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upon each of them to secure the most accurate market information and, in
turn, to supply the market with the most attractive opportunities possible.
Only in the absence of market equilibrium, and in the state of incom-
plete knowledge on the part of market participants, does market agitation
and entrepreneurial activity emerge. Market equilibrium, and the set of
conditions necessary for the existence of equilibrium prices, represent a
mental construction whose most useful purpose is to help understand the
nature of the market activity that is characteristic of the absence of equi-
librium. Sometimes expressions are used by economists suggesting that the
market situation satisfying the conditions for equilibrium marked out by a
given set of data is achieved, more or less automatically and immediately,
by the mere existence of these data. Such a notion would overlook the
process whereby equilibrium could conceivably be reached. It would be-
stow upon the state of equilibrium an emphasis that hardly fits into the
analysis of any imaginable real world where the basic data of the market,
tastes and initial commodity endowments, are themselves subject to drastic
changes over time.
This becomes immediately apparent when one does, in fact attempt to
apply the analysis of this chapter to a world of change. Thus far we have
been employing "static" assumptions. We have been assuming that each
day each participant is endowed with the same initial commodity bundle
as yesterday; that each day each participant, regardless of past experiences,
has the same tastes as yesterday. The only difference between one market
day and the following one was that plans made for trading during the latter
day are based on estimates of prices learned through the market experience
of the previous day. Agitation in the market was caused by rapid changes
in plans made by the various participants as market experience steadily
spread more information and repeatedly indicated fresh opportunities for
profitable trade. When one superimposes upon this already complicated
picture a particular pattern of unforeseen changes in initial commodity-
endowments and in individual tastes, things become far more complex.
With changes in incomes and tastes, market agitation proceeds from
two analytically distinct sets of causes. First of all, as in our previous
analysis, participants each day will revise their trading plans under the
impact of the disappointments and other market experiences of the previous
trading day. In addition, participants will be revising their plans simply
because they face a new set of conditions. They find themselves with a
scale of values, with respect to additional quantities of the various commodi-
1 34 MARKET THEORY AND THE PRICE SYSTEM


ties, different from yesterday, because they no longer have the same tastes
and attitudes as yesterday, and because they find themselves in possession
of initial stocks of the various commodities different from yesterday. Any
market changes that might have brought trade closer to the equilibrium
pattern, from the standpoint of yesterday's income and tastes, is continually
disrupted by the emergence today of a totally different structure of income
and tastes. Long before equilibrium conditions appropriate to the data
of any one day have been attained, the market is faced with data calling for
a totally different set of equilibrium conditions.
In addition, once we admit changes in tastes and income into our
analysis, we must include the possibility that market participants, in plan-
ning their buying and selling for the day, make guesses concerning the
changes, in the incomes and tastes of other people, that might have taken
place. In other words participants might not rely on the knowledge gained
during the market experience of the previous day. In this way a new
source of imperfection in market knowledge is opened up; namely, that due
to inability to correctly gauge changes in tastes and incomes. On the other
hand, a new range for entrepreneurial activity is opened at the same time.
Those with a keener sense of the tastes and attitudes of others, and those
with swifter access to relevant information, are in a position to foresee more
accurately the set of market prices that will emerge on a particular day and
will be able to profit by exploiting their superior knowledge.
All this suggests that in any real world where static assumptions are
useful only as preliminary tools, the market will be characterized by contin-
ual agitation, a constant seething and absence of placidity. By focusing our
attention on the data relevant for a particular day, we can understand the
changes likely to be generated in the market purely by these data, and then
we can proceed to examine the likely consequences upon individual market
plans generated by the impact of a particular change in tastes or incomes.
In this kind of analysis, the static analysis making up this chapter has its
most fruitful applications.16

SUMMARY
Chapter 7 examines the market process as it would proceed in an
economy where no production is possible. The process is based on the
interplay of numerous individual consumer decisions (each consumer being
naturally endowed with some bundle of commodities). The analysis of the

16 In the appendix dealing with multi-period planning, the reader will find (see pp.
311 ft) an outline of how the market process would work in a pure exchange economy
when each of the participants is free to make decisions to transfer consumption from one
period of time to later periods.
MARKET PROCESS IN A PURE EXCHANGE ECONOMY 1 35


market process in such a pure exchange economy will facilitate the analysis
in later chapters of more complex and realistic models.
In the market each individual finds it necessary to compete with others.
He is forced either as buyer or seller to offer opportunities to the market
that are no less attractive than those made by others.
The competitive process can be most easily analyzed by reference to the
market for a single commodity; by imagining what would occur if knowl-
edge were perfect, it is possible to state immediately the conditions for
equilibrium in such a market. The detailed analysis of why these conditions
and no others can be consistent with equilibrium represents the basis for all
further market analysis.
When the perfect-knowledge assumption is abandoned, further analysis
shows how initial buying and selling decisions that fail to dovetail give rise
to "disappointments" and thus lead to revised decisions that are gradually
adjusted toward the equilibrium pattern.
Still further analysis extends the range of inquiry to the market process
involving numerous consumer goods. This case is considerably more
complicated than the preceding one. Nevertheless, once again the state
of affairs that would result from universally perfect knowledge is shown to
be the equilibrium situation for the multi-commodity market. Detailed
analysis shows how the absence of perfect knowledge brings about "mis-
taken" decisions, and how the disappointments suffered as a consequence
convey the information required for revisions of these decisions in the
"right" direction.
By imagining cases where one or more of the commodities appear in
the endowments of only one market participant, it is possible to analyze
how the market process operates in the presence of monopoly. The analysis
of the decisions of a monopolist in a world without production serves as an
introduction to the more complicated monopoly cases to be considered later.
The analysis of a pure exchange economy clarifies why a market may
be expected to be in constant agitation as a consequence of the acquisition
of new knowledge. Moreover it becomes clear, in particular, how such
agitation is set in motion by the activities of entrepreneurs who become
aware, more swiftly than others, of the most advantageous opportunities
available.
Suggested Readings
Böhm-Bawerk, E. v., Capital and Interest, Vol. 2, Positive Theory of Capital,
Libertarian Press, South Holland, Illinois, 1959, Bk. 3, Part B, Chs. 2, 3.
Wicksteed, P. H., Common Sense of Political Economy, Routledge and Kegan Paul
Ltd., London, 1933, pp. 493-526.
Wicksell, K., Lectures on Political Economy, Routledge and Kegan Paul Ltd., Lon-
don, 1951, Vol. 1, Part 1.
MARKET THEORY AND THE PRICE SYSTEM
136

