conversation. Marginal cost and profits have been
calculated for different output scenarios assuming that the price for a long distance voice channel
is $120 per month (column 3).
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Cost
Table 8-1 Short-Run Profit Maximizing Output Using Satellite Technology
Voice
channels
0
200
400
600
800
1000
Total
Revenue
($/mo.)
0
24000
48000
72000
96000
120000
Price
(=AR)
($/vo.ch)
120
120
120
120
120
Total
Cost
($/mo.)
30000
50000
70000
90000
130000
250000
Average
Cost
($/Vo.Ch.)
250
175
150
162.5
250
Marginal
Cost
($/Vo.Ch.)
100
100
100
200
600
Variable
Cost
($/mo.)
0
20000
40000
60000
100000
220000
Av.Variable
Cost
($/Vo.Ch.)
100
100
100
125
220
Note: Fixed costs are $30,000 because at zero output, you still can’t get rid of them even if you
produce nothing; your total cost is $30,000. Profit is total revenue minus total cost at each
output. Marginal cost per channel is estimated by dividing the increment to total cost by the
increment in channels, 200. Average total cost and average variable cost are found by dividing
their respective totals by the number of voice channels.
Notice that all of the output scenarios result in losses for Sprint. However, the largest
loss (-$30,000) results from producing nothing; Sprint must still pay for the fixed resources
associated with the satellite equipment, even if it doesn't use it. By offering 600 voice channels
Sprint loses only $18,000. In other words, Sprint defrays $12,000 (=$30,000-$18,000) of its
fixed cost by offering the service.
The average cost curve, graphed in Figure 8-1 from the data in Table 8-1, never reaches
as far down as the price of $120, but the average variable cost curve falls as low as $100, which
marks the shut down price for Sprint. As long as the price is above average variable cost, Sprint
helps to defray the fixed cost of its network by providing service. This explains why Sprint
should still produce in the short run even though it experiences losses.
Figure 8-1.
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Cost
SATELLITE SHORT RUN COST
$/VOICE
CHANNEL
600
500
400
MC
300
ATC
200
100
Shut down price
AVC
0
0
200
400
600
800
1000
VOICE CHANNELS
NOTE: That part of the marginal cost curve which is above the average variable cost curve is the
short run supply curve. Profit is maximized where price equals marginal cost.
====================================================================
EXAMPLE #2: SHORT RUN AVERAGE COSTS WITH FIBER OPTIC TECHNOLOGY
Sprint was willing to incur losses in anticipation of profits that it would receive after its
fiber optic network was completed. Continuing from the quotation in example #1, the New York
Times reported:
The carrier [Sprint] plans to move much of this traffic onto its all fiber-optic
network now under construction.
U.S. Sprint is also sacrificing profits to gain market share, analysts said....4
To see why it might sacrifice profits for market share, let's construct a cost equation for
connecting two cities with fiber optic cable. The examples, used in the rest of the chapter,
preserve the basic cost relationships (verified by the planning curves of engineers), among the
transmission technologies.5 Sprint faces something like the following costs:
(a)
The fixed inputs including fiber optic cable and repeater stations (FC). Fiber optic cable
for transmitting laser light signals is costly to install because it is usually buried
underground. Repeater stations are spaced along the cable to reinforce the light signals.
Suppose the fixed costs (FC) of installing and maintaining the network are $80,000 per
month.
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Cost
(b)
The variable inputs including transmitting and receiving equipment (VC). This
equipment must be located at both ends of a cable and it determines the number of voice
channels which are available for simultaneous transmission of voice conversations.
Suppose each voice channel (Q) costs $10 per month. Then variable costs (VC) are:
(8-7) VC = $10*Q
The total cost (TC) equation is the sum of the two types of costs:
(8-8) TC = FC + VC = $80,000 + $10*Q
Since this total cost equation is linear it is easy to graph and marginal cost and average variable
cost are easy to identify as shown in Figure A-1 in Appendix I. Equation (2-8) indicates that
marginal cost and average variable cost are $10 per voice channel. For any price above $10 per
voice channel, Sprint should expand output even when it is taking losses because the expansion
reduces the loss and at high enough output results in profit.
No wonder that Sprint was willing to sacrifice profit in the short run for market share!
Greater market share would mean more profit once it went to its fiber optic network.
====================================================================
SECTION 3. LONG RUN DECISIONS
Accepting the responsibility for achieving goals without the flexibility to mobilize the
necessary resources is a manager's ticket to involuntary retirement. In the short run, a manager
has the flexibility to alter only a few resources. Short run choices are adequate to make the most
efficient and profitable production decision within the constraints imposed by existing plant and
equipment. However, in the long run, a manager has the flexibility to vary all resources. Only
with flexibility to vary all resources- which is possible only with long run choices--can a manager
make the most efficient and profitable investment decision --such as where to locate a plant,
what technology to use, or whether to enter or exit from a market.
Long run and short run choices are very different kinds of decisions, and the distinction
between them has nothing to do with the amount of time involved. However, the time horizon
for a decision may dictate what factors are considered fixed and which are considered variable. In
the short run the time horizon is so short that some factors must be considered fixed; in the long
run, the time horizon is sufficient to consider varying all factors.
A decision maker should define the incremental revenues and costs that will be incurred
over the entire time horizon for any given decision. If the time horizon is longer than a year, then
future revenues and costs must be discounted back to the present. In long run choices about a
firm's capacity, the incremental revenue (TR) can be computed from the difference between the
13
Cost
total revenue with the additional capacity (TR2) and without the additional capacity (TR1):
14
(8-9) R = (TR2 - TR1)
Similarly the incremental cost (TC)cost (_TC) is the difference between the total cost with the
additional capacity (TC2) and without (TC1):
(8-10) TC = (TC2 - TC1)
When a large number of homogeneous projects are being considered, then the increments can be
used to define a long run cost schedule, long run marginal costs and the long run average cost of
expanding capacity.
A. Long Run Cost Schedule.
A long run cost schedule lists different output scenarios and the lowest cost of production
for each scenario. Many different technologies may be available for producing any given output.
If so, the construction of a cost schedule requires that a comparison of costs be made for each
and every output to find the technology achieving the lowest cost. Once the least cost
technologies have been selected, long run marginal and average cost can be computed from the
long run cost schedule just as short run marginal and average cost would be computed from a
short run cost schedule.
B. Long Run Marginal Cost
In a long run cost schedule, each increase in capacity allows a firm to produce an
increment of output. The output before (Q1) and after (Q2) the capacity has been added, define
the long run marginal cost (LRMC):
(8-11)
LRMC =
TC2-TC1
------Q2-Q1
Even if it is not possible to increase output one unit at a time, this formula provides an estimate
of the true marginal cost. If a firm can add a large number of increments of output then a long
run marginal cost curve can be drawn.
