The forgetting curve hypothesizes the decline of memory
retention in time. This curve shows how information is lost over time
when there is no attempt to retain it. A related concept is the strength of memory that refers to the durability that memory traces in the brain. The stronger the memory, the longer period of time that a person is able to recall it. A typical graph of the forgetting
curve purports to show that humans tend to halve their memory of newly
learned knowledge in a matter of days or weeks unless they consciously
review the learned material.
The forgetting curve supports one of the seven kinds of memory
failures: transience, which is the process of forgetting that occurs
with the passage of time.
History
From 1880 to 1885, Hermann Ebbinghaus ran a limited, incomplete study on himself and published his hypothesis in 1885 as Über das Gedächtnis (later translated into English as Memory: A Contribution to Experimental Psychology).
Ebbinghaus studied the memorisation of nonsense syllables, such as
"WID" and "ZOF" (CVCs or Consonant–Vowel–Consonant) by repeatedly
testing himself after various time periods and recording the results. He
plotted these results on a graph creating what is now known as the
"forgetting curve". Ebbinghaus investigated the rate of forgetting, but not the effect of spaced repetition on the increase in retrievability of memories.
Ebbinghaus's publication also included an equation to approximate his forgetting curve:
Here, represents 'Savings' expressed as a percentage, and
represents time in minutes. Savings is defined as the relative amount
of time saved on the second learning trial as a result of having had the
first. A savings of 100% would indicate that all items were still known
from the first trial. A 75% savings would mean that relearning missed
items required 25% as long as the original learning session (to learn
all items). 'Savings' is thus, analogous to retention rate.
In 2015, an attempt to replicate the forgetting curve with one
study subject has shown the experimental results similar to Ebbinghaus'
original data.
Hermann's experiment contributed a lot to experimental
psychology. He was the first to carry out a series of well-designed
experiments on the subject of forgetting, and he was one of the first to
choose artificial stimuli in the research of experimental psychology.
Since his introduction of nonsense syllables, a large number of
experiments in experimental psychology has been based on highly
controlled artificial stimuli.
Increasing rate of learning
Hermann
Ebbinghaus hypothesized that the speed of forgetting depends on a
number of factors such as the difficulty of the learned material (e.g.
how meaningful it is), its representation and other physiological
factors such as stress and sleep.
He further hypothesized that the basal forgetting rate differs little
between individuals. He concluded that the difference in performance
can be explained by mnemonic representation skills.
He went on to hypothesize that basic training in mnemonic
techniques can help overcome those differences in part. He asserted that
the best methods for increasing the strength of memory are:
better memory representation (e.g. with mnemonic techniques)
His premise was that each repetition in learning increases the
optimum interval before the next repetition is needed (for near-perfect
retention, initial repetitions may need to be made within days, but
later they can be made after years). He discovered that information is
easier to recall when it’s built upon things you already know, and the
forgetting curve was flattened by every repetition. It appeared that by
applying frequent training in learning, the information was solidified
by repeated recalling.
Later research also suggested that, other than the two factors
Ebbinghaus proposed, higher original learning would also produce slower
forgetting. The more information was originally learned, the slower the
forgetting rate would be.
Spending time each day to remember information will greatly
decrease the effects of the forgetting curve. Some learning consultants
claim reviewing material in the first 24 hours after learning
information is the optimum time to re-read notes and reduce the amount
of knowledge forgotten.
Evidence suggests waiting 10–20% of the time towards when the
information will be needed is the optimum time for a single review.
However, some memories remain free from the detrimental effects
of interference and do not necessarily follow the typical forgetting
curve as various noise and outside factors influence what information
would be remembered.
There is debate among supporters of the hypothesis about the shape of
the curve for events and facts that are more significant to the subject. Some supporters, for example, suggest that memories of shocking events such as the Kennedy Assassination or 9/11 are vividly imprinted in memory (flashbulb memory).
Others have compared contemporaneous written recollections with
recollections recorded years later, and found considerable variations as
the subject's memory incorporates after-acquired information. There is considerable research in this area as it relates to eyewitness identification testimony, and eyewitness accounts are found demonstrably unreliable.
Equations
Many
equations have since been proposed to approximate forgetting, perhaps
the simplest being an exponential curve described by the equation:
where is retrievability (a measure of how easy it is to retrieve a piece of information from memory), is stability of memory (determines how fast falls over time in the absence of training, testing or other recall), and is time.
Simple equations such as this one were found by Rubin, Hinton, and Wenzel (1999) to provide a good fit to the available data.
Ebbinghaus was born in Barmen, in the Rhine Province of the Kingdom of Prussia, as the son of a wealthy merchant, Carl Ebbinghaus. Little is known about his infancy except that he was brought up in the Lutheran faith and was a pupil at the town Gymnasium. At the age of 17 (1867), he began attending the University of Bonn, where he had planned to study history and philology. However, during his time there he developed an interest in philosophy. In 1870, his studies were interrupted when he served with the Prussian Army in the Franco-Prussian War. Following this short stint in the military, Ebbinghaus finished his dissertation on Eduard von Hartmann's Philosophie des Unbewussten
(philosophy of the unconscious) and received his doctorate on August
16, 1873, when he was 23 years old. During the next three years, he
spent time at Halle and Berlin.