APPENDIX
In this appendix a diagrammatic exposition is presented of the factors
that determine the equilibrium price of a single non-producible commodity
in a competitive market. This exposition will at the same time clarify the
statement that price is determined by supply and demand.

Price
K




c
^`”^^

K" X

Figure 7-2
In Figure 7-2, the horizontal axis measures quantities of the commodity,
while prices (whether bid or asked) are measured along the vertical axis.
Since we deal with a non-producible commodity, a certain fixed quantity
of it is owned (during each period of time) by market participants as a
whole. (This quantity of the commodity, we assume, is endowed by nature
to holders of it, during each period.) It is from this stock that any pur-
chases must be made in a given period. The size of this stock of the com-
modity is represented in the diagram by the distance OR'. RR' is a vertical
line erected on R'. The line KK'K" is drawn so that the abscissa of any
point on the line represents the quantity of the commodity that the holders
of the commodity would like, in aggregate, to own, when the market price
of the commodity is represented by the ordinate of the point. Thus, when
the price of the commodity is OA, holders of it wish to keep for their own
use, in aggregate, only the quantity AB. Since AB is less than AC (=OR'),
which is the aggregate quantity that holders actually do own, it follows
that at price AB, holders of the commodity seek to sell the quantity BC out
of their holdings. At a lower price, OG, holders of the commodity do not
wish (in aggregate) to sell any amount at all; they wish to keep their entire
endowments for their own use. Should price be lower yet, holders would
attempt (vainly, of course) to increase their holdings by buying more. Thus
at price OH, the owners of the commodity would be seeking to buy the
additional aggregate quantity EF (besides the quantities of the commodity
that ??orc-holders might seek to buy). It is clear, then, that the segment
37
MARKET PROCESS IN A PURE EXCHANGE ECONOMY

K'K" (of the KK'K") line represents (with K' being on the price axis) the
(aggregate) demand curve for the commodity of the group of market partici-
pants who are naturally endowed with holdings of the commodity. (Simi-
larly, it is clear, the horizontal distances between the KK' segment, and RK',
represent the quantities of the commodity that will be supplied to the mar
ket, at various prices greater than OG.)

Price




In Figure 7-3(a), the K'K" segment is drawn separately (with K' on the
price axis). In Figure 7-3(b), the line LL' represents the demand curve for
the commodity of all market participants who are not naturally endowed
with quantities of it. Figure 7-3(c), shows the line DD' obtained by lateral
summation of the K'K", LL' lines. Any point on the line shows the aggre-
gate quantity that will be purchased at a given price by the entire market.
It is clear that for prices higher than OG, the DD' line is identical with the
LL' line (since we have seen that no holders of the commodity would wish
to buy at prices higher than OG).

Price




N X

Figure 7-4

In Figure 7-4, the SS' line is the market supply curve for the commodity.
This shows, for each possible price, the aggregate quantity that would be
138 MARKET THEORY AND THE PRICE SYSTEM

offered for sale by the initial commodity holders. It is clear that for any
price (such as OB), the abscissa of the corresponding point on the supply
curve (such as C) is identical with the horizontal distance between the KK'
and K'R lines in Figure 7-2 (such as BC). (In fact it is obvious that the
supply curve is derived from Figure 7-2 simply by reversing the KK' segment
about the axis K'R. Keeping K' in its initial position in Figure 7-2, and
transposing the KK' line until it lies symmetrically to the right of the K'R
line, yields the line 55'. Thus, OS=OG=R'K'; OR'=ON; and NS'=OK).

Price




D' X

Figure 7-5
In Figure 7-5, the DD' line [from Figure 7-3(c)] has been superimposed
upon the SS' line (of Figure 7-4). This is the typical supply-demand dia-
gram. It demonstrates that the equilibrium market price will be p and that
the quantity of commodity sold will be q, yielded by the intersection of the
curves. A higher price would mean that sellers would be induced to offer
a quantity greater than that which buyers wish to buy at the price; a lower
price would mean that buyers would seek to buy a quantity greater than that
which sellers are prepared to sell at the price.
It is unnecessary, in the case of the non-producible commodity that we
are considering to isolate the market supply curve (as was done in Figures
7-4 and 7-5). Since the SS' line was derived, as we have seen, directly from
Figure 7-2, it is clear that market "supply" is nothing else but an indirect
reflection of the strength (or weakness) of the demand for the commodity
by its initial holders (as seen in the line KK'K" in Figure 7-2). This can be
seen very clearly by considering Figure 7-6. In this figure the line T T ' is
obtained by the lateral summation of the line KK'K" (from Figure 7-2), and
the line LL' [from Figure 7-3(b)]. This line is not the market demand curve.
This line represents, for each price, the aggregate quantity of the commodity
that the market would like to own at that price. (This quantity thus includes
some quantities of the commodity that the initial holders of it do, in fact,
139
MARKET PROCESS IN A PURE EXCHANGE ECONOMY

already own.) By erecting the ordinate R'P on R' (where OR', as in Figure
7-2, represents the entire endowment o£ the commodity), it can be shown
that equilibrium market price must be R'P. At any price below R'P, the
market as a whole would be seeking to acquire or to retain an aggregate
amount greater than is in existence. Competition would drive prices
higher. On the other hand, at any price greater than R'P, the market
would seek to hold in aggregate a quantity falling short of the natural en-
dowment. The competition of unwilling commodity holders would drive
price down.




