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between ˜historical™ and ˜logical™ time.
one.18 So long as the theory of the firm is confined to the ˜short period™
there need not be any logical problems. The problems that are alleged to
Problems with the firm™s long-run equilibrium exist arise only when the theory (i.e. the Principle of Substitution) is
applied in the long-run period to the short-run constraints.
Marshall™s Victorian style lends itself easily to distortion. What he meant
Applications of the Principle of Substitution involve some form of
by certain words in one place may not have the same meaning in another.
maximization (or minimization) facing fixed constraints. In the short run,
For example, the term ˜increasing returns™ is used in two different senses;
all the variables which (by definition) cannot be varied constitute the short-
both result from his implicit assumption that the firm is always growing;
run constraints (e.g. the short run may presume capital is fixed while labour
hence size and time go together. In Book V he uses the term to describe the
is variable). In the long run everything except the production function is
observation that average productivity rises over time for any given input
supposed to be variable (by definition); but this raises a major
levels [p. 377]. This use is at variance with modern usage. Earlier, in Book
methodological problem. Anything which is variable must logically be
IV, he employs the term in the limited modern sense to mean an increase in
subjected to the Principle of Substitution. This means that the variables that
output which is proportionally greater than the increase in the size of the
served as fixed constraints in the short run become endogenous variables in
firm [p. 266]. A similar confusion derives from his use of the term ˜margin™
the long run. But this also means that there are no constraints in the long
when discussing his ˜representative firm™. By definition, the representative
run and this leaves the Principle of Substitution inoperable in the long run.
firm is at the ˜turning point™ on the life-cycle trajectory. At that point
In the long period, then, the conjunction of the assumptions of a price-
average and marginal cost both equal price; thus it is possible to use the
taker, (a), of the changeability of all variables in the production function,
average and marginal magnitudes interchangeably. But another use of the
(b), and of profit maximization with regard to all changeable variables, (c),
term ˜marginal™ emerges when he refers to the representative firm™s
seems to deny any limit to the size of the individual firm “ as if size has
contribution to its industry™s output.
nothing to do with time (this interpretation of Marshall™s theory of the firm,
These confusions are merely irritants. The major problem is the one
by its focusing only on the internal logic of maximization, is quite contrary
which occurs when critics ignore the element of time inherent in the
to the views expressed in Book IV).
˜statical method™ whenever that method is applied to long-run equilibria (as
The methodological problem of explaining the size of the firm (as a
noted above). Although the difficulty is primarily logical, it results from
© LAWRENCE A. BOLAND
34 Principles of economics Marshall™s ˜Principles™ and the ˜element of Time™ 35
consequence of maximization) seems to have troubled many of Marshall™s example, while profit maximization implies the equality of marginal cost
followers although it did not seem to trouble him since his Principle of and marginal revenue, zero excess profits implies an equality between
Continuity discourages extreme viewpoints, such as long-run equilibria. average cost and average revenue (the price). Thus, when marginal revenue
The problem only arises when one attempts to apply the Principle of is less than the price, the firm must be operating where there are increasing
Substitution to the size of the firm in the long run. Today this problem is returns (since marginal cost must be less than average cost) which is
avoided (i.e. swept under the rug) by saying that one should only explain contrary to statement (b). Note that a firm can still be a price-taker even
the size of the industry. But this tactic merely raises other questions such as when its average revenue is falling with the quantity supplied.