The supply curve for the long run consists of the same points as the long run marginal
cost curve with two caveats:
(a)
(b)
Again the firm can have no influence over the market price, and
The long run marginal cost curve ceases to be a supply curve when it falls below the
minimum possible long run average cost.
If the long run average cost declines with greater output, then marginal cost will be lower than
14
Cost
long run average cost and there will be no supply curve.
15
C. Long Run Average Cost. Long Run Average Cost
In making a long-run decision the manager should be able to find the least cost
technology for producing any rate of output. The long run average cost curve indicates the
lowest possible average cost for producing each and every level of output. This curve is
frequently referred to as a planning curve because it can be used to identify the technologies that
are most efficient technically and cost effectively for producing any given output, and it locates
the output that can be produced most efficiently and cost effectively.
To identify the most efficient technologies for any given output, short-run average costs
must be estimated. At any given output, the planning curve corresponds to a point on a short run
average cost curve of some technology-- the least cost technology for that output. By drawing
the short run average cost curves of all available technologies and plant sizes, we can identify the
least cost technology for any output. The collection of points representing these least cost
choices is the long run average cost (LRAC) curve, and it is, mathematically, "the envelope" of
the short run average cost curves.
Suppose a firm was considering entry into a market but had to choose from the plants for
which the short run average cost curves are shown in Figure 8-2. Given the choices depicted
there, the optimum size of plant depends on the output the manager wishes to produce. Plant 1
with SAC1 is the best for outputs of Q1 or less; plant 2 for outputs between Q1 and Q2, and the
process continues until the long-run average cost curve (heavy dots) is completely defined. The
long run average cost curve is composed of sections of the short-run average cost curves of the
available plant sizes. It forms the envelope of the least cost choices of technology.
The market-entry decision, which is a long run decision, requires that the market price be
at least equal to average cost. When price is expected to fall below the minimum of long run
average cost, a new firm will not enter a market and existing firms will make the opposite kind of
long run decision--to exit.
15
16
Cost
Figure 8-2
TELECOMMUNICATION AVERAGE COST
800
700
Copper
600
500
Fiber Optic
400
Microwave
300
Satellite
200
100
LONG RUN AVERAGE COST
0
0
200
400
600
800
1000
1200
1400
NOTE: The long run average cost curve (dark line) is the envelope of the short run average cost
curves (broken lines).
EXAMPLE: U.S. SPRINT'S CHOICE OF TECHNOLOGY
William T. Esrey joined United Telecom as chief of corporate planning in 1980. In
setting up Sprint, Esrey described the decision to enter the long distance business: "We knew the
risks were substantial" but with the market being opened to all comers, "you seldom have
opportunities like this."6 Esrey had to make sure that the least-cost technology was chosen.
The transmission technologies available for new entrants like Sprint included satellite,
microwave, copper cable, and fiber optic cable. For a typical long distance communication path
between two cities, Table 8-2 indicates differences among the average costs of using each of the
four technologies. For each output scenario (column 1) Sprint could choose the technology
which had the lowest average cost (column 7).
16
17
Cost
Table 8-2 Average Costs for Competing Technologies
Voice
Channels
(1)
0
Satellite
(2)
Microwave
(3)
Copper
cable
(4)
Fiber
optic
(5)
Exit
(6)
Long-run
Average cost
(7)
-
-
-
-
0
0
200
250
290
770
410
0
250
400
175
165
395
210
0
165
600
150
123
270
143
0
123
800
162
102
207
110
0
102
1000
250
90
170
90
0
90
1200
unfeasible
92
145
77
0
77
1400
"
150
127
67
0
67
NOTE: The lowest average cost for each output scenario for any technology is underlined. The
long run average cost curve (column 7) is the envelope of those points.
The short run average cost curve for each technology is shown in Figure 8-2. The long
run average cost curve consists of the envelope of those curves. At a zero output level, exit is the
least cost choice. At positive rates of output, each of the long distance technologies (except
copper cable) has a niche where it is the least cost technology and therefore has the lowest cost
per voice channel. The satellite technology is most cost effective at capacities below 400 voice
channels; microwave is most cost effective between 300 and 1000 voice channels, and fiber optic
cable is most cost effective at capacities greater than 1000 voice channels.
The least cost choices on the long run average cost curve generally do not occur where
the individual plants are most efficient in the short run. The greatest efficiency in the short run is
achieved where short run average cost is at a minimum. For example, in the case of the satellite
technology, the lowest short run average cost occurs at 600 voice channels, but satellite is the
least cost technology only below 400 voice channels. The long run cost effective choices do not
generally consist of the most efficient short run choices. The single exception is the technology
which sits at the bottom of the typical U-shaped long-run average cost curve.
The most important feature of the resulting long run average cost curve is its downward
slope. Using the long run average cost data in column 7 of Table 8-2, total cost and marginal
cost can be computed at each output (as is required in the section problems). The downward
slope of the long-run average cost curve means (a) marginal cost is always below long run
average cost and (b) that there is no long run supply curve. As long as marginal cost is below the
17
18
Cost
market price, a firm like Sprint would have every incentive to expand as quickly and as much as
possible.
Price would eventually be driven downward too, until other firms were forced out of the
market. In the long run, a market like this would most likely be dominated by a single firm- and
Sprint hoped to be that firm by moving down the fiber optic average cost curve. The longer
AT&T took to convert to fiber optics, the better the chances for Sprint... or any other new entrant.
SECTION 4. ECONOMIES AND DISECONOMIES OF SCALE
In informal conversations about improving business, a manager will sometimes claim that
economies of scale can be achieved because producing more would lower a firm's unit cost.
Most likely the manager is describing the greater efficiency that can be achieved if a given plant
is utilized at the production rate which it was designed to handle. However, this is short run
thinking. Economies of scale is a long run concept, which presumes that all inputs--including the
size of a plant--can be adjusted in the most efficient way possible. The existence of economies
of scales means that the long run average cost curve for a firm is downward sloping.
As a practical matter, it may be difficult to compute and graph a long run average cost
curve. However, as shown in Table 8-3, if we know the relative size of both average and
marginal cost, we can infer what is happening to the long run average cost curve.
Table 8-3. Economies of Scale
Scale
Relationship of average
cost and marginal cost
Cost elasticity of output Slope of long run
average cost
(c)
Economies of scale MC < AC
c < 1
Downward sloping
Constant returns to MC = AC
scale
c = 1
Flat
Diseconomies of
scale
c > 1
Upward sloping
MC > AC
The ratio of marginal cost to average cost is referred to as the cost elasticity of output, C. The
formula for the cost elasticity is more commonly written:
percentage change in cost
(8-12) C = cost elasticity of output =
percentage change in output
As shown in the table, a cost elasticity coefficient greater than 1.0 means that there are
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Cost
19
diseconomies of scale and, as a result, average cost rises with output. A cost elasticity less than
1.0 means that there are economies of scale and average cost is falling. A cost elasticity of 1.0
indicates constant average cost.