Professional career
After acquiring his PhD,
Ebbinghaus moved around England and France, tutoring students to
support himself. In England, he may have taught in two small schools in
the south of the country (Gorfein, 1885). In London, in a used bookstore, he came across Gustav Fechner's book Elemente der Psychophysik (Elements of Psychophysics),
which spurred him to conduct his famous memory experiments. After
beginning his studies at the University of Berlin, he founded the third
psychological testing lab in Germany (third to Wilhelm Wundt and Georg Elias Müller). He began his memory studies here in 1879. In 1885 — the same year that he published his monumental work, Über das Gedächtnis. Untersuchungen zur experimentellen Psychologie, later published in English under the title Memory: A Contribution to Experimental Psychology — he was made a professor at the University of Berlin, most likely in recognition of this publication. In 1890, along with Arthur König, he founded the psychological journal Zeitschrift für Physiologie und Psychologie der Sinnesorgane ("The Psychology and Physiology of the Sense Organs'").
In 1894, he was passed over for promotion to head of the philosophy department at Berlin, most likely due to his lack of publications. Instead, Carl Stumpf received the promotion. As a result of this, Ebbinghaus left to join the University of Breslau (now Wrocław, Poland), in a chair left open by Theodor Lipps (who took over Stumpf's position when he moved to Berlin). While in Breslau,
he worked on a commission that studied how children's mental ability
declined during the school day. While the specifics on how these mental
abilities were measured have been lost, the successes achieved by the
commission laid the groundwork for future intelligence testing. At Breslau, he again founded a psychological testing laboratory.
In 1902, Ebbinghaus published his next piece of writing entitled Die Grundzüge der Psychologie (Fundamentals of Psychology). It was an instant success and continued to be long after his death. In 1904, he moved to Halle where he spent the last few years of his life. His last published work, Abriss der Psychologie (Outline of Psychology) was published six years later, in 1908. This, too, continued to be a success, being re-released in eight different editions. Shortly after this publication, on February 26, 1909, Ebbinghaus died from pneumonia at the age of 59.
Research on memory
Ebbinghaus was determined to show that higher mental processes could actually be studied using experimentation,
which was in opposition to the popularly held thought of the time. To
control for most potentially confounding variables, Ebbinghaus wanted to
use simple acoustic encoding and maintenance rehearsal for which a list of words could have been used. As learning
would be affected by prior knowledge and understanding, he needed
something that could be easily memorized but which had no prior
cognitive associations. Easily formable associations with regular words
would interfere with his results, so he used items that would later be
called "nonsense syllables" (also known as the CVC trigram). A nonsense syllable is a consonant-vowel-consonant
combination, where the consonant does not repeat and the syllable does
not have prior meaning. BOL (sounds like "Ball") and DOT (already a
word) would then not be allowed. However, syllables such as DAX, BOK,
and YAT would all be acceptable (though Ebbinghaus left no examples).
After eliminating the meaning-laden syllables, Ebbinghaus ended up with
2,300 resultant syllables.
Once he had created his collection of syllables, he would pull out a
number of random syllables from a box and then write them down in a
notebook. Then, to the regular sound of a metronome, and with the same voice inflection, he would read out the syllables, and attempt to recall them at the end of the procedure. One investigation alone required 15,000 recitations.
It was later determined that humans impose meaning even on
nonsense syllables to make them more meaningful. The nonsense syllable
PED (which is the first three letters of the word "pedal") turns out to
be less nonsensical than a syllable such as KOJ; the syllables are said
to differ in association value.
It appears that Ebbinghaus recognized this, and only referred to the
strings of syllables as "nonsense" in that the syllables might be less
likely to have a specific meaning and he should make no attempt to make
associations with them for easier retrieval.
Limitations to memory research
There
are several limitations to his work on memory. The most important one
was that Ebbinghaus was the only subject in his study. This limited the
study's generalizability
to the population. Although he attempted to regulate his daily routine
to maintain more control over his results, his decision to avoid the use
of participants sacrificed the external validity of the study despite sound internal validity.
In addition, although he tried to account for his personal influences,
there is an inherent bias when someone serves as researcher as well as
participant. Also, Ebbinghaus's memory research halted research in
other, more complex matters of memory such as semantic and procedural memory and mnemonics.
Contributions to memory
In 1885, he published his groundbreaking Über das Gedächtnis ("On Memory", later translated to English as Memory. A Contribution to Experimental Psychology) in which he described experiments he conducted on himself to describe the processes of learning and forgetting.
Ebbinghaus made several findings that are still relevant and supported
to this day. First, Ebbinghaus made a set of 2,300 three letter
syllables to measure mental associations that helped him find that
memory is orderly. Second, and arguably his most famous finding, was the
forgetting curve. The forgetting curve describes the exponential loss of information that one has learned.
The sharpest decline occurs in the first twenty minutes and the decay
is significant through the first hour. The curve levels off after about
one day.
The learning curve
described by Ebbinghaus refers to how fast one learns information. The
sharpest increase occurs after the first try and then gradually evens
out, meaning that less and less new information is retained after each
repetition. Like the forgetting curve, the learning curve is
exponential. Ebbinghaus had also documented the serial position effect,
which describes how the position of an item affects recall. The two
main concepts in the serial position effect are recency and primacy. The
recency effect describes the increased recall of the most recent
information because it is still in the short-term memory. The primacy
effect causes better memory of the first items in a list due to
increased rehearsal and commitment to long-term memory.