What prevents any one firm from taking over the industry as a monopoly? It could be speculated that all of the controversies surrounding the long-
Although there is considerable discussion of industries in the Principles, run theory of the individual firm are merely about which of the five
statements should be dropped.19 Moreover, most of the controversies have
Marshall™s explanatory Principle of Substitution is applied only to the
(short-run) decisions of the individual firm. The industry is merely an ignored the element of time. There is no doubt that if one ignores the
epiphenomenon “ the logical consequence of what all individual firms do. element of time (which differs according to the statement one is
This is a standard neoclassical viewpoint. However, this viewpoint has considering) and, instead, views the above statements as holding at a single
always posed certain puzzles concerning the interaction of demand and (static) point of time, then logically some of the statements are mutually
supply in the market. The difficulty is that both the market and the industry inconsistent. As argued by Piero Sraffa [1926] and Joan Robinson
are defined for a specific good but the market is related to the individual [1933/69], something must give. A realistic interpretation is that the idea of
firm only through the going price. The price by itself says nothing about a price-taker, (a), must go, but Marshall™s statical method of dealing with
quantities except that aggregate quantity demanded must equal industry his problem of explanation “ distinguishing between very short periods and
supply. But, if individual firms must determine the quantity supplied the short run “ blocks that avenue. Allowing that prices may not be market-
independently of each other, the aggregate quantity supplied is only an determined would lead to a conclusion that is contrary to Marshall™s
epiphenomenon. In terms of Marshall™s individualistic methodology, this objective. If prices were not determined in a market, then demand could
approach to the relationship between firm and industry appears rather only play a role in the determination of the size of the industry “ that is,
mysterious. given the life-cycle, demand determines the number of firms in an industry
To overcome the mystery, Marshall offers the infamous heuristic fiction, “ in the long run. Prices are left to be determined by technical and social
the representative firm. Unfortunately, whenever one tries to use the considerations within and between firms (e.g. without ˜spoiling the market™
representative firm, instead of Book IV, to explain the size of the firm as [p. 313]).
just another consequence of an application of the Principle of Substitution, Today, such conclusions seem to be ideologically unacceptable or
another methodological problem is created. Recall that the representative mathematically inconvenient for economic theorists “ hence we simply
firm is defined [p. 285] as a firm at the ˜turning point™ and it is also a firm have stopped talking about Marshallian economics since what he promised
on the margin of the industry (older firms will be making less than normal (namely, a role for demand and utility maximization in the determination of
profits). As a profit maximizer at the turning point (where profits are just prices) seems doomed. What I am suggesting here is that things may not be
normal), the representative firm must face constant returns to scale (at least as desperate as everyone seems to fear. Perhaps all that is required is a
˜locally™ [see Baumol 1977, p. 578]). On the other hand, as a representative proper examination of the element of time.
of the industry, it must be constrained by the negatively sloped demand
curve. This latter constraint means that we have a fifth statement which
The distinction between logical and historical time
must be conjoined with the other four, namely:
Contrary to Marshall™s view, it is claimed by post-Keynesians that one
(e) The representative firm™s marginal revenue must be less than the
must carefully distinguish between ˜historical™ and ˜logical™ time [e.g.
price.
Robinson 1974]. Historical time refers to the usual calendar or clock time
The problem is that either statements (e) and (a) are mutually contradictory within which decision processes are irreversible. In logical time decisions
or one of the other statements must be denied. With respect to any one firm are reversible. For example, the life-cycle hypothesis is in historical time
it is not possible for all five statements to be true simultaneously. For since it is assumed that the firm always gets older; it cannot get younger.
© LAWRENCE A. BOLAND
36 Principles of economics Marshall™s ˜Principles™ and the ˜element of Time™ 37
One might say that this is because with the passage of time the firm is NOTES
learning but it cannot ˜unlearn™. The stability analysis of equilibrium theory 1 My approach is much like Negishi™s [1985]. As Negishi noted, ˜What is
is in logical time since the analysis is always conducted in terms of important is not whether a particular interpretation of a past theory is correct,
questions such as What if the price were higher or lower than the but whether it is useful in developing a new theory in the present™ [p. 2]. Thus
the onus is on me and Negishi to show that we have learned something from
equilibrium price? Logical time is concerned with conceivably possible
reading Marshall.
alternative worlds (regardless of actual events) at any given point in time,
2 For a discussion of the problem of time in neo-Walrasian and Austrian models,
whereas historical time may be concerned with the (necessarily) singular see Boland [1982a, Chapter 6].
event occurring at that time and the accumulation of learning which has 3 Unless indicated otherwise, all page references enclosed in brackets are to
transpired up to that point. Marshall [1920/49] which is the eighth edition of his Principles, reset in 1949.