A. Economies of Scale.
In addition to using average and marginal cost, it is sometimes possible to identify
economies of scale by examining the production process. Economies of scale are thought to
derive from the following factors, although it is unlikely and certainly unnecessary, for all to be
present in any given situation for economies of scale to occur.
1.
2.
3.
4.
5.
Specialization and division of labor. This factor was recognized by Adam Smith who,
writing in his famous Wealth of Nations, discussed the economies which occurred when a
pin factory was increased in size (scale). The workers in such a factory were able to
specialize in their tasks and in the process, became much more adept and did not lose
time moving from one task to another.
Indivisibilities. Many inputs are indivisible so that a large amount of the resource must
be used before any output can be provided. In the short run such indivisibilities result in
large fixed costs.
Dimensional relationships. Output grows faster than cost when cost is related to some
dimension besides output, or only is related indirectly to output. For example, a six inch
pipe has a cross-section four times larger than that of a three inch pipe, but it does not
cost four times as much, nor require four times as much maintenance.
Market Size and Network Externalities. Since many costs such as research and
development, advertising, and maintenance may remain unchanged, when market size
increases, costs are spread over more customers yielding lower average total cost for the
firm. The benefits experienced by users of a network when more people are added to the
network are referred to as network externalities.
Multiplant Economies. A large firm may operate multiple plants. With more plants it is
often possible to share inputs like research and development, advertising, a large
servicing unit, distribution, and management resources.
Some advantages of size are external to a production process. For example, with greater size a
firm may be able to take advantage of discounts when purchasing resources and advertising. If
prices of inputs change systematically and inversely with the size of a firm they may also
contribute to economies of scale.
Generally, when one producer can supply any given amount of output at a lower cost than
any number of other producers, costs are said to be subadditive. Subadditivity is reflected in
the downward-sloping long run average cost curve. A technology characterized by subadditivity
is likely to result in control of the market by one producer--a circumstance referred to as natural
monopoly . In a natural monopoly, a single producer's total cost of satisfying the entire market
19
Cost
20
demand is less than the sum of the total costs of any possible combination of two or more
producers. The downward sloping nature of the long run average cost curve induces firms to
expand as rapidly as demand allows. The firm which can capture the largest market share, can
set prices below the average cost of competitors and force them out of business. Without the
threat of government interference or mitigating market influences, that firm is likely to dominate
the entire market.
B. Diseconomies of Scale. Diseconomies of Scale
Diseconomies of scale come from a variety of sources:
1.
Physical Constraints. Practical limitations to expansion can take many forms; a limited
amount of real estate, lack of dump sites, inadequate transportation, lack of water, legal
restrictions, or more intangible social constraints. Average costs increase when
constraints suddenly become binding.
2.
Managerial Control Loss. As output is expanded more supervisors are needed. But after
a certain number of supervisors have been added, another layer of managers to supervise
the supervisors must be created. Costs rise more than proportionately to output under a
process which continues to add new bureaucratic layers.
3.
Costs of Centralization. Firms are often organized into a small number of very large
units. Such centralization may trigger increases in other costs such as (a) greater
transportation costs when given locations are no longer served by small units, (b) higher
costs incurred when there are massive breakdowns or service interruptions, and (c)
increased vulnerability to regulation, public visibility, and strikes.
Where diseconomies prevail, a market can be characterized by a large number of small firms
because larger firms would have higher average costs.
C. Exit, Entry, and Efficiency. Exit, Entry, and Efficiency
We have already observed that firms have an incentive to expand quickly, like U.S.
Sprint, when economies of scale predominate. However, when diseconomies begin to offset and
rise faster than economies the long run average cost curve reaches a minimum and then rises.
The resulting U-shaped long run average cost curve has been verified for many markets. The
minimum of such a curve has strategic importance to entry and exit in a market.
1. Minimum Efficient Scale. Minimum Efficient Scale
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Cost
21
The lowest output at which a firm reaches the minimum on a long-run average cost curve
is referred to as the minimum efficient scale (MES) of plant. An entrepreneur who knows the
MES can enter a market with the lowest possible initial investment, can undercut or equal the
prices of any other firm in the market, and can still earn a normal profit. Building several plants
of minimum efficient scale may provide the flexibility to locate in many different markets, rather
than risk a single plant location.
But, how can an entrepreneur determine the MES in a given industry or market? The
median size of firms in a market is one way to approximate MES. The median size for a firm is
that one which is at the middle of the distribution when we array the firms from smallest to
largest on the basis of their sales. For example, suppose the interstate long distance market is
served by only three firms; AT&T with 83.6% of the market, MCI with 10.4% of the market, and
U.S. Sprint with 6.0% of the market. The "median-size" firm would be MCI with a market share
of 10.4%, and, the long distance market would be one of the minority of markets where the
median-size firm garnered more than 10% of the market. Table 8-4 shows the results of a study
of 110 different markets by Bruce Kaufman7. In only 22.7% of the 110 markets in different
industries that he examined was there a median-size plant which had a market share of more than
10%. In the example below we'll see that this isn't a bad estimate of MES from U.S. Sprint's
point of view.
Table 8-4 Market Share of Median-Size Plant
Median firm market share 0-0.009
0.010-0.049
0.050-0.099
0.10+
Total
Number of markets
29
38
18
25
110
Percent of total market
26.4
34.5
16.3
22.7
100.0
In markets where competition forces prices down to the minimum of long run average
cost, firms with high unit costs are forced to exit from the market. The survivor technique should
then reveal the most efficient size for a firm.
2.
The Survivor Technique.
Planning curves like those in the previous three sections are ex ante guesses about the
true long run costs in a market. The ex post verification of the shape of a long run average cost
curve of a firm can be obtained indirectly by examining the size and number of firms that survive
in the market. Economists use the survivor technique to infer the true shape of the long run
average cost curve in a market:
(a)
(b)
Economies of scale are most likely in markets dominated by a single firm or where the
market share of small firms is declining relative to the market share of larger firms.
Diseconomies of scale are most likely in markets where there are many small firms or
21
Cost
(c)
22
where the market share of small firms is rising relative to the market share of larger firms.
Flat long run average costs are most likely if firms in a market are of many different sizes
and there is no discernible change in the market share of any size-group of firms.
However, the conclusions drawn from the survivor technique should be used with caution. They
may be incorrect if there are significant market distortions or if there is significant government
interference in the market.
====================================================================
SECTION 5. ECONOMIES OF SCOPE
In a typical merger, a reporter interviews the key decision makers and learns that the
merger will produce "synergies." Often the synergies are explained in terms of cost reductionsuch as the elimination of redundant jobs, better utilization of resources, and greater efficiencies
from "rationalization." The costs associated with running the two separate companies are viewed
to be higher than those of the two companies combined.