T' X

Figure 7-6

It can be shown easily that the result obtained in Figure 7-6 is identical
with that obtained by isolating supply from demand, as in Figure 7-5. The
abscissa of a point on the TT' line is the sum of the abscissas of the cor-
responding points on the KK'K" line and the LL' lines. The first of these
latter two abscissas is equal to the distance OR' minus the horizontal dis-
tance between the point and the RR' line (for prices above OG). For the
price at which the abscissa of the point on the TT' line is equal to OR' (as
at P in Figure 7-6), therefore, it follows that the abscissa of the correspond-
ing point on the LL' line equals the horizontal distance between the KK'
line and the RK' line. But this latter distance is equal to the abscissa of
the corresponding point on the SS' line (for all prices above OG); while the
former distance is equal to the abscissa of the corresponding point on the
DD' line (for prices above OG). Thus, the price the TT' line intersects
the R'P line at (in Figure 7-6) is the same price the DD' and SS' lines inter-
sect at (in Figure 7-5). (The proof is formally valid also for prices below
OG, but at such prices no exchange at all would ensue, since no quantities
at all of the commodity would be supplied by holders of it at such prices.)
Figure 7-6 (as compared with Figure 7-5) emphasizes the supremacy of
demand considerations in the determination of the price of a non-producible
140 MARKET THEORY AND THE PRICE SYSTEM


good. Price is determined by the strength of the demand for the com-
modity; the demand of those who already hold some of it, and the demand
of those who hold none of it. On the other hand, the diagrams leading
up to Figure 7-5 demonstrate also the quantity of the commodity that will
be bought at the market price, depending on the initial distribution of
holdings. Figure 7-6 emphasizes, then, that the initial distribution of hold-
ings, while it affects the equilibrium quantity sold, can in no way affect the
equilibrium market price (with a given demand situation).17
The line TT' can be considered as ranking the degrees of eagerness with
which all market participants desire to hold successive single units of the
commodity. (In this ranking, therefore, are merged both the "sellers'
list" and the "buyers' list" referred to in the text of this chapter.) When
the unit is reached that exhausts the entire endowment of the commodity,
market price is represented directly by the eagerness to hold this unit of
the market participant involved (that is, the market participant who is more
eager to own this unit”in terms of his readiness to pay higher prices for it
or to forgo the opportunity to sell it for higher prices”than is anyone else).
All the more eager owners (or would-be owners) enjoy a consumer's surplus
to the extent that they need sacrifice, for a unit of the commodity, only the
amount that the marginal consumer of the commodity is prepared to sacri-
fice (instead of the higher sums that they themselves would be prepared to
sacrifice, if this were necessary).
Finally we may notice the special case where the KK'K" line (of Figure
7-2) is a vertical line at the origin (and thus coinciding with the price axis).
This case corresponds to the situation where those holding the commodity
initially have no desire to own any of it, no matter how low the price. The
SS' line corresponding to such a situation is, of course, also a vertical straight
line erected at a distance OR' from the price-axis (since the quantity sup-
plied at a given price is the horizontal distance from the KK'K" line at
that price to the RR' line, and this distance is now the same for all prices,
the distance OR'). Demand in this case is dependant entirely on the de-
mand of the non-holders. Supply is completely inelastic. With a given
aggregate commodity endowment, market price will depend entirely on the
strength of the demand of non-holders; supply will be completely passive in
this respect. The standard example of this kind of situation is that of a
market for perishable fish caught by fishermen. Ignoring the demand of
the fishermen forfishas food for their own families, it is clear that the entire
catch will be thrown on the market for whatever it can bring. With given
demand strength, price will depend on the quantity endowed (that is, the
size of the catch); with a given sized catch, price will depend solely on the
I 7 For further discussion of this point, and of other matters discussed in this appen-
dix, see Wicksteed, P., Common Sense of Political Economy, Routledge and Kegan Paul
Ltd., London, Bk. 2, Ch. 4.
141
MARKET PROCESS IN A PURE EXCHANGE ECONOMY

strength of demand for fish on the part of the public. This situation is
illustrated in Figure 7-7. Here SS' is a vertical line; market price will de-

Pr¡ce




0 S X
Figure 7-7

pend only on (a) the shape and position of the DD' line, and (b) on the
distance OS.
8

Production Theory



JL HUS FAR, our analysis of individual
economic activity and of the interaction in the market of the economic
activity of numerous individuals has been confined to a world where no pro-
duction was considered possible. The market process we were able to
analyze was a process where all participants participated directly as con-
sumers. Our principal purpose in this book, however, is to analyze a market
process where the wants of participants in their role of consumers may be
met not only through exchange but also by acts of production from re-
sources. In the pure exchange economy of the preceding chapter, a partici-
pant could improve his position (from that he finds himself placed in by
natural endowment at the start of each day) only through acts of exchange.
In the full market process, which we wish to investigate, a participant may
improve his position not only by direct exchange of endowed consumer good
for endowed consumer good but also by acts of production and of exchanges
of resources and products for the resources and products of others.
In this and the following chapter we take up the analysis of the
activity of the individual participant in his role of producer. In Chapters
10 and 11 we will examine the market process forged out of the interactions
of numerous individuals acting in their capacities of resource owner, pro-
ducer, and consumer. The economic analysis of production affects the
analysis of the market process, of course, through the supply side. In this
chapter and the next we inquire into the way the quantity of product that
will be offered to the market at a given product price depends upon the
pattern of production costs. In this chapter we lay the groundwork by set-
ting up the problem of production in its proper economic framework, indi-
cating the kinds of alternatives a would-be producer is free to choose among,
and showing especially how this range of alternatives is circumscribed by
what we will discover to be the Laws of Variable Proportions. In Chapter
142
PRODUCTION THEORY 1 43


9 we will proceed to show how the principles of production theory, de-
veloped in the present chapter, can be applied to the analysis of production
costs and upon the way these costs affect supply.