Another important discovery is that of savings. This refers to the amount of information retained in the subconscious even after this information cannot be consciously accessed. Ebbinghaus would memorize a list of items until perfect recall
and then would not access the list until he could no longer recall any
of its items. He then would relearn the list, and compare the new
learning curve to the learning curve of his previous memorization of the
list. The second list was generally memorized faster, and this
difference between the two learning curves is what Ebbinghaus called
"savings". Ebbinghaus also described the difference between involuntary
and voluntary memory, the former occurring "with apparent spontaneity
and without any act of the will" and the latter being brought "into
consciousness by an exertion of the will".
Prior to Ebbinghaus, most contributions to the study of memory
were undertaken by philosophers and centered on observational
description and speculation. For example, Immanuel Kant used pure description to discuss recognition and its components and Sir Francis Bacon
claimed that the simple observation of the rote recollection of a
previously learned list was "no use to the art" of memory. This
dichotomy between descriptive and experimental study of memory would
resonate later in Ebbinghaus's life, particularly in his public argument
with former colleague Wilhelm Dilthey. However, more than a century before Ebbinghaus, Johann Andreas Segner invented the "Segner-wheel" to see the length of after-images by seeing how fast a wheel with a hot coal attached had to move for the red ember circle from the coal to appear complete.
Ebbinghaus's effect on memory research was almost immediate. With
very few works published on memory in the previous two millennia,
Ebbinghaus's works spurred memory research in the United States in the 1890s, with 32 papers published in 1894 alone. This research was coupled with the growing development of mechanized mnemometers, or devices that aided in the recording and study of memory.
The reaction to his work in his day was mostly positive. Noted psychologist William James called the studies "heroic" and said that they were "the single most brilliant investigation in the history of psychology". Edward B. Titchener also mentioned that the studies were the greatest undertaking in the topic of memory since Aristotle.
Other contributions
Ebbinghaus
can also be credited with pioneering sentence completion exercises,
which he developed in studying the abilities of schoolchildren. It was
these same exercises that Alfred Binet had borrowed and incorporated into the Binet-Simon intelligence scale. Sentence completion had since then also been used extensively in memory research, especially in tapping into measures of implicit memory, and also has been used in psychotherapy as a tool to help tap into the motivations and drives of the patient. He had also influenced Charlotte Bühler, who along with Lev Vygotsky and others went on to study language meaning and society.
The Ebbinghaus Illusion. Note that the orange circles appear of different sizes, despite them being equal.
Ebbinghaus is also credited with discovering an optical illusion now known after its discoverer—the Ebbinghaus illusion,
which is an illusion of relative size perception. In the best-known
version of this illusion, two circles of identical size are placed near
to each other and one is surrounded by large circles while the other is
surrounded by small circles; the first central circle then appears
smaller than the second central circle. This illusion is now used
extensively in research in cognitive psychology, to find out more about the various perception pathways in our brain.
Ebbinghaus is also largely credited with drafting the first
standard research report. In his paper on memory, Ebbinghaus arranged
his research into four sections: the introduction, the methods, the
results, and a discussion section. The clarity and organization of this
format was so impressive to contemporaries that it has now become
standard in the discipline, and all research reports follow the same
standards laid out by Ebbinghaus.
After Ebbinghaus worked on memory, he also had a contribution
with color vision. In 1890, Ebbinghaus came up with the double pyramid
design where corners were rounded off.
Unlike notable contemporaries like Titchener and James, Ebbinghaus did not promote any specific school of psychology
nor was he known for extensive lifetime research, having done only
three works. He never attempted to bestow upon himself the title of the
pioneer of experimental psychology, did not seek to have any "disciples", and left the exploitation of the new field to others.
Discourse on the nature of psychology
In
addition to pioneering experimental psychology, Ebbinghaus was also a
strong defender of this direction of the new science, as is illustrated
by his public dispute with University of Berlin colleague, Wilhelm Dilthey.
Shortly after Ebbinghaus left Berlin in 1893, Dilthey published a paper
extolling the virtues of descriptive psychology, and condemning
experimental psychology as boring, claiming that the mind was too complex, and that introspection
was the desired method of studying the mind. The debate at the time had
been primarily whether psychology should aim to explain or understand
the mind and whether it belonged to the natural or human sciences.
Many had seen Dilthey's work as an outright attack on experimental
psychology, Ebbinghaus included, and he responded to Dilthey with a
personal letter and also a long scathing public article. Amongst his
counterarguments against Dilthey he mentioned that it is inevitable for
psychology to do hypothetical
work and that the kind of psychology that Dilthey was attacking was the
one that existed before Ebbinghaus's "experimental revolution". Charlotte Bühler
echoed his words some forty years later, stating that people like
Ebbinghaus "buried the old psychology in the 1890s". Ebbinghaus
explained his scathing review by saying that he could not believe that
Dilthey was advocating the status quo of structuralists like Wilhelm Wundt and Titchener and attempting to stifle psychology's progress.
Some contemporary texts still describe Ebbinghaus as a
philosopher rather than a psychologist and he had also spent his life as
a professor of philosophy. However, Ebbinghaus himself would probably
describe himself as a psychologist considering that he fought to have
psychology viewed as a separate discipline from philosophy.
Influences
There
has been some speculation as to what influenced Ebbinghaus in his
undertakings. None of his professors seem to have influenced him, nor
are there suggestions that his colleagues affected him. Von Hartmann's
work, on which Ebbinghaus based his doctorate, did suggest that higher
mental processes were hidden from view, which may have spurred
Ebbinghaus to attempt to prove otherwise. The one influence that has
always been cited as having inspired Ebbinghaus was Gustav Fechner's two-volume Elemente der Psychophysik.