Synergies are easy to claim, but difficult to verify. Economists include the notion of
synergy into the very comprehensive notion of economies of scope. Economies of scope occur
where the cost of producing a given product mix is lower when the goods are produced by a
single firm than when each good is produced by a separate firm. Economies of scope are not the
same thing as economies of scale. Greater economies of scale result in a lower unit cost of
producing a single good by one firm. By contrast, economies of scope refer to the production of
more than one good, a product mix.
The savings from economies of scope, ES, can be measured by comparing the cost of
producing items together and producing them separately:
(8-14) ES = TC(Q1) + TC(Q2) - TC(Q1,Q2)
TC(Q1,Q2)
The formula consists of the total costs, TC(Q1) and TC(Q2), of producing the two goods in
separate production processes and the total cost, TC(Q1,Q2), that can be achieved by producing
the two goods jointly.
====================================================================
EXAMPLE: ECONOMIES OF SCOPE AND BREAKING UP AT&T
In the telecommunication market, a local telephone network is a primary input for the
production of long distance telephone service. However, the same network can also be used with
very little additional cost to transmit local telephone, cable television, computer, yellow pages,
and other information services. The network produces such great economies of scope that no
22
Cost
23
other firm could compete in these lines of business if the local network firms were allowed in to
the market.
23
Cost
24
Before 1984 AT&T controlled most local telephone service through the Bell
System, and long distance service as well. New competitors in the long distance market
still had to connect through the AT&T network to reach their customers. The Justice
Department wanted to give new long distance firms a better chance to compete by
separating AT&T from its local Bell companies. Two economists, Evans and Heckman,
used a cost function to demonstrate that decentralization of services, such as the
separation of local service from long distance telephone service, would have resulted in
efficiencies (cost savings) of between 35% and 50% from 1963 onward.8 Heckman and
Evans provided ammunition for the Justice Department in its efforts to break up AT&T.
As part of the consent decree of 1982, AT&T agreed to divest itself of 22 regional bell
operating companies which accounted for $87 billion of AT&T's $136 billion in assets.
The newly independent bell operating companies thrived after the breakup. As
they experimented with the increased capacity potential of fiber optics they suddenly
found that there might indeed be economies of scope to be captured by entering
information services- even though the consent decree had prevented them from doing so.
Suppose one of the new bell operating companies that experienced $8 billion in costs
(=TC(Q2)) from offering local service planned to take over an information service
company with $4 billion in costs (=TC(Q1)), but that the merger would mean there were
only $10 billion of costs (=TC(Q1,Q2)) without any loss of business or any change in
revenues. The savings, ES, from economies of scope would be:
(8-15) ES = TC(Q1) + TC(Q2) - TC(Q1,Q2)
TCj(Q1,Q2)
= $4 billion + $8 billion - $10 billion
$10 billion
= 20%
If such savings were possible, local bell companies would be eager to provide both
services. In 1991, they succeeded in getting the 1984 agreement modified so that they
could take advantage of such economies of scope in information services.
If Heckman and Evans were right, the local Bell operating companies would have
no incentive to enter long distance service. However, using a special type of cost
function Lars-Hendrik Roller, found: "rather strong economies of scope, cost
complementarities, and economies of scale seem to exist. Furthermore, the evidence is
consistent with the natural monopoly hypothesis."9 In other words, existing firms would
have an incentive to put the natural monopoly back together again, but this time it would
be the local Bell companies, not AT&T. The Baby Bells were quick in knocking on the
door to provide long distance service. By 2000 they gained their first access to long
distance markets as Congress deregulated telecommunications. As of 2002, AT&T’s
stock had lost 2/3 of its highest value, MCI had become bankrupt after its acquisition by
Worldcom, and Sprint was downsizing.
24
Cost
25
5. ECONOMIES OF SCOPE
In a typical merger, a reporter interviews the key decision makers and learns that
the merger will produce "synergies." Often the synergies are explained in terms of cost
reduction-such as the elimination of redundant jobs, better utilization of resources, and
greater efficiencies from "rationalization." The costs associated with running the two
separate companies are viewed to be higher than those of the two companies combined.
Synergies are easy to claim, but difficult to verify. Economists include the notion
of synergy into the very comprehensive notion of economies of scope. Economies of
scope occur where the cost of producing a given product mix is lower when the goods are
produced by a single firm than when each good is produced by a separate firm.
Economies of scope are not the same thing as economies of scale. Greater economies of
scale result in a lower unit cost of producing a single good by one firm. By contrast,
economies of scope refer to the production of more than one good, a product mix.
6. TECHNOLOGICAL CHANGE AND INVENTION
Technological change can impose revolutionary impacts on markets.
Technological change occurs through invention, a scramble to innovate, and diffusion of
the technology throughout the market. Invention is the process by which new
technologies are discovered. Innovation is the process of experimenting with a new
technology until ways can be found to produce commercially profitable products and
services using the invention. Diffusion is the process by which firms adopt the new
technology. With the diffusion of new technology, firms utilizing the old technology will
be forced to exit from the market. New firms enter, and the whole structure of the market
can change.
Although economists have investigated patterns of invention extensively, they
have not been able to predict when or how they occur. It is difficult to determine whether
patents which are supposed to provide financial incentives for inventors do, in fact,
stimulate invention. Nevertheless, many firms have been forced to do some form of
technological forecasting. They can use the Delphi technique to poll experts and to form
a consensus view about the timing and importance of technological change. Alternatively
they may attempt to forecast what will happen to a technology based on similar
experiences with a comparable technology. Finally, a firm may be able to describe a
particular dimension of performance that is crucial to their business, and forecast
improvements on the basis of trends observed in past. Such technological forecasting has
become a rich source of investigation in economics, but to use these tools requires the
understanding of logarithms.... (see Economist Tool Box). But if you’re willing to take on
logarithms, the next section provides the tools for analyzing the rate at which
technological change occurs.
ECONOMIST’S TOOL BOX: LOGARITHMS.
25
Cost
26
One of the big problems in examining a series of data through time is that there is
an upward or downward drift to the data. As with most economic data, the general
upward drift means that a given amount of change measured in dollars or index numbers
represents a smaller and smaller percentage change through time. For example, the Dow
Jones dropped from 381 points on September 1, 1929 to 41 points by June 8, 1932. That
340 drop devastated the economy. By contrast, in 1987 a 580 point drop in one day
hardly affected the economy. A semi-logarithmic graph over long periods of time of the
Dow Jones average will typically allows the eye to see an 89% drop in 1929 as exactly
the same size as an 89% drop today. The great advantage of logarithms is that percentage
changes appear constant, not the units of measurement.