THE ECONOMIC ASPECT OF PRODUCTION
The economist examines production from a very special point of view.
From a purely physical perspective, of course, production is simply the
process where quantities of raw materials and labor are transformed into
quantities of product, the quantities being rigidly determined by the laws
of physical science. For the technologist the interest lies wholly in these
physical laws, describing the various results that can be expected to follow
on different patterns of resource combination.
The economist's perspective on production, however, is a quite different
one. Production is a process not of physical nature but of human action.
In seeking to improve their positions, men find it worthwhile to act as pro-
ducers as well as consumers. As consumers they act to spend their incomes
on the goods and services they consider most important. In exactly the
same way they may seek to improve their positions by producing goods and
services”either those they consider most important for themselves or those
that can be sold to command the goods they consider most important. The
very same categories, such as purpose, means, ends, and cost, which make
possible the analysis of consumer demand, reappear unchanged in connec-
tion with the actions of men engaged in production. And the economist
analyzes production with these categories making up the focus of his atten-
tion, rather than the physical laws within whose framework productive
activity is carried on.
The essence of the economist's outlook is thus that he sees the pro-
ducer as a man making choices among alternatives of a certain order of
complexity. By considering the range of possible alternatives, the econo-
mist is able to analyze the way these choices are made and the way action
will change in response to changes in the range of alternatives that choice
is made from.

PRODUCTION BY THE ISOLATED INDIVIDUAL
Production would take place of course, even in the absence of a market.
Robinson Crusoe and his production plans are accorded frequent attention
in economic treatises. An isolated individual finds himself with a severely
limited stock of goods ready for immediate consumption. These may not be
sufficient to satisfy even his immediate subsistence needs and fall very short
of satisfying all his "wants." On the other hand, he finds himself in com-
mand of productive resources of certain kinds and in certain quantities. He
Ì44 MARKET THEORY AND THE PRICE SYSTEM


himself is capable of supplying labor power”for a more or less definite
number of hours per day and possibly capable of being applied in a number
of directions requiring special skills and aptitudes. He has possibly at his
disposal raw materials of various kinds, as well as perhaps a number of
tools, or, at any rate, natural objects capable of being used, with or without
alteration, as rough implements. He finds himself, finally, subject to
rigid physical laws that determine quite precisely the outcomes of different
ways resources are combined. These are the data.
With these data at his disposal, the isolated individual recognizes that
he is faced with choice among rather definite alternative situations. It is
a physical law that a plot of land, a quantity of seed, a number of imple-
ments, and a good deal of labor can yield a crop of grain. This fact is
translated by man as constituting an opportunity; the discovery of this fact
means the recognition of one alternative open to him, if he sees fit to adopt
it. The individual, however, will be aware that the data afford other oppor-
tunities as well. He may see himself capable of building a house, plant-
ing a vegetable garden, or catching fish or game. Finally, he is certainly
aware of the opportunity, through leisure, to avoid expending labor alto-
gether, and thus to leave untapped also the other resources”except inso-
far as they can be used for direct enjoyment such as sunning oneself on the
plot of land. Of course, ignorance on the part of the individual may blind
him to a number of possible opportunities that the data of his situation
actually make feasible. He may not know his own skills, he may not know
the full capabilities of the soil, raw materials, and implements at his dis-
posal. He may be ignorant of the techniques by which his resources can
be most successfully exploited. But the opportunities he is ignorant of
simply do not enter into the range of alternatives he recognizes his power to
choose from, and in no way affect his actions (except, of course, insofar as
he may believe there are opportunities he is ignorant of and for whose dis-
covery he is prepared to forgo other already known alternatives).
Even the known alternative courses of action the individual "producer"
is able to choose from, it must be further noticed, are by no means certain
in their outcomes. The physical laws the farmer knows and on the basis
of which he plants his crops, tell him also that unfavorable weather can
drastically alter the results of his activities. And the farmer can know little
of weather conditions months in the future. To some extent, in fact,
every course of activity open to him leaves some range of uncertainty con-
cerning the outcome.
Thus, when the isolated individual has finally ploughed his field;
sown, grown, and reaped a crop of wheat; the productive process consti-
tutes in retrospect an example of human action capable of analysis from
the economic point of view. In producing his crop of wheat the farmer
has made and carried out a chain of decisions, (a) He decided to put his
PRODUCTION THEORY 145