("Elements of Psychophysics", 1860), a book which he purchased
second-hand in England. It is said that the meticulous mathematical
procedures impressed Ebbinghaus so much that he wanted to do for psychology what Fechner had done for psychophysics. This inspiration is also evident in that Ebbinghaus dedicated his second work Principles of Psychology to Fechner, signing it "I owe everything to you."
In industry, models of the learning or experience curve effect express the relationship between experience producing a good and efficiency
of production, ie. efficiency gains that follow investment in the
effort. The effect has large implications for effect of market share,
which can increasing competitive advantage over time due to experience
curve effects.
History: from psychological learning curves to the learning curve effect
An early empirical demonstration of learning curves was produced in 1885 by the German psychologist Hermann Ebbinghaus. Ebbinghaus was investigating the difficulty of memorizing verbal stimuli.
He found that performance increased in proportion to experience
(practice and testing) on memorising the word set (More detail about
the complex processes of learning are discussed in the Learning curve article).
Wright's law and the discovery of the learning curve effect
Work
in human memory was found later to generalize - the more times a task
has been performed, the less time is required on each subsequent
iteration. This relationship was probably first quantified in the
industrial setting in 1936 by Theodore Paul Wright, an engineer at Curtiss-Wright in the United States, Wright found that every time total aircraft
production doubled, the required labour time for new craft fell by 20%.
Subsequent studies in other industries have yielded different values
ranging from only a couple of percent up to 30%, but in most cases, the
value in each industry was a constant percentage and did not vary at
different scales of operation. The learning curve model posits that for
each doubling of the total quantity of items produced, costs decrease by
a fixed proportion. Generally, the production of any good or service
shows the learning curve or experience curve effect. Each time
cumulative volume doubles, value added costs (including administration,
marketing, distribution, and manufacturing) fall by a constant
percentage.
The phrase experience curve was proposed by Bruce D. Henderson and the Boston Consulting Group (BCG) based on analyses of overall cost behavior in the 1960s. While accepting that the learning curve formed an attractive explanation, he used the name experience curve, suggesting that "the two are related, but quite different." In 1968, Henderson and BCG began to emphasize the implications of the experience curve for strategy. Research by BCG in the 1960s and 70s observed experience curve effects for various industries that ranged from 10 to 25%.
Unit curve
Mathematically,
Wright's law takes the form of a power function. Empirical research has
validated the following mathematical form for the unit cost of
producing unit-number x (Px), starting with unit P1 for a wide variety of different products and services:
,
where 1-b is the proportion reduction in the unit cost with
each doubling in the cumulative production. To see this, note the
following:
The exponent b is a statistical parameter and thus does not
exactly predict the unit cost of producing any future unit. However, it
has been found to be useful in many contexts. Across numerous
industries (see below), estimates of b range from 0.75 to 0.9 (i.e., 1-b ranges from 0.1 to 0.25).
The unit curve was expressed in slightly different nomenclature by Henderson:
These effects are often expressed graphically. The curve is plotted
with the cumulative units produced on the horizontal axis and unit cost
on the vertical axis. The BCG group used the value of b to name a given
industry curve. Thus a curve showing a 15% cost reduction for every
doubling of output was called an “85% experience curve”.
Reasons for the effect
Examples
NASA quotes the following experience curves:
The primary reason for why experience and learning curve effects
apply is the complex processes of learning involved. As discussed in
the main article,
learning generally begins with making successively larger finds and
then successively smaller ones. The equations for these effects come
from the usefulness of mathematical models for certain somewhat
predictable aspects of those generally non-deterministic processes.
They include:
Labour efficiency: Workers become physically more
dexterous. They become mentally more confident and spend less time
hesitating, learning, experimenting, or making mistakes. Over time they
learn short-cuts and improvements. This applies to all employees and
managers, not just those directly involved in production.
Standardization, specialization, and methods improvements: As
processes, parts, and products become more standardized, efficiency
tends to increase. When employees specialize in a limited set of tasks,
they gain more experience with these tasks and operate at a faster rate.
Technology-driven learning: Automated production technology
and information technology can introduce efficiencies as they are
implemented and people learn how to use them efficiently and
effectively.
Better use of equipment: As total production has increased,
manufacturing equipment will have been more fully exploited, lowering
fully accounted unit costs. In addition, purchase of more productive
equipment can be justifiable.
Changes in the resource mix: As a company acquires experience, it can alter its mix of inputs and thereby become more efficient.
Product redesign: As the manufacturers and consumers have
more experience with the product, they can usually find improvements.
This filters through to the manufacturing process. A good example of
this is Cadillac's testing of various "bells and whistles" specialty
accessories. The ones that did not break became mass-produced in other
General Motors products; the ones that didn't stand the test of user
"beatings" were discontinued, saving the car company money. As General
Motors produced more cars, they learned how to best produce products
that work for the least money.
Network-building and use-cost reductions (network effects):
As a product enters more widespread use, the consumer uses it more
efficiently because they're familiar with it. One fax machine in the
world can do nothing, but if everyone has one, they build an
increasingly efficient network of communications. Another example is
email accounts; the more there are, the more efficient the network is,
the lower everyone's cost per utility of using it.
Shared experience effects: Experience curve effects are
reinforced when two or more products share a common activity or
resource. Any efficiency learned from one product can be applied to the
other products. (This is related to the principle of least astonishment.)
Experience curve discontinuities
The experience curve effect can on occasion come to an abrupt stop.