Because of the wide use of logarithms in business, Excel gives options for
logarithmic curve fitting and data transformation. To use logarithms you only need to
know one command in Excel, the “paste function” which appears as fx. It appears on one
of the buttons, usually next to the summation button, . When you click that button it
gives you the “paste function” menu to choose from. The “all” or “math and trig”
function categories on the left both contain the “LOG10” function in the right hand side
of the menu. After clicking on that function, press the “OK” button on the bottom right
and you will get another menu that looks something like the following:
LOG10
Number
=number
Returns the base 10 logarithm of a number
Number is the positive real number for which you want the base-10 logarithm
Formula result =
?
OK
Cancel
Click on the white box in the menu, and then click the mouse on the cell in the
spreadsheet containing the number for which you want the corresponding logarithm.
Back to the menu box click “OK” and your logarithm appears… unless you tried to take
the logarithm of a negative number or zero for which you cannot take logarithms.
With relative references (no $ signs in front of the column and row designators)
you can drag a box with the logarithm command just as you can for any other function
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27
and create a column or row of logarithms- particularly useful for regression analysis.
Once you have performed operations on the logarithms you must convert back out
of the logarithms. Use any logarithmic number as an exponent to the base of “10.” So if
you have a logarithm in A1 then typing “=10^A1” in any cell gives you the number that
corresponds to the logarithm. If you put numbers into logarithms you have to take them
back out of logarithms. Meanwhile you don’t care what a logarithm is. But if you want
to impress a technician say that you have just performed an “antilog transformation.”
They may think you’ve died and gone to heaven.
By the way, there are several different logarithmic functions… but you don’t care
about that either. Just use the base 10 logarithm.
============================================================
EXAMPLE: INVENTION IN TELECOMMUNICATIONS
A view of the history of telephone transmission technologies explains how
technological change led to the demise of AT&T's monopoly. Table 8-5 shows the dates
at which different technologies were first demonstrated.
Table 8-5. First Demonstration of Transmission Technology
Transmission Medium10
Date of First Demonstration
Metallic cable for telephone
-Loaded cable*
-Coaxial cable
1878
1900
ca. 1940
Radio telephones
-Microwave**
1930
ca. 1945
Satellite***
1962 (Telstar)
Fiber optic cable****
1976 (Dorset, England)
When only the old copper, coaxial technology was available, there were strong
economies of scale. The network was an indivisible expense and provided network
externalities. As a result, AT&T had a natural monopoly.
However, microwave technology was above ground and satellite technology had
flexible routing; there were fewer indivisible costs to be spread. Furthermore, expansion
of both microwave and satellite capacity required the dedication of more bands in the
electromagnetic spectrum, and there were physical constraints on the number of bands
available. As a result, long run average costs eventually rose for both of those
technologies. Nevertheless, for small ranges of output these technologies were less
27
Cost
28
expensive than copper cable and provided niches for MCI, Sprint and other entering
firms.
Fiber optic cable has all of the characteristics of coaxial, copper cable that lead to
economies of scale, but it is cheaper over broad ranges of output than any of the other
three technologies; the long distance market has the potential of being dominated once
again by a single firm--and not necessarily AT&T. Technological change can both open
and close a market to entry of new firms.
===============================================================
A. INNOVATION AND THE LEARNING CURVE
A new business that is expanding rapidly, often experiences rapid decreases in
unit costs. However, it is frequently an error to assume that the reason for the decline is
economies of scale. Many managers will often correctly ascribe at least some of the
decline in average costs to the learning curve.
As more experience is accumulated with a production process, unit costs decline
through learning-by-doing. The sources of the increased efficiency include improved
work methods, improved work flow, reduction in the amount of waste of materials,
reduced maintenance, and reduced skilled labor required to produce a given output as
tasks are repeated. If a manager can distinguish such learning-by-doing effects from scale
effects (namely, movements along the average cost curve), then future average costs can
often be reliably predicted.
A learning curve can be graphed to show how average costs (Y-axis) decrease at
a decreasing rate as cumulative output increases (X-axis). Learning is estimated for a
given technology, and constant input prices and output scale. There is an important
distinction to be made between cumulative output--the total output that has been
produced since production commenced--and the amount of output produced in a single
period. Changes in output for a single time period correspond to a movement along a
long run average cost curve. By contrast changes in cumulative output as time passes
yield shifts of the long-run average cost curve. It is the change in cumulative output
(which is a surrogate for how much experience you have had) which moves you along a
learning curve.
The learning curve can be expressed in exponential form as follows:
(10) AC = aQb
where AC,a,Q>0 and b<0
where AC = Average cost
Q=
the cumulative number of that units have ever been produced
a=
the theoretical cost of the first unit of quantity, Q
b = the percentage decrease in average cost for a percentage increase in cumulative
28
Cost
29
quantity, Q
When an equation of this form is estimated from the early cost experience with a
production process, predictions can be made about how quickly average cost will fall as
additional units are produced. But first it must be transformed into a linear function so
that we can use regression analysis to estimate the parameters. This is done by taking
logarithms on both sides of equation (10) to get:
After taking the logarithms of both sides of the equation (16), it is possible to
estimate a learning curve using linear regression. Such a logarithmic equation takes the
following form:
(11) Log AC = Log a + b Log Q
By the way, that’s another nice thing about logarithms that made them so popular before
computers. They convert division and multiplication signs to addition and subtraction
signs. Similarly they convert positive exponents to multiplication signs (compare (10)
and (11) ).
The reliability of learning curve predictions is so great that buyers such as the
government often require of their suppliers price discounts based on projected declines in
average costs based on the learning curve and everyone in business uses it to justify
starting all over again. The regularity and predictability inherent in the learning curve is
so attractive that there is an understandable desire to apply it more broadly. The results of
any such broader application of the learning concept may be referred to as an experience
curve. The experience effects usually fall in the range of 10% to 30% cost reductions as
cumulative output doubles. However, it is more difficult to rely on the predictability of
such experience effects because so many different phenomena besides learning influence
costs.11
In spite of the difficulties of forecasting them, learning and the broader experience
effects can provide firms with strategic advantages. In E-commerce particularly, the first
firm which enters a market can often stay one step ahead of any future entrant and may be
able to dominate the market. In such a case the learning curve actually serves as a
barrier-to-entry. However, if the learning effect is small it may not be substantial enough
to provide such a strategic advantage. On the other hand, if such effects are very large,
but exist only for the first one or two years after a product has been introduced, then
entering firms can expect to catch up with the firms who get the early start- an example of
the counterpunch strategy used by Microsoft and which continually had Jim Clark
running.