4 Specifically, there must be what modern theorists might call the
The distinction between historical and logical time corresponds respect-
˜connectedness™ of choice options [see Chipman 1960].
ively to Books IV and V. But the intellectual separation of these concepts
5 The entrepreneur (or manager of the firm) must always make a judgement as to
(and Books) into mutually exclusive classes is a direct contradiction of whether day-to-day changes in the market will be long-lasting enough to justify
Marshall™s Principle of Continuity. Marshall does not claim that these investment and hiring decisions [see p. 314].
concepts or books should be separated. To the contrary, Books IV and V go 6 Remember, according to the Principle of Continuity everything is a matter of
degree.
together. Reality for Marshall is on the continuum between the two extreme
7 His reference to Cournot has often misled modern commentators to think that
concepts, that is, reality involves both Books in full measure. Any
the mathematical conception is all that Marshall was saying “ rather than the
explanation of the behaviour of an enterprise must be both grounded in more important methodological issue of relative degrees.
history (i.e. irreversible past decisions and learning) and explanatorily 8 This is one key element in the methodological ˜hidden agenda™ of neoclassical
complete (i.e. it must at least imply a stable determination of the values of economics. In neoclassical economics everything explained is seen to be the
consequence of the decisions made by individuals. The explained decisions are
the variables to which the Principle of Substitution has been applied).
represented by the endogenous variables in the explanatory model. The
acceptable exogenous variables are limited to natural givens (i.e. to things that
cannot be chosen). For more about the role of so-called methodological
SOME CRITICAL CONSIDERATIONS
individualism, see Boland [1982a, Chapter 2].
Most of modern neoclassical economic analysis concerns only the 9 One must be careful to distinguish between the logical validity of an
explanation and the verifiability of its truth status [see Boland, 1982a, pp.
mathematics of Book V. The reason, I think, is simply that Book V is the
102“4 and Chapter 1].
only part of Marshall™s Principles that is compatible with the
10 See note 5 of Chapter 1. For more on the role of inductivism in economics, see
methodological doctrine that dominates economic theory today “ Boland [1982a, Chapters 1 and 4].
Conventionalism “ namely, the methodology that restricts research to 11 The variables to be treated later, then, are ˜independent™ variables.
questions of logical validity instead of empirical truth. 20 Economists today 12 Marshall allows for price differences that result from transportation costs [p.
271].
do not wish to discuss the ˜truth™ of economic theories but only examine
13 That is, the very short run is not realistic [p. 304], and the logical consequence
their logical validity. The reason why logical validity rather than empirical
of a long-run equilibrium is a stationary state [p. 315, footnote 1]; but a
truth is the preferred object is that with the help of mathematical analysis stationary state is alleged to be ˜a fiction™ [p. 305].
the former can be established more quickly. Even though Marshall stressed 14 I will discuss Marshallian models of the firm which try to accommodate
the importance of gradual, slow change, those economists in a hurry will downward sloping demand curves in Chapter 5. For a different discussion, see
Boland [1986a, pp. 25“8].
find the logic or mathematics of static equilibria more interesting. Logical
15 Book V discusses only the logical possibility of a long-run equilibrium.
analysis can be very quick but real change takes real time and thus may not
16 For a discussion of the Instrumentalism associated with Friedman, see Boland
be disposed to conveniently easy analysis. [1982a, Chapter 9].
17 For a more detailed discussion of the question of time in neoclassical economic
theory, see Boland [1982a, pp. 97“8].
18 I will examine this relationship between these statements much further in
Chapter 5.
19 This is a speculation to be explored more fully in Chapter 5.
© LAWRENCE A. BOLAND
38 Principles of economics
20 Conventionalism is the defeatist doctrine based on the recognition that an
3 Marshall™s ˜Principle of
inductive proof is impossible. The Conventionalist alternative to inductive
Continuity™
proofs is to prove something else. Rather than look for a proof of the one true
theory, Conventionalism would have us choose the best theory recognizing that
the best may not be true (as I noted earlier in this chapter). See further, Agassi
[1963], Tarascio and Caldwell [1979] and Boland [1982a, Chapters 7 and 8].