resources to productive use rather than leave them unused, or used only for
leisure purposes, (b) He decided to grow wheat rather than produce
another type of product, and to grow wheat rather than any other crop.
(c) He decided on the method of production that he used, what tools to use,
what kind of ploughing and planting methods to employ, how to irrigate,
and so on. (d) He decided on the size of crop to raise; that is, he decided on
the quantity of his total supply of resources to apply to this one branch of
production.
These decisions meant choice among alternatives. They meant the
rejection of other alternatives in favor of those adopted. In order to obtain
his wheat the farmer sacrificed possible leisure; he sacrificed those other
goods whose production would have been possible with the resources
actually devoted to wheat; he rejected alternative methods of raising wheat,
alternatively proportioned combinations of the resources, and alternatively
proportioned allocation of the resources between wheat and other uses.
To the isolated individual these rejected and sacrificed alternatives are his
costs of production. The production of wheat cost him leisure; it cost him
a possible tobacco crop, corn crop, a house, or anything that could have been
produced with any other disposition of the resources that the farmer de-
voted to wheat.
The decision to incur these costs of course, was simply the decision to
produce wheat rather than any of these other goods with any other methods.
Its basis was the preference of the producer for what he could obtain from
his resources when devoted to wheat (in the way they were devoted), over
what he believed he could obtain from these resources on any other disposi-
tion. This preference, of course, was completely subjective; it expressed his
taste for wheat as compared with other goods and other crops; it expressed
his relative degree of confidence in his success as a wheat grower in the face
of the inevitable uncertainties, as compared with his assessment of the
uncertainties in the other kinds and methods of production; and through-
out, this preference expressed his subjective beliefs as to the objective efficacy
of the different ways of using resources, these beliefs being based perhaps
on supposed scientific knowledge, religious convictions, or reliance on
magic. One of the main differences between such "preference" for the pro-
duction of wheat (with a specific method of production), on the one hand,
and "preference" as it appears in direct consumer behavior, on the other
hand, lies merely in the complexity of the operating influences expressed
in the former. While it is true that production yields a product that is
measurable and thus differs radically from the utility that is involved in
the analysis of demand, nevertheless these subjective factors, especially when
an obtainable product is considered ex ante, go far to maintain the essential
homogeneity of human action in both consumption and production.
Whether or not the costs conceived in this sense of forgone alterna-
1 46 MARKET THEORY AND THE PRICE SYSTEM


tives were justified in retrospect depends on a number of factors. Looking
back at this use of his resources, the producer may regret his decisions. He
may have discovered that the alternatives he chose among were not quite
as he had imagined them to be. Perhaps the soil was less fertile than
imagined; perhaps he discovered himself to dislike agricultural labor more
than he had thought; perhaps events proved him over optimistic to the
uncertain factors in farming, and perhaps over pessimistic to the uncertain-
ties in other kinds of production; perhaps experience showed him mistaken
in the supposed scientific or other knowledge on whose basis he assessed the
outcomes of different productive efforts. And, of course, during the wheat
production, the farmer's tastes may have changed so that he no longer pre-
fers wheat over, say, vegetables. Under these circumstances, the producer's
product proves to be worth less than it cost to produce”he has incurred a
"loss." In other words, the producer thinks he made the "wrong" decisions;
one or more of the rejected alternatives has proved preferable to the one
adopted.
But, of course, it may well be that the producer is highly satisfied with
his course of actions. Events may have proven his choice among alterna-
tives an eminently wise one. The costs in this case are considered well
expended”the producer has "profited" by his actions. All this means is
that the wheat produced is still preferred over the goods that might have
been produced with the same resources.
Looked at in this way, it is not difficult to understand how production
decisions depend on the data of the situation and to envisage the alterations
in the production pattern of the individual that would be the consequence
of changes in these data. The same isolated individual might engage in
a different kind of production if the available alternatives were different, or
if his subjective tastes or his way of gauging future uncertainties were differ-
ent. If the available resources were different in kind, relative quantities, or
quality, the individual wrould find the opportunities he could choose among
rather different. The discovery of a new tract of fertile land, the discovery
of new techniques”even the discovery, through bitter experience, of the
mistakes made in the past use of the same resources”will alter the range of
alternatives and may well bring about different production patterns.
The analysis of the productive activity of the isolated individual could
be carried much further. But our principal interest is in the theory of pro-
duction as it is carried on in the market economy. The case of Crusoe pro-
duction was merely an introduction to the more complex kind of production
decisions performed under the guiding pressure of market forces. And we
shall find that the more detailed analysis of production for the market covers
the activities of the autarkic producer as well.
PRODUCTION THEORY 147


PRODUCTION IN SOCIETY
It is possible to imagine a society where all production would be carried
on without a market. Such would be a society of self-sufficient farmers each
growing his own food, making his own clothes, and providing for all his
other wants to the best of his own unaided ability. Resources would be
neither bought nor sold; each autarkic producer would use only his own
resources. Products would be neither bought nor sold; each household
would enjoy only the fruits of its own productive efforts. For the purposes
of economic analysis, such a society would be simply a congregation of
isolated islanders.
Our analysis of demand has already shown that a society without ex-
change is extremely unlikely. The discrepancies between the scales of
value of the different householders are likely to generate situations where
exchange of consumer goods between numerous pairs of householders are
mutually profitable. Where the individuals are engaged in production,
the scope for such profitable exchanges becomes greatly widened. This
occurs because the resources at the command of different individuals are
likely to be different. In the first place, this will generate exchange of
resources to some extent; and in the second place (especially where pro-
nounced differences in resources cannot be diminished through direct ex-
change”for example, special labor skills), this will generate a continual
recurrence of situations where the products of different individuals, each
produced with resources relatively unavailable to the other producers, can
be profitably exchanged against one another.
This fosters the further development of the phenomenon of division
of labor”a social process that takes advantage of the intransferable special
resources at the disposal of individual members of society and forges out
of them the social organization of production through exchanges in the
market place. It is unnecessary to expand here on the advantages of divi-
sion of labor.1 It is sufficient to notice that the process of division of labor
feeds on itself, continually making possible further gains for individuals
by progressvely wider and more intricate division of labor. The economic
history of modern society consists chiefly in such a progressive widening of
the range of specialization and exchange.
Production in a society based on division of labor, specialization, and
exchange, is carried on with almost complete responsiveness to the pressure
of market forces. Individuals produce primarily for sale on the market;
they produce largely with resources bought in the market. The production
decisions are thus made on the basis of alternatives and opportunities rigidly
l The classic statement of the advantages of division of labor is Smith, Adam, The
Wealth of Nations, Bk. 1, Ch. 1; see also Miscs, L.v., Human Action, Yale University
Press, New Haven, Connecticut, 1949, pp. 157-164.
148 MARKET THEORY AND THE PRICE SYSTEM


determined by market prices, in addition to the framework of purely physi-
cal laws production is carried on within. This chapter is principally con-
cerned with production as it is carried on within the market economy, to
which we now turn.