==============================================================
EXAMPLE: LOWER AVERAGE COST OF LAYING FIBER OPTIC CABLE
The data in the EXCEL spreadsheet of Table 2 show the declining outlay (per
voice channel) of laying a transatlantic fiber optic cable (col 2) for different years
29
Cost
30
(1983=1). The average cost of laying cable fell due to reduced fiber loss in fiber optic
cable, increased capacity, better coupling and interconnection efficiency, and a reduction
in number of repeater stations required in the undersea environment. Since more than the
cost of labor is involved, Figure 2 is probably best described as an experience curve.
Table 2 Experience Curve Effect
Year
Av. Outlay
(1983=1) $1000/v.ch.
1
22.63
6
8.33
10
4.6
Log of
Year
Log of Av.
Outlay
0 1.354684554
0.77815125 0.920645001
1 0.662757832
The average outlay is similar to an average cost and is the dependent variable while the number
of years is a surrogate for cumulative output. With a regression on the last two columns of Table
2, we get the following results:
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.986445
R Square
0.973074
Adjusted R Square
0.946149
Standard Error
0.081147
Observations
3
ANOVA
df
Regression
Residual
Total
Intercept
Year
1
1
2
SS
0.237968
0.006585
0.244553
Coefficients Standard Error
1.368679
0.079931
-0.65683
0.109261
MS
0.237968
0.006585
F
Significance F
36.13924
0.104938
t Stat
P-value
Lower 95%
17.12334 0.037136
0.353068
-6.01159 0.104938
-2.04512
RESIDUAL OUTPUT
Observation
Predicted Outlay
1
1.368679
2
0.857563
3
0.711845
Residuals Standard Residuals
-0.01399
-0.2439
0.063082
1.099387
-0.04909
-0.85549
NOTE: The predicted Outlay are found using the estimated equation.
30
31
The linear regression equation is:
(12) log AC = 1.37 - 0.657 log Q
But we can convert it back.
The constant term, a, in the equation (10) can be found by the following antilog
transformation:
(13) a = 101.37 = $23.4
which is supposed to be (and is!!!) very close to the true first unit cost of $22.63. With this
information we can now replace the parameters in the learning curve equation as follows:
(14) AC = aQb
= 23.4Q-0.657
The exponent, -0.657, indicates that for every 1% increase in cumulative output, Q, (as measured
by the number of years since 1983), there is a 0.657% reduction in average cost. The coefficient,
23.4, indicates the cost of laying fiber optic cable in the initial year, 1983.
Now lets assume that the same rate of cost reduction continues through time. What
would be the average cost per voice channel of laying transatlantic cable in 2005 (23 years from
1983)? Substituting in "23" for Q we find:
AC = 23.4 x 23-0.657
= 2.98
A firm planning to lay fiber optic cable in 2005, should expect to incur a cost of $2,980 per voice
channel.
=============================================================
B. DIFFUSION AND THE LOGISTIC CURVE
A new technology is not universally adopted the moment it is introduced. First, there is a
period where the value and usefulness of the new technology must be demonstrated. As the
results of such demonstrations are communicated, new users slowly begin to adopt. As more and
more information indicates the success of the new technology, larger numbers of new users begin
to adopt it. Finally, new adoptions slow as the limit of potential users of the new technology is
reached. An entrepreneur must nurture this process with a marketing strategy.
Unlike the rate of invention which cannot easily be forecast, the rate at which diffusion
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Cost
32
occurs can be forecast. A graph showing the percentage of potential buyers who adopt a new
technology over time generally appears in an S-shaped pattern which is called a logistic curve or
S-curve. The equation for a logistic curve indicates the fraction, P%t, of the potential buyers in a
market who will have adopted a particular invention by a given time, t. The following
logarithmic equation can be used to provide a rough estimate of the parameters of the logistic
equation (1):
(15) Log [P%t/(1-P%t)] = a + bt
The parameter, b, shows the rate at which time changes the adoption rate. Economists have
found that the parameter, b, is affected both by the profitability of switching to the new
technology as well as the cost of installing and using the new technology.12
If we undo the logarithms equation (15) becomes:
(16) P%t = 1/ (1+10-(a +bt))
a,b = parameters of the equation.
Logistic curves can be used to describe and predict the diffusion process quite well.
===============================================================
EXAMPLE: ADOPTION OF ONLINE TRADING.
.
US Bancorp- Piper Jaffrey keeps track of online trades as a percentage of total retail
trades of stocks by households. In 1997 there was only a 17% adoption rate by traders, but this
increased to 27% by 1998 and 43% by 1999.1 Let’s arbitrarily assume that on-line trading
effectively started in 1993. The way to organize this data in EXCEL to predict adoption rates
would be as follows:
Scurve Year Adoption
Year 1993=1
%
1997
5
0.17
1998
6
0.27
1999
7
0.43
Adoption
Ratio
Log Adoption
0.204819277 -0.688629171
0.369863014 -0.431959096
0.754385965
-0.1224064
The adoption ratio is found by dividing the adoption percentage by one minus the adoption
percentage as required by equation (16). Then in the last column the logarithm of this adoption
ratio is taken, which then becomes the dependent variable. Unlike the learning curve above, we
don’t take the logarithm of time because equation (16) doesn’t require us to do so. So straight
time is the independent variable and the resulting regression looks as follows:
SUMMARY OUTPUT
Regression Statistics
1 Andrew Fraser “The Great Equalizer” in The Wall Street Journal (Monday, June 12, 2000) p. R6 of the Wall
Street Journal supplement on online investing.
32
Cost
33
Multiple R
R Square
Adjusted R Square
Standard Error
Observations
0.998549
0.997101
0.994202
0.021589
3
ANOVA
df
Regression
Residual
Total
1
1
2
SS
0.160304
0.000466
0.16077
Coefficients
Standard Error
-2.113
0.09244
0.283111
0.015266
Intercept
Year 1993=1
MS
0.160304
0.000466
F
Significance F
343.9299
0.034295
t Stat
P-value Lower 95%
-22.8582 0.027833
-3.28755
18.54535 0.034295
0.089141
RESIDUAL OUTPUT
Observation
1
2
3
Predicted Log Adoption
-0.69744
-0.41433
-0.13122
Residuals Standard Residuals
0.008814
0.57735
-0.01763
-1.1547
0.008814
0.57735
In this case we don’t have any work to do except straight substitution into equation (16) to get:
P%t = 1/ (1+10-(-2.113 +.283111*t))
If we want to find the adoption rate in 2005 (=13 if 1993=1), then substitution gives us (WATCH
THOSE NEGATIVE SIGNS):
P%t = 1/ (1+10(2.113 -.283111*13)) = 97%
By the way, even though the significant digits are only 2 or 3 in most business applications, for
calculation purposes it is advisable to keep the significant digits until the end of the calculation
because large errors can crop up (another way of saying that such calculations are imprecise at
best). But this isn’t bad. According to our calculation, in four years everyone will essentially
have their work done through on-line trades.