If the book has any special character of its own, that may perhaps be
said to lie in the prominence which it gives to ... applications of the
Principle of Continuity.
Alfred Marshall [1920/49, p. vi]


Neoclassical economics is primarily a method of analysis. It is the method
of explaining all behaviour as the logical consequences of one behavioural
assumption “ namely, maximization subject to explicit constraints. 1 But,
many critics ask, is the maximization hypothesis a sufficient basis for
neoclassical economics? We saw in the previous chapter that according to
Marshall the use of the neoclassical maximization hypothesis necessarily
depends on what he called the Principle of Continuity. Contrary to the
modern preoccupation with Marshall™s Principle of Substitution (in the
form of the neoclassical maximization hypothesis), in the first preface to
his Principles Marshall clearly indicates that he gives primacy to the other
principle. If the Principle of Continuity is so important, clearly it must be a
fertile ground for critical study. For this reason it is important to understand
what Marshall meant by his Principle of Continuity and why he thought it
was so important.
The obvious reason for giving prominence to the relatively unknown
Principle of Continuity is that the continuity of the domain of the
maximization function is a necessary condition for application of the usual
assumption of maximizing behaviour.2 And even though continuity is
necessary, too often it is taken for granted. Thus, Marshall rightfully
devotes most of his Principles to an examination of the nature of an
economy to determine when the Principle of Continuity can be applied.
And for those circumstances where it is applicable, he devises an
admittedly ˜unrealistic™, mechanical method of overcoming the problem of
its necessity. This is his ˜statical method™ which I discussed in Chapter 2.
The objective of this chapter is a critical examination of the methodological
© LAWRENCE A. BOLAND
38 Principles of economics Marshall™s ˜Principle of Continuity™ 39
presumption of continuity. Since Marshall so strongly emphasizes It was apparently well known that ˜organization increases efficiency™ [p.
continuity, it is important that his method of assuring its applicability be 200]. For nineteenth-century economists, the key to this ˜biological
understood.3 doctrine™, whenever it applies to economics, was the recognition that the
growth of an organization goes hand-in-hand with an increasing division
among its functions “ which can be viewed as either increasing
MARSHALL™S PRINCIPLE OF CONTINUITY AND HIS
disaggregation or decentralization, so to speak, or as breaking down into
BIOLOGICAL PERSPECTIVE
smaller and more specialized functions. But the more specialized (and
The non-mathematical version of the application of the Principle of hence decentralized) a functional part becomes, the greater the need for
Continuity was very popular at the end of the nineteenth century “ organization to keep all the functional parts coordinated and cooperative.
especially among aficionados of biology. But Marshall wishes to go far The growth of an industrial organization was seen in these terms. But
beyond biology. He attempts to apply this principle to everything by Marshall recognizes that there were certain drawbacks to increasing
showing that everything is a matter of degree. Modern axiomatic model- organization.
builders discuss a form of the Principle of Continuity which is considered a While initially the increasing organization facilitates a division of labour
question of the ˜connectedness™ of choice options [e.g. see Chipman 1960]. and its resulting economies, eventually the size of the organization reaches
Specifically, the range of possible choice options must be continuous even a limit where, given the size of the market, further growth or development
when the continuum is subdivided into finite sets of categories (with no of the organization tends to reduce the effectiveness of the organization.
gaps or empty categories). Discreteness of choice options does not imply a Thus, Marshall can see a life-cycle continuum which goes from increasing
non-continuity. Even when one defines the choice set as a finite set of returns to decreasing returns. This proposition “ the inevitability of
discrete (or lumpy) options, the discreteness of the options must have been decreasing returns as size increases “ is considered to be true by analogy
defined over a continuous background range.4 That is, what we call a with biological systems. Marshall™s objective, however, is to establish both
discrete point will be defined in terms of one or more continuous the continuity of (average) returns and the fact that the (average) returns
dimensions such that the point is located at one distinct location on a must eventually diminish. Once that objective is reached, Marshall has, in
continuum. In short, it is impossible to avoid continuity, thus the only effect, shown that since an average cannot go from increasing to decreasing
question of applicability is whether there are external limits (constraints) without a fall in the margin, marginal returns must be diminishing with
on the choice set. regard to the extent of organizational development.