PRODUCTION IN THE MARKET ECONOMY
Production decisions in a market economy are made by entrepreneurs.
Entrepreneurs take the initiative in undertaking productive activity in con-
junction with the market, buying and combining the productive resources
to obtain the product, and selling the product on the market. The essen-
tial element in the entrepreneurial role is, for the economist, that the
entrepreneur undertakes ventures whose outcome is uncertain. This specu-
lative element is present, to be sure, in all human action, since action being
necessarily involved in the flow of time is always directed at some moment
in the future”and hence is always undertaken in the face of uncertainty.
Nevertheless, in economic analysis we distinguish, in every act of buying or
selling, between this "entrepreneurial" element on the one hand, and the
act of buying or selling seen as if it could be carried on with uncertainty
absent. In production within the framework of a market society, the de-
cisions to produce are essentially entrepreneurial. All the resources re-
quired for the emergence of the product can be bought in the market; the
entrepreneur in actually buying them”and thus allowing the product to
emerge”has made his decisions to pay prices for the resources completely
on the basis of his appraisal of the future value of the product to him in
the market. In this sense decisions to produce are purely speculative: they
involve the present purchase of resources (that is, the purchase of the
"product" in the form necessary to physically produce it) in the hope of
being able to resell them (that is, to sell the "resources" in the form of the
finished product) at a higher price in the future.
The direct motive for production in the market economy is thus the
profit motive in its simplest sense. Under the impulse of this motive the
entrepreneur makes his choices among the alternatives the market offers
to him. The range of these alternatives depends on the extent of the
market and on the degree of specialization already attained. In a highly
developed market economy an entrepreneur must choose from innumerable
possibilities; he can choose to produce any of innumerable kinds of goods
and services”the necessary resources can be obtained somewhere at a price;
and he can choose to produce any one particular good by any one of the
possibly numerous methods technologically conceivable for the purpose.
Very few of these alternatives, however, promise to be profitable. An
entrepreneur might produce air in a laboratory”but this product would
fetch nothing in the market. He might produce shoes by hiring labor to
PRODUCTION THEORY 1 49


make them by hand and be able to sell them for a price,”but would prob-
ably be unable to recoup his costs. To win profits the entrepreneur must
seek to produce a good, the resources for whose production can be bought
for a sum less than the sum likely to be obtainable from the product's sale.
The entrepreneur scans the available alternatives in order to seek those
offering the greatest difference between these two sums.
Specifically, the entrepreneur must decide (a) what good to produce;
(b) what quantity, per unit of time, to produce of this product; and (c) what
method of production to employ. Included in these basic decisions, of
course, are decisions where to buy resources, where to sell the product, what
quality of resources to use, and so on. The market presents the possibilities;
quantities of given resources can be bought for given prices and quantities
of given product can be expected to be sold for given prices. Technical
facts determine the quantities of product obtainable from given resource
combinations. The entrepreneur, at any given moment, seeks the one
opportunity he believes to be most profitable.
Once an entrepreneur has embarked upon a productive venture, he
frequently finds that his choices as to production in later periods of time
are to a considerable extent decisively influenced by his past activities. A
man who has been a shoe producer for some years may have gained so
thorough a knowledge of this line that continuation in it seems for this
reason alone the most profitable available productive enterprise. A man
may have in the past purchased equipment for the production of a certain
commodity, and the continued availability to him of this equipment makes
the production of this commodity the most profitable available undertaking
in subsequent periods. This frequently tends to make individual entre-
preneurs identify themselves with the production of definite commodities or
services. Thus, the decision an entrepreneur must make as to what to pro-
duce frequently does not have to be explicitly made at all; it is only at fairly
wide intervals that this question demands even casual attention.
This is the reason why a good deal of the analysis of production in the
market economy centers around the theory of the firm. The firm is an
entrepreneurial unit committed to some degree to the production of a
specific output. The theory of the firm involves principally its decisions
as to the level of its output and the particular resource combination to em-
ploy. It must never be forgotten, however, that entrepreneurs are as com-
pletely under the discipline of the market with respect to the product that
they produce as with all aspects of their productive activities. Entrepre-
neurs constantly experiment with new products, diversify their output, close
down plants, and switch to other products under the pressure of market
prices. The decision of a firm to continue with an established line of prod-
ucts means that this line promises greater profits than other lines of product.
It is of the essence of the market process that the pattern of production
1 50 MARKET THEORY AND THE PRICE SYSTEM

changes in response to changes in the basic data, namely, the resources availa-
ble to the economy and the wishes of the consumer. Both kinds of change
will exert a decisive influence on the type of product that an entrepreneur
will be producing at different periods of time.