EXAMPLE: ADOPTION OF FIBER OPTIC CABLE.
.
Sometimes the media only gives adoption rates for only two different periods of time.
We can still project the diffusion from this limited information. Here’s a good example from the
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Cost
34
telecommunication industry.
Since fiber optic cable is clearly superior transmission technology, it should rapidly have
replaced copper cable. R.S. Wolff, district manager of Bellcore, and a participant in a
Technology Forecasting Users Group convened to examine the spread of fiber optic technology,
assessed the rapidity with which copper was being replaced by fiber optic circuitry:
Data sets for a total of 32 individual operating companies were used in the
analysis. The U.S. companies ... represent about 85% of the access lines in the United
States...Data for future years were to be obtained from company plans... The percentage
of circuits on fiber was 25.7% in 1987 and is planned to be 41.4% in 1989.13
We can find the logistic equation by substituting his two years of survey information into the
logarithmic equation (8-2):
(8-25)
log(25.7/74.3) = -1.06162 = a + 4b
log(41.4/58.6) = -0.34745 = a + 6b
We're assuming year 0 is 1983, the date when fiber optic cable became a serious contender to
copper cable; this means 4 is associated with 1987; 6 with 1989. Since there are two equations
and two unknowns we can solve for the parameters: a=-2.49 and b=.3571 The equation for the
curve is:
1
(8-26) P% = ------------------------------1 + 2.718-(-2.49 + 0.3571 t)
which is the logistic curve graphed in Figure 8-6.
By substituting the appropriate numbers into equation 8-1 we can make forecasts for later
years as shown in Figure 8-6. By the year 2003 (=20 in equation 8-4) Figure 8-6 forecasts that
99% of the long distance transmission lines will be fiber optic. Wolff's projection, using a
similar model and much more data is a bit more optimistic. His model forecasts the 99% usage
level five years earlier (by 1998).
34
Cost
35
Figure 8-6
THE LOGISTIC CURVE FOR FIBER
OPTIC CABLE TECHNOLOGY
Fiber Optic Circuitry as
100
a % of total circuits
90
80
70
LOGISTIC EQUATION
60
50
41.4
40
30
p% =
1
-(-2.49+.3571*Y)
1 + 2.718
25.7
20
10
actual
observations
0
83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 0
YEAR
1
2
3
NOTE: The S-shape of the logistic curve indicates the rate of diffusion of a new technology.
Fiber optic cable is beginning to dominate the other four telecommunications
technologies. Although economies of scale, economies of scope, and experience effects may
suggest that the long distance market may become dominated by one firm, there are several
factors which could allow a number of long distance firms to survive. Government regulation
restricts the entry of major competitors into many markets. Furthermore, because economies of
scale diminish on high capacity routes, several firms may be able to survive since cost
disadvantages are small. Finally, technological changes such as a new superconducting material
may eventually supplant fiber optic cable. This may open up opportunities for new entry, just as
we have seen with other transmission technologies.
SECTION 9. SUMMARY
Decisions should be made incrementally. As long as economic profit, the difference
between total revenue and total economic cost of an incremental choice is positive, a project
should be undertaken. In computing incremental economic cost, implicit costs must be included
and costs which do not change with the decision should be excluded. In this chapter the
incremental approach was applied to the choice of transmission technologies.
Decisions should be made with an adequate amount of flexibility and authority over
35
Cost
36
resources required to achieve desired goals. In production decisions, it may not be possible to
vary all factors, and a short run analysis may involve shutting down a plant or increased capacity
utilization. By contrast, in investment decisions, all factors can be affected by decisions
involving changes in capacity, entry, or exit, since these are long run decisions. In this chapter
the selection of a transmission technology was the long run decision and the decision about
shutting down was a short run decision.
The nature of costs in the long run help determine the structure of the market. Substantial
economies of scale can lead to natural monopoly. Diseconomies even at low levels of output are
likely to mean that many small firms can survive in a market. For example, in the auto market
there are substantial economies of scale which have contributed to the relatively small number of
auto producers in the world today. Economies of scope provide a rationale for a single firm to
produce many different goods or services. In the case of telecommunications, this chapter has
shown that both economies of scale and economies of scope have been important.
The existence of large economies in telecommunications suggests that one firm would
predominate in the long run. After the breakup of AT&T, several attempts have been made to
eliminate the number of competitors- the failed Sprint merger with MCI and the acquisition of
AT&T itself by SBC. However, the long distance market is experiencing entry from many
different sources due to technological change. Perhaps the most important is the internet which
permits long distance telephone calls very inexpensively. Furthermore, there are many new kinds
of telecommunication markets such as the wireless market that provide footholds for different
firms. The telecommunications industry is therefore experiencing continual pressures to
concent6rate and pressures toward deconcentration.
DEFINITIONS
Average cost or average total cost (AC): Total cost divided by the associated output. The
average cost curve is a graph of average cost (y-axis) associated with each unit of output (xaxis). Average variable cost (AVC) and average fixed cost (AFC) are similarly computed and
graphed. (S. 2, C. 8) The long run average cost curve (LRAC) is a collection of points
representing the least cost combination of rewources required to produce any level of output. It
is drawn as the envelope along all possible short run average cost curves (SRAC). (S. 3, C. 8)
Breakeven: The output at which total revenue is equal to total cost. (S. 2, C. 8)
Cost elasticity of output: The ratio of percentage change in total cost to the percentage change
in output. (S. 4, C. 8)
Diffusion: The process by which users adopt a new technology. (S. 6, C. 8)
36
Cost
37
Economic costs: The total opportunity cost - both explicit and implicit - of the resources used to
produce an output. By contrast, accounting cost includes only explicit costs. Economic profit is
found by subtracting total economic cost from total revenue (S. 1, C. 8)
Economies of scale: The ability to produce a given amount of output of one good more cheaply
with one firm than by more than one. This also means that as a firm produces more output its
long run average costs are lower with a cost elasticity of less than 1.0. By contrast diseconomies
of scale are indicated by a cost elasticity above 1.0 and result in an upward sloping long run
average cost curve. (S. 4, C. 8)
Economies of scope: The ability to produce a given mix of goods jointly by one firm (or
production process) more cheaply than when the goods are produced independently by different
firms (or production processes). (S. 5, C. 8)
Entry: A long run decision for a new firm to invest in capacity to produce output in a market.
(S. 3, C. 8)
Exit: A long run decision to sell off all existing capacity to produce output in a market. (S. 3, C.