Graphically, the curve is truncated. Existing processes become obsolete
and the firm must upgrade to remain competitive. The upgrade will mean
the old experience curve will be replaced by a new one. This occurs
when:
Competitors introduce new products or processes that you must respond to
Key suppliers have much bigger customers that determine the price of
products and services, and that becomes the main cost driver for the
product
Technological change requires that you or your suppliers change processes
The experience curve strategies must be re-evaluated because
they are not producing a marketing mix that the market values
Strategic consequences of the effect
BCG founder Henderson published on the development of the experience curve. According to Henderson, its first "attempt to explain cost behavior over time in a process industry" began in 1966.
The datum he focussed on was the striking correlation between
competitive profitability and market share. Using price data in the
semiconductor industry supplied by the Electronic Industries
Association, he suggested that not one but two patterns emerged.
"In one pattern, prices, in current dollars, remained
constant for long periods and then began a relatively steep and long
continued decline in constant dollars. In the other pattern, prices, in
constant dollars, declined steadily at a constant rate of about 25
percent each time accumulated experience doubled. That was the
experience curve."
The suggestion was that failure of production to show the learning
curve effect was a risk indicator. The BCG strategists examined the
consequences of the experience effect for businesses. They concluded
that because relatively low cost of operations is a very powerful
strategic advantage, firms should invest in maximising these learning
and experience effects and that market share is underestimated as an
enabler of this investment.
The reasoning is increased activity leads to increased learning, which
leads to lower costs, which can lead to lower prices, which can lead to
increased market share, which can lead to increased profitability and
market dominance. This was particularly true when a firm had an early
leadership in market share. It was suggested that if a company cannot
get enough market share to be competitive, it should exit that business
and concentrate resources where it was possible to take advantage of
experience effects and gain (preferably dominant) market share. The BCG
strategists developed product portfolio techniques like the BCG Matrix (in part) to manage this strategy.
One consequence of experience curve strategy is that it predicts
that cost savings should be passed on as price decreases rather than
kept as profit margin increases. The BCG strategists felt that
maintaining a relatively high price, although very profitable in the
short run, spelled disaster for the strategy in the long run. High
profits would encourage competitors to enter the market, triggering a
steep price decline and a competitive shakeout.
If prices were reduced as unit costs fell (due to experience curve
effects), then competitive entry would be discouraged while market share
increases should increase overall profitability.
Criticisms
Ernst R. Berndt claims that in most organizations, experience effects are so closely intertwined with economies of scale (efficiencies arising from an increased scale of production) that it is impossible to separate the two.
In practice, this view suggests, economies of scale coincide with
experience effects (efficiencies arising from the learning and
experience gained over repeated activities). The approach, however,
accepts the existence of both as underlying causes. Economies of scale
afford experience and experience may afford economies of scale.
Attempts to use the learning curve effect to improve competitive
advantage, for instance by pre-emptively expanding production have been
criticised, with factors such as bounded rationality and durable
products cited as reasons for this.
As quantity of production increases from Q to Q2, the average cost of each unit decreases from C to C1. LRAC is the long-run average cost
In microeconomics, economies of scale
are the cost advantages that enterprises obtain due to their scale of
operation (typically measured by the amount of output produced), with cost per unit
of output decreasing with increasing scale. At the basis of economies
of scale there may be technical, statistical, organizational or related
factors to the degree of market control.
Economies of scale apply to a variety of organizational and
business situations and at various levels, such as a production, plant
or an entire enterprise. When average costs start falling as output
increases, then economies of scale occur.
Some economies of scale, such as capital cost of manufacturing
facilities and friction loss of transportation and industrial equipment,
have a physical or engineering basis.
Another source of scale economies is the possibility of purchasing inputs at a lower per-unit cost when they are purchased in large quantities.
The economic concept dates back to Adam Smith and the idea of obtaining larger production returns through the use of division of labor. Diseconomies of scale are the opposite.
Economies of scale often have limits, such as passing the optimum
design point where costs per additional unit begin to increase. Common
limits include exceeding the nearby raw material supply, such as wood
in the lumber, pulp and paper industry.
A common limit for a low cost per unit weight commodities is saturating
the regional market, thus having to ship product uneconomic distances.
Other limits include using energy less efficiently or having a higher
defect rate.
Large producers are usually efficient at long runs of a product
grade (a commodity) and find it costly to switch grades frequently.
They will, therefore, avoid specialty grades even though they have
higher margins. Often smaller (usually older) manufacturing facilities
remain viable by changing from commodity-grade production to specialty
products.
Economies of scale must be distinguished from economies stemming
from an increase in the production of a given plant. When a plant is
used below its optimal production capacity,
increases in its degree of utilization bring about decreases in the
total average cost of production. As noticed, among the others, by Nicholas Georgescu-Roegen (1966) and Nicholas Kaldor (1972) these economies are not economies of scale.
Overview
The simple meaning of economies of scale is doing things more efficiently with increasing size. Common sources of economies of scale are purchasing
(bulk buying of materials through long-term contracts), managerial
(increasing the specialization of managers), financial (obtaining lower-interest charges when borrowing from banks and having access to a greater range of financial instruments), marketing (spreading the cost of advertising over a greater range of output in media markets), and technological (taking advantage of returns to scale in the production function). Each of these factors reduces the long run average costs (LRAC) of production by shifting the short-run average total cost (SRATC) curve down and to the right.