FACTORS OF PRODUCTION
In order to produce products the entrepreneur must buy resources.
Resources sufficient for the production of a given product are known as the
factors of production. A factor of production (also termed an input) may
be a commodity, such as a raw material; or a service, such as a type of skilled
or unskilled labor; or a piece of information, such as the knowledge of a
technical formula. It is obvious that there are innumerable such factors,
different kinds of raw materials, different kinds of tools and equipment,
different kinds of labor services, and so on. At one time economists con-
sidered it expedient to group factors into three broad classes: land, labor,
and capital. Capital was the produced "factor," the class of resources that
had been produced, in turn, through the combination of other resources.
Land and labor were the "original" factors, "labor" including all services
provided directly by human beings and "land" covering all other nature-
given objects and services that could be used for production.
This classification was adopted on the belief that different economic
laws governed the returns earned in the market by each of these classes.
This belief is no longer held by modern economists so that this classifica-
tion, while it provides a grouping useful enough for a number of purposes,
is no longer considered as expressing a distinction of any fundamental eco-
nomic significance. The laws governing the prices of productive factors
are common to them all.
Nevertheless, it is economically significant to distinguish some impor-
tant characteristics attached to some groups of factors that play a role in
the determination of the actions of producers, with respect to both these
and other factors. Such characteristics, for example, are the substitutability
and complementarity of factors. We have already met these categories in
the theory of demand. The fact that a productive process, unlike an act
of consumer choice, yields a measurable result makes it possible to formulate
the categories, in the case of productive factors, in a somewhat different
way. A given quantity of factor A is a substitute for a given quantity of a
factor B when, in a process of production that utilizes factor B, the outcome
expected of the process is unchanged with the replacement of the given
quantity of factor B by the given quantity of factor A. If the conditions
under which the quantities of the two factors could be obtained were com-
pletely similar, then an entrepreneur would have no reason to prefer the
one quantity of factor over the other. It may be immaterial, for example,
PRODUCTION THEORY 1 51


to the owner of a factory whether its walls are painted grey or green. Grey
and green paint are to this extent substitutes.
Perfect substitutability would mean that under all circumstances a
given quantity of factor B is a substitute for a given quantity of factor A.
No matter what the purpose is, no matter how much of factor A or factor
B is already being used, a replacement of the quantity of the one factor by
that of the other leaves the expected outcome unchanged. It is noticed
that if two goods or services were discovered to be perfect substitutes for
one another in production in this way, then we would consider them, from
the economic point of view, as constituting a single factor of production.
Economic goods, whether those of lowest order (consumer goods) or of
higher order (factors of production) are considered as units of the same good
not on the basis of physical homogeneity but on the basis of economic
homogeneity. Units of a physically homogeneous group are considered
the "same good" because there is no reason to prefer one unit over any other.
If there is no reason to prefer, for any purpose, a unit of one good over a
fixed number of units of a physically different good, then, economically
speaking, a unit of the first good, and the fixed number of units of the second
good, are both units of the same good, even though there may be physical
differences between them.
The concept of substitutability thus provides the basis for distinguish-
ing between factors. A single factor consists of all goods or services that are
perfect substitutes for one another. A factor A is not the same as a different
factor B, if the two are not perfect substitutes for one another. Thus, while
for some purposes grey and green paint are substitutes for one another,
nevertheless they are two distinct factors of production since there are
numerous purposes for which only the one or the other will do. Substi-
tution between different factors, we will discover, plays an important role in
the decisions made by the entrepreneur.
Complementarity in the case of factors of production is very similar to
complementarity in the case of consumer goods. Factor B is complementary
to factor A if a given increase in the employment of A (other things remain-
ing unchanged) yields an increment of output that is greater when a larger
quantity of factor B cooperates in the process than when a smaller quantity
of B is in use. Production invariably requires the cooperation of a num-
ber of factors. Raw material without labor can yield no product. Labor
without materials and equipment yields no product. Even a singer requires
a hall or a stage to produce his product. One factor by itself cannot pro-
duce. It requires the cooperation of complementary factors of production.
A given factor for the production of a certain product may require the co-
operation of a complementary factor which has no close substitutes. In
order to produce a typed letter a secretary can do nothing without a type-
writer. Or merely the cooperation is required of any one of a group of
1 52 MARKET THEORY AND THE PRICE SYSTEM


factors that are to some extent substitutes for each other. In either case,
as we will see, the quantity of a factor an entrepreneur will buy depends
in part on the price and availability of the factors complementary to it. The
typical situation with a productive process is that a group of complementary
factors is required between which, however, a degree of substitutability
exists. This will be discussed later in this chapter.
Another category relating to factors that must be discussed is specific-
ity. A resource is a factor specific to the production of a certain product
when there is no other product it can be a factor for. The resource is
either employed in the production of one particular product, or it must
remain unemployed. A spare part designed to fit a machine of a particu-
lar make might be mentioned as a possible example of a specific factor; it
is likely to be useless for any other purpose. It is extremely difficult, how-
ever, to give a good example of a completely specific factor. Specificity must
be considered as the limiting case in a spectrum that ranks factors accord-
ing to their versatility. A factor that is non-specific is to some degree versa-
tile”it is useful for more than one productive purpose. Although it is
difficult to locate examples of perfectly specific factors, it is not at all a
difficult task to find factors with extremely low versatility. Such factors
are considered as specialized for the production of one or more products.
From the point of view of the entrepreneur, it is far more productive in
these productive processes than in any others. An intricate machine may
be "specialized" because its use as scrap is far less productive than the use
it was designed for.
The specific or specialized character of a factor plays an important
part in decisions concerning the disposition of resources in production.
In the case of the isolated individual as a producer, use of a factor in a
production process for which it is specific involves no opportunity cost.
The product that he obtains by the use of the factor in its particular use
is not offset by the loss of any product that he could have obtained by em-
ploying it in any other way. He will tend to use this factor rather than its
substitutes, wherever these substitutes have alternative uses. In a market
economy the entrepreneur of a firm in an industry where a factor is specific,
however, cannot expect to obtain the factor without cost. Although the
factor will not be sought by any other industry, nevertheless, other firms
in the same industry will be competing for it thus forcing up its price.
The factor specific to a certain industry will hardly be specific to a partic-
ular firm within the industry. From the point of view of the owner of
the resource, however, the price he receives for its allocation to any one
firm in the industry is greater than the minimum necessary to persuade
him to allow it to be used in the industry. This is so since he can obtain
nothing by selling it to a firm in any other industry. It follows that any-
thing causing the income to the owner of a specific factor to fall (for
PRODUCTION THEORY 1 53