8)
Experience curve: A graph showing the reduction in average total cost as experience with a
process increases. Generally, it shows the path of average cost as cumulative output rises, given
constant technology, input prices and output scale. (S. 6, C. 8)
Explicit costs: Costs for which monetary payments are actually made by the firm to owners of
resources. These costs correspond to accounting costs. (S. 1, C. 8)
Fixed cost (FC): That part of short run economic cost that remains the same regardless of the
output level, and which must be paid even when output is zero. (S. 2, C. 8)
Historical cost: The dollar cost at which resources were originally purchased. (S. 1, C. 8)
Implicit costs: Costs of resources for which payments are not actually made but which impose
an opportunity cost on their owners when used in producing an output. (S. 1, C. 8)
Indivisibilities: The impossibility of subdividing capital or other inputs. In order to operate at
all, a firm must purchase a large quantity of inputs because of the inability to subdivide them. (S.
4, C. 8)
Innovation: The process of experimenting with a new technology until ways can be found to
produce commercially profitable products and services with a new invention. (S. 6, C. 8)
37
Cost
38
Invention: The process by which new technologies are discovered. (S. 6, C. 8)
Investment decision: A long run decision such as exit, entry, expansion or contraction of
capacity in which all inputs are variable. (S. 3, C. 8)
Learning curve: A tool for measuring the rate at which short run average costs (usually labor
costs) are reduced as labor learns to do a task (producing a product) more efficiently after doing it
over and over gain. It shows the path of average cost as cumulative output rises, given constant
technology, input prices and output scale. (S. 6, C. 8)
Logistic (S-) curve: An S-shaped curve showing the percentage of potential buyers (Y-axis) who
adopt a new technology at different time periods (X-axis). (S. 6, C. 8)
Long run: Decision making over a time horizon in which all factors can be varied. (S. 3, C. 8)
Marginal cost: The change in total cost resulting from a one unit change in output. The
marginal cost curve is a graph of marginal cost (y-axis) associated with each unit of output (xaxis). (S. 2, C. 8)
Minimum efficient scale: The lowest output at which a firm first reaches the lowest possible
long run average cost (S. 4, C. 8)
Natural monopoly: A market dominated by a single firm because the total cost of satisfying
market demand is less for one firm than the sum of the total costs of any possible combination of
two or more firms producing the same amount of output. (S. 4, C. 8)
Opportunity cost: The value of a resource in its next best alternative use; the value of the best
alternative forgone when choosing a course of action. (S. 1, C. 8)
Planning curve: A graph of the average costs a firm expects to incur at various levels of output
based upon engineering estimates or experience with similar processes. (S. 1, C. 8)
Production decision: A short run decision to increase output, decrease output, or shut down
(but not to enter, exit, or change capacity). (S. 3, C. 8)
Replacement cost: The lowest cost required to buy the resource or the equivalent capacity of a
close, up-to-date substitute on the market (C. 8, S. 1)
Reproduction value: The cost of buying the identical resource on the market (C. 8, S. 1)
Shut down price: The price that is equal to the minimum of a short run average variable cost
38
Cost
39
curve; if price falls below this level a firm shuts down, which means it produces no output. (S. 2,
C. 8)
Subadditivity: The ability of one producer to supply any given amount of output at a lower cost
than any combination of other producers. This condition results in the downward sloping long
run average cost curve. (S. 4, C. 8)
Supply: Quantities of a good that a seller(s) is willing and able to buy at alternative prices,
during a given period of time, ceteris paribus. Three different types of supply can be
distinguished depending upon the seller and how the seller is viewed:
Individual supply applies strictly to a single buyer.
Market supply applies to all of the sellers within a given market.
Supply from the firm's point of view applies to all sellers who are willing and able to sell
the product to a specific group of buyers.
The supply curve is identical to the marginal cost curve above average variable cost, as long as a
firm faces a flat demand curve.
Supply determinants. Any variable which has the ability to cause a shift in the supply curve;
includes prices of resources, technological change, the opportunity costs of using resources for
other purposes, seller's expectations about the economic climate of the market in the future, and
the number of sellers. These influences are assumed constant when drawing a supply curve. (S.
2, C. 8)
Short run: A time horizon in which some factors cannot be varied. (S. 2, C. 8)
Sunk costs: The costs of inputs which a firm has previously incurred and which therefore, do
not influence current decisions. (S. 1, C. 8)
Survivor technique: A method for judging economies or diseconomies of scale based on the
number of firms in a market. If there are many small firms or the market share of small firms
increases through time, then there are likely to be diseconomies of scale. If there is one large
firm or market share for the large firms increases, then, economies of scale. The existence of
firms of many different sizes is likely to mean constant long-run average cost over the range of
their sizes. (S. 4, C. 8)
Variable cost (VC): Those costs that vary with output. (S. 2, C. 8)
1. William C. Symonds, et. al. "People aren't Laughing at U.S. Sprint Anymore" in Business Week (July 31, 1989)
p. 83.
2.
See for example James P. Womack, Daniel T. Jones & Daniel Roos. The Machine that Changed the World
39
Cost
40
(New York: Maxwell Macmillan International, 1990).
3. Calvin Sims, "2 Phone Concerns Post Profits: But US Sprint Has a Loss" in The New York Times (Feb. 10,
1987) p. 36.
4. ibid.
5. The examples in this chapter have been modeled after Sharizi and Arouzoulla. Institute of Electrical and
Electronic Engineers (CH2314-3/86/0000-0927, 1986 pp. 26.5.1-5 (pp. 827-831)). However, for pedagogical
purposes variable costs in the chapter are much larger than real variable costs.
6. Symonds et. al., op. cit. (Business Week July 31, 1989) p. 83.
7. Bruce Kaufman, "Scale of Plant Relative to Market Size in U.S. Manufacturing" Southern Economic Journal
(October 1979, 46-2, p. 637.
8. David S. Evans and James J. Heckman. "A Test for Subadditivity of the Cost Function with an application to the
Bell System" in American Economic Review. v. 74 #4 (Sep 1984) pp. 615-623.
9. Lars-Hendrik Roller. "Proper Quadratic Cost Functions with an Application to the Bell System" Review of
Economics and Statistics, May 1990, 72(2), pp. 202-210.
10. Encyclopedia Britannica, 15th ed., 1974 *18-85, **15-430, ***16-262, ****18-96, Sharifi op. cit. (1985) p.
828, and International Resource Development Inc.**
11. The discussion here is based on Graham Hall and Sydney Howell. "The Experience Curve from the Economist's
Perspective" in Strategic Management Journal, Vol. 6, (1985), pp. 197-212 and Linda Argote and Dennis Epple.
"Learning Curves in Manufacturing" in Science, V. 247 (23 Feb. 1990) pp. 920-923.
12.
See "Diffusion of technology" in The New Palgrave: A Dictionary of Economics, Eatwell, Milgate, and
Newman, eds., Vol. I (London: MacMillan, 1987) p. 843.
13. R.S. Wolff. "What's Ahead for Copper?" TE&M Special Report: technology forecast. (October 1, 1988).
40