Economies of scale is a concept that may explain real-world
phenomena such as patterns of international trade or the number of firms
in a market. The exploitation of economies of scale helps explain why
companies grow large in some industries. It is also a justification for free trade
policies, since some economies of scale may require a larger market
than is possible within a particular country—for example, it would not
be efficient for Liechtenstein
to have its own carmaker if they only sold to their local market. A
lone carmaker may be profitable, but even more so if they exported cars
to global markets in addition to selling to the local market. Economies
of scale also play a role in a "natural monopoly".
There is a distinction between two types of economies of scale:
internal and external. An industry that exhibits an internal economy of
scale is one where the costs of production fall when the number of firms
in the industry drops, but the remaining firms increase their
production to match previous levels. Conversely, an industry exhibits an
external economy of scale when costs drop due to the introduction of
more firms, thus allowing for more efficient use of specialized services
and machinery.
The determinants of economies of scale
Physical and engineering basis: economies of increased dimension
Some of the economies of scale recognized in engineering have a physical basis, such as the square-cube law,
by which the surface of a vessel increases by the square of the
dimensions while the volume increases by the cube. This law has a
direct effect on the capital cost of such things as buildings,
factories, pipelines, ships and airplanes.
In structural engineering, the strength of beams increases with the cube of the thickness.
Drag
loss of vehicles like aircraft or ships generally increases less than
proportional with increasing cargo volume, although the physical details
can be quite complicated. Therefore, making them larger usually results
in less fuel consumption per ton of cargo at a given speed.
Heat loss from industrial processes vary per unit of volume for
pipes, tanks and other vessels in a relationship somewhat similar to the
square-cube law.
In some productions, an increase in the size of the plant reduces the
average variable cost, thanks to the energy savings resulting from the
lower dispersion of heat.
Economies of increased dimension are often misinterpreted because
of the confusion between indivisibility and three-dimensionality of
space. This confusion arises from the fact that three-dimensional
production elements, such as pipes and ovens, once installed and
operating, are always technically indivisible. However, the economies of
scale due to the increase in size do not depend on indivisibility but
exclusively on the three-dimensionality of space. Indeed, indivisibility
only entails the existence of economies of scale produced by the
balancing of productive capacities, considered above; or of increasing
returns in te utilisation of a single plant, due to its more efficient
use as the quantity produced increases. However, this latter phenomenon
has nothing to do with the economies of scale which, by definition, are
linked to the use of a larger plant.
Economies in holding stocks and reserves
At
the base of economies of scale there are also returns to scale linked
to statistical factors. In fact, the greater of the number of resources
involved, the smaller, in proportion, is the quantity of reserves
necessary to cope with unforeseen contingencies (for instance, machine
spare parts, inventories, circulating capital, etc.).
Transaction economies
A
larger scale generally determines greater bargaining power over input
prices and therefore benefits from pecuniary economies in terms of
purchasing raw materials and intermediate goods compared to companies
that make orders for smaller amounts. In this case we speak of pecuniary
economies, to highlight the fact that nothing changes from the
"physical" point of view of the returns to scale. Furthermore, supply
contracts entail fixed costs which lead to decreasing average costs if
the scale of production increases.
Economies deriving from the balancing of production capacity
Economies
of productive capacity balancing derives from the possibility that a
larger scale of production involves a more efficient use of the
production capacities of the individual phases of the production
process. If the inputs are indivisible and complementary, a small scale
may be subject to idle times or to the underutilization of the
productive capacity of some sub-processes. A higher production scale can
make the different production capacities compatible. The reduction in
machinery idle times is crucial in the case of a high cost of machinery.
Economies resulting from the division of labour and the use of superior techniques
A
larger scale allows for a more efficient division of labour. The
economies of division of labour derive from the increase in production
speed, from the possibility of using specialized personnel and adopting
more efficient techniques. An increase in the division of labour
inevitably leads to changes in the quality of inputs and outputs.
Managerial Economics
Many
administrative and organizational activities are mostly cognitive and,
therefore, largely independent of the scale of production.
When the size of the company and the division of labour increase, there
are a number of advantages due to the possibility of making
organizational management more effective and perfecting accounting and
control techniques.
Furthermore, the procedures and routines that turned out to be the
best can be reproduced by managers at different times and places.
Learning and growth economies
Learning and growth economies
are at the base of dynamic economies of scale, associated with the
process of growth of the scale dimension and not to the dimension of
scale per se. Learning by doing implies improvements in the ability to
perform and promotes the introduction of incremental innovations with a
progressive lowering of average costs. Learning economies are directly proportional to the cumulative production (experience curve).
Growth economies occur when a company acquires an advantage by
increasing its size. These economies are due to the presence of some
resource or competence that is not fully utilized, or to the existence
of specific market positions that create a differential advantage in
expanding the size of the firms. That growth economies disappear once
the scale size expansion process is completed. For example, a company
that owns a supermarket chain benefits from an economy of growth if,
opening a new supermarket, it gets an increase in the price of the land
it owns around the new supermarket. The sale of these lands to economic
operators, who wish to open shops near the supermarket, allows the
company in question to make a profit, making a profit on the revaluation
of the value of building land.
Capital and operating cost
Overall
costs of capital projects are known to be subject to economies of
scale. A crude estimate is that if the capital cost for a given sized
piece of equipment is known, changing the size will change the capital
cost by the 0.6 power of the capacity ratio (the point six to the power
rule).
In estimating capital cost, it typically requires an
insignificant amount of labor, and possibly not much more in materials,
to install a larger capacity electrical wire or pipe having
significantly greater capacity.