While the relatively unknown Book IV of Marshall™s Principles is A necessary condition for maximization of a function over the domain
seldom discussed today, it is central since it is devoted almost exclusively of a given variable is that the value of the first derivative (i.e. the margin)
to the question of whether one can truthfully assume the applicability of the be falling at the point of the maximum. In Book IV, Marshall establishes
Principle of Continuity. Marshall™s objective is to establish one of the the continuity and the necessity of a maximum by means of biological
primary conditions of maximization “ namely, the continuously diminish- analogies. With such analogies he also establishes the necessity (the ˜law™)
ing margin. He rests the weight of his argument for continuity primarily on of diminishing marginal productivity in the supply of all goods. It should
a foundation of biological analogies. Biology was an attractive source of be noted that Marshall has little difficulty in establishing the corresponding
analogies because in Marshall™s day it was seen primarily as the study of law of diminishing marginal utility. Marshall simply asserts in Book III
slow, gradual and progressive change along a continuum. In many cases, that there are continual ˜gradations of consumers™ demand™ [Chapter 3] and
Marshall™s argument for continuity of a variable rests only on an observa- that obviously all wants must be satiable “ that is, for any good there is a
tion that the variable can be changed in degrees. He refers to ˜man™s power quantity at which utility is maximum. Thus the result is obtained that if
of altering the character of the soil™ [p. 122]; and he often discusses growth: total utility can go continuously from zero to a positive value and back
Growth of Population [Chapter 4], and of Wealth [Chapter 7]. Although toward zero, average utility must eventually fall with increasing
growth can be distinguished from development, development usually consumption. By the same mathematical argument that is used for
depends on growth, thus Marshall devotes most of Book IV to the productivity, whenever the average is falling the marginal must be less than
consideration of the development of a growing enterprise. The continuum the average. Thus, specifically, marginal utility must (eventually) be falling
that Marshall wishes to establish concerns the ˜division of labour™. since eventually average utility must fall.
© LAWRENCE A. BOLAND
40 Principles of economics Marshall™s ˜Principle of Continuity™ 41
Marshall thus establishes to his satisfaction that every theory that has objective physics at the other extreme. Thus he draws parallels between
anything to do with demand or supply must involve ˜continuous economics and biology by seeing them both as studies of growth and
gradations™. Furthermore, by adding his life-cycle theory of the firm and development of organisms or organizations. The mutability of the character
his assertion that all wants are satiable, he has completed the foundation and purpose of individuals and groups (˜races™) of individuals in response
(i.e. the necessary conditions) for his programme of economic analysis. to changing conditions is the key to the parallels. He says the same must be
true for economic analysis [pp. 30“1].
Many writers, such as G.F. Shove [1942], have noted Marshall™s
MARSHALL™S PRINCIPLE OF SUBSTITUTION AS A RESEARCH
apparent love for biological analogies. But why was Marshall so
PROGRAMME
enamoured of biological analogies? Marshall™s advocacy of a biological
It would appear then that, once the Principle of Continuity is applied and perspective in economics appears to be due to the prevailing dissatisfaction
the appropriate diminishing margins are established, the way is clear for a with both the mechanics of physical analogies and the dreaded ˜hedonism™
direct application of the Principle of Substitution to all decisions implied by basing economics on the psychology of the individual.
concerning demand or supply. But as I noted in Chapter 2, Marshall claims Marshall™s use of biological analogies can be better appreciated when it
to the contrary; there are difficulties with the ˜element of Time™ [pp. 92 and is contrasted with the prevailing public opinion at the time he began work
274]. The difficulties, however, lie in his conception of the essence of on his Principles. Prior to the French Revolution at the end of the
˜scientific™ explanation “ namely, the notion of cause and effect relations. eighteenth century, most intellectuals on both sides of the Atlantic were
The problem with economic explanations, according to Marshall, is that at convinced that the apparent success of Newtonian mechanics demonstrated
any point of time there are too many exogenous conditions to consider. the correct approach to solving all social problems. Namely, if everyone

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