The cost of a unit of capacity of many types of equipment, such
as electric motors, centrifugal pumps, diesel and gasoline engines,
decreases as size increases. Also, the efficiency increases with size.
Crew size and other operating costs for ships, trains and airplanes
Operating crew size for ships, airplanes, trains, etc., does not increase in direct proportion to capacity.
(Operating crew consists of pilots, co-pilots, navigators, etc. and
does not include passenger service personnel.) Many aircraft models
were significantly lengthened or "stretched" to increase payload.
Many manufacturing facilities, especially those making bulk
materials like chemicals, refined petroleum products, cement and paper,
have labor requirements that are not greatly influenced by changes in
plant capacity. This is because labor requirements of automated
processes tend to be based on the complexity of the operation rather
than production rate, and many manufacturing facilities have nearly the
same basic number of processing steps and pieces of equipment,
regardless of production capacity.
Economical use of byproducts
Karl Marx noted that large scale manufacturing allowed economical use of products that would otherwise be waste.
Marx cited the chemical industry as an example, which today along with
petrochemicals, remains highly dependent on turning various residual
reactant streams into salable products. In the pulp and paper industry
it is economical to burn bark and fine wood particles to produce process steam and to recover the spent pulping chemicals for conversion back to a usable form.
Economies of scale and returns to scale
Economies
of scale is related to and can easily be confused with the theoretical
economic notion of returns to scale. Where economies of scale refer to a
firm's costs, returns to scale describe the relationship between inputs
and outputs in a long-run (all inputs variable) production function. A
production function has constant returns to scale if increasing all inputs by some proportion results in output increasing by that same proportion. Returns are decreasing if, say, doubling inputs results in less than double the output, and increasing
if more than double the output. If a mathematical function is used to
represent the production function, and if that production function is homogeneous,
returns to scale are represented by the degree of homogeneity of the
function. Homogeneous production functions with constant returns to
scale are first degree homogeneous, increasing returns to scale are
represented by degrees of homogeneity greater than one, and decreasing
returns to scale by degrees of homogeneity less than one.
If the firm is a perfect competitor in all input markets, and
thus the per-unit prices of all its inputs are unaffected by how much of
the inputs the firm purchases, then it can be shown that at a
particular level of output, the firm has economies of scale if and only
if it has increasing returns to scale, has diseconomies of scale if and
only if it has decreasing returns to scale, and has neither economies
nor diseconomies of scale if it has constant returns to scale. In this case, with perfect competition
in the output market the long-run equilibrium will involve all firms
operating at the minimum point of their long-run average cost curves
(i.e., at the borderline between economies and diseconomies of scale).
If, however, the firm is not a perfect competitor in the input
markets, then the above conclusions are modified. For example, if there
are increasing returns to scale in some range of output levels, but the
firm is so big in one or more input markets that increasing its
purchases of an input drives up the input's per-unit cost, then the firm
could have diseconomies of scale in that range of output levels.
Conversely, if the firm is able to get bulk discounts of an input, then
it could have economies of scale in some range of output levels even if
it has decreasing returns in production in that output range.
In essence, returns to scale refer to the variation in the relationship between inputs and output.
This relationship is therefore expressed in "physical" terms. But when
talking about economies of scale, the relation taken into consideration
is that between the average production cost and the dimension of scale.
Economies of scale therefore are affected by variations in input prices.
If input prices remain the same as their quantities purchased by the
firm increase, the notions of increasing returns to scale and economies
of scale can be considered equivalent. However, if input prices vary in
relation to their quantities purchased by the company, it is necessary
to distinguish between returns to scale and economies of scale. The
concept of economies of scale is more general than that of returns to
scale since it includes the possibility of changes in the price of
inputs when the quantity purchased of inputs varies with changes in the
scale of production.
The literature assumed that due to the competitive nature of reverse auctions,
and in order to compensate for lower prices and lower margins,
suppliers seek higher volumes to maintain or increase the total revenue.
Buyers, in turn, benefit from the lower transaction costs and economies
of scale that result from larger volumes. In part as a result, numerous
studies have indicated that the procurement volume must be sufficiently
high to provide sufficient profits to attract enough suppliers, and
provide buyers with enough savings to cover their additional costs.
However, surprisingly enough, Shalev and Asbjornse found, in
their research based on 139 reverse auctions conducted in the public
sector by public sector buyers, that the higher auction volume, or
economies of scale, did not lead to better success of the auction. They
found that auction volume did not correlate with competition, nor with
the number of bidders, suggesting that auction volume does not promote
additional competition. They noted, however, that their data included a
wide range of products, and the degree of competition in each market
varied significantly, and offer that further research on this issue
should be conducted to determine whether these findings remain the same
when purchasing the same product for both small and high volumes.
Keeping competitive factors constant, increasing auction volume may
further increase competition.
Economies of scale in the history of economic analysis
Economies of scale in classical economists
The first systematic analysis of the advantages of the division of labour capable of generating economies of scale, both in a static and dynamic sense, was that contained in the famous First Book of Wealth of Nations (1776) by Adam Smith, generally considered the founder of political economy as an autonomous discipline.
John Stuart Mill, in Chapter IX of the First Book of his Principles, referring to the work of Charles Babbage
(On the economics of machines and manufactories), widely analyses the
relationships between increasing returns and scale of production all
inside the production unit.
The economies of scale in Marx and Distributional consequences
In “Das Kapital” (1867), Karl Marx, referring to Charles Babbage,
extensively analyses economies of scale and concludes that they are one
of the factors underlying the ever-increasing concentration of capital.
Marx observes that in the capitalist system the technical conditions of
the work process are continuously revolutionized in order to increase
the surplus by improving the productive force of work. According to
Marx, with the cooperation of many workers brings about an economy in
the use of the means of production and an increase in productivity due
to the increase in the division of labour. Furthermore, the increase in
the size of the machinery allows significant savings in construction,
installation and operation costs. The tendency to exploit economies of
scale entails a continuous increase in the volume of production which,
in turn, requires a constant expansion of the size of the market.
However, if the market does not expand at the same rate as production
increases, overproduction crises can occur. According to Marx the
capitalist system is therefore characterized by two tendencies,
connected to economies of scale: towards a growing concentration and
towards economic crises due to overproduction.
In his 1844 Economic and Philosophic Manuscripts, Karl Marx
observes that economies of scale have historically been associated with
an increasing concentration of private wealth and have been used to
justify such concentration. Marx points out that concentrated private
ownership of large-scale economic enterprises is a historically
contingent fact, and not essential to the nature of such enterprises. In
the case of agriculture, for example, Marx calls attention to the sophistical nature of the arguments used to justify the system of concentrated ownership of land:
As for large landed property, its defenders have always
sophistically identified the economic advantages offered by large-scale
agriculture with large-scale landed property, as if it were not
precisely as a result of the abolition of property that this advantage,
for one thing, received its greatest possible extension, and, for
another, only then would be of social benefit.
Instead of concentrated private ownership of land, Marx recommends that economies of scale should instead be realized by associations:
Association, applied to land, shares the economic advantage of
large-scale landed property, and first brings to realization the
original tendency inherent in land-division, namely, equality. In the
same way association re-establishes, now on a rational basis, no longer
mediated by serfdom, overlordship and the silly mysticism of property,
the intimate ties of man with the earth, for the earth ceases to be an
object of huckstering, and through free labor and free enjoyment becomes
once more a true personal property of man.
Economies of scale in Marshall
Alfred Marshall
notes that "some, among whom Cournot himself", have considered "the
internal economies [...] apparently without noticing that their premises
lead inevitably to the conclusion that, whatever firm first gets a
good start will obtain a monopoly of the whole business of its trade …
". Marshall believes that there are factors that limit this trend toward monopoly, and in particular:
the death of the founder of the firm and the difficulty that the successors may have inherited his/her entrepreneurial skills;
the difficulty of reaching new markets for one's goods;
the growing difficulty of being able to adapt to changes in demand and to new techniques of production;
The effects of external economies, that is the particular type of
economies of scale connected not to the production scale of an
individual production unit, but to that of an entire sector.
Sraffa’s critique
Piero Sraffa
observes that Marshall, in order to justify the operation of the law of
increasing returns without it coming into conflict with the hypothesis
of free competition, tended to highlight the advantages of external
economies linked to an increase in the production of an entire sector
of activity. However, “those economies which are external from the
point of view of the individual firm, but internal as regards the
industry in its aggregate, constitute precisely the class which is most
seldom to be met with”. “In any case - Sraffa notes – in so far as
external economies of the kind in question exist, they are not linked
to be called forth by small increases in production”, as required by the
marginalist theory of price.
Sraffa points out that, in the equilibrium theory of the individual
industries, the presence of external economies cannot play an important
role because this theory is based on marginal changes in the quantities
produced.
Sraffa concludes that, if the hypothesis of perfect competition
is maintained, economies of scale should be excluded. He then suggests
the possibility of abandoning the assumption of free competition to
address the study of firms that have their own particular market. This stimulated a whole series of studies on the cases of imperfect competition
in Cambridge. However, in the succeeding years Sraffa will follow a
different path of research that will bring him to write and publish his
main work Production of commodities by means of commodities
(Sraffa, 1960). In this book Sraffa determines relative prices assuming
no changes in output, so that no question arises as to the variation or
constancy of returns.
Economies of scale and the tendency towards monopoly: ‘Cournot's dilemma’
It
has been noted that in many industrial sectors there are numerous
companies with different sizes and organizational structures, despite
the presence of significant economies of scale. This contradiction,
between the empirical evidence and the logical incompatibility between
economies of scale and competition, has been called the ‘Cournot
dilemma’.
As Mario Morroni observes, Cournot's dilemma appears to be unsolvable
if we only consider the effects of economies of scale on the dimension
of scale.
If, on the other hand, the analysis is expanded, including the aspects
concerning the development of knowledge and the organization of
transactions, it is possible to conclude that economies of scale do not
always lead to monopoly. In fact, the competitive advantages deriving
from the development of the firm's capabilities and from the management
of transactions with suppliers and customers can counterbalance those
provided by the scale, thus counteracting the tendency towards a
monopoly inherent in economies of scale. In other words, the
heterogeneity of the organizational forms and of the size of the
companies operating in a sector of activity can be determined by factors
regarding the quality of the products, the production flexibility, the
contractual methods, the learning opportunities, the heterogeneity of
preferences of customers who express a differentiated demand with
respect to the quality of the product, and assistance before and after
the sale. Very different organizational forms can therefore co-exist in
the same sector of activity, even in the presence of economies of scale,
such as, for example, flexible production on a large scale, small-scale
flexible production, mass production, industrial production based on
rigid technologies associated with flexible organizational systems and
traditional artisan production. The considerations regarding economies
of scale are therefore important, but not sufficient to explain the size
of the company and the market structure. It is also necessary to take
into account the factors linked to the development of capabilities and
the management of transaction costs.