example, a special tax on the income from this resource) will have no effect
(at any rate in the short run) on production.
Entrepreneurial decision making concerning the purchase of factors
will be influenced considerably by the institutional circumstances defining
the length of time the commitment is to be made for. A man buying a
machine makes a decision relevant not only to the immediate production
period but to periods in the future as well. On the other hand, when
a firm rents a machine (on a short-term lease), the decision to purchase
the machine's services may be reviewed at fairly frequent intervals. Labor
services are usually bought on a short-term basis, but if labor could be
bought only through long-term contracts (or if one could buy labor only
through buying a slave) then here too the decision would have overriding
influence on future production periods. When making a long-term factor
purchase of this kind, the entrepreneur, besides engaging in current pro-
duction, is investing resources for the sake of future production and profits.
While it is true that some element of investment is present in all produc-
tive activities, nevertheless, in a first analysis of production theory the
complications introduced by these investment components are often con-
veniently ignored. There is considerable justification for initially ab-
stracting from the existence of time differences between the purchase of
factors of production and the sale of the product. For most of the re-
mainder of this chapter we will consider production from the point of
view of this simplification We must of course not allow this simplification
to obscure the essentially speculative character of production. But it
will enable us to abstract provisionally from the complications introduced
by the once-for-all purchase of factors that will yield productive services
over a period of time. These are principally (a) the complication that
current decision making is powerfully influenced by past decisions on such
purchases, and (b) the complications introduced into an entrepreneur's
decision making for current production, by the fact that a part of the
price he pays for factors needed for such current production may only be
recouped by the production yielded by these factors in future periods of ;
time.- /

PRODUCTION FUNCTIONS AND ISOQUANTS
Much of what has been discussed thus far in this chapter can be sum-
marized and formalized with the aid of the concept of the production
function. In mathematics a function is the expression of the precise re-
lationship existing between a number of variables, where the value of one
of the variables depends on the value of the others. The production
-' In the Appendix on multi-period planning (see pp. 316 f®) some explicit attention is
paid to the time-consuming aspect of all production.
154 MARKET THEORY AND THE PRICE SYSTEM

function formalizes the relationship between the quantity of output yielded
by a productive process, and the quantities of the various inputs used in
that process. Thus a single typed letter is produced by combining some
minutes of secretarial services, a sheet of paper, the use of a typewriter
for some minutes, and so on. Algebraically a production function may
be written x ” ’ (ait a2, a?>, . . . an). The equation reports that the quantity
x, of the product X, that is produced, depends on the quantities alf a2, a·¿
. . . an (of the inputs Ax, A2, Az . . . An, respectively) employed in the pro-
ductive process. The factors, for which the quantities are not zero, are
the complementary factors for the production of X. If the quantity of
any of the a's in the production function has a constant value, for a given
value of x, in all possible methods of production, then the factor con-
cerned has no substitutes. As a rule, however, it will be the case that
for a given quantity x, the a quantities are variables, denoting a degree
of substitutability between the ^4's.
For the analysis of production it is frequently convenient to visualize
the available alternatives with the aid of graphical methods. In this
regard the production function is of particular use. The limitations of
three-dimensional space make it necessary to limit the exposition to a pro-
duction function involving only two variable productive factors, but the
insights thus obtained can be intuitively extended to more complex proc-
esses.




Input of

(b)


In the diagram [Figure 8-1 (a)] the two horizontal axes refer respectively
to the quantities used (per unit of time) of two factors, Alf A2, and the verti-
cal axis refers to the quantity of output of the product X that is produced
by the factors (during the given time period). A point in the space (such
as the point C) relates a quantity of the factor A1 (such as the quantity
PRODUCTION THEORY 1 55


OD) and a quantity of the factor A2 (such as the quantity OE), with a quan-
tity (CN) of the product X. If the relationship associated with such a point
is technically feasible, then the point is said to be on the production surface.
The production surface (of which ODCE in the diagram is an arbitrarily cut
portion) represents the outputs possible with all conceivable combinations
of the two factors.3 The line KL is drawn on the production surface so that
all points on the line are the same vertical distance from the horizontal plane
passing through the origin. The line KL thus indicates all the different
ways of combining factors Alf A2, that will produce a given quantity of out-
put. Thus, for example, in the diagram the output LH can be produced
either by using the quantity OD of Ax together with the quantity OG of A2,
or by using the quantity OF of Ax together with OE of A2, or by using any of
the other combinations corresponding to points on the line KL.
The situation set forth in Figure 8-1 (a) can be conveniently further
analyzed by means of a number of separate two-dimensional diagrams.
Thus Figure 8-l(b) shows a projection of the production surface onto the
horizontal plane passing through the origin”a "map" of the surface. The
line KL appears here as a "contour line" on the production surface, repre-
senting points of equal "altitude." Such a line is termed an isoquant. For
any production surface there will be any number of such isoquants, one for
each possible output level. The coordinates of any point on this line
represent for the entrepreneur one of the alternative "packages" of inputs
that he may be able to buy in order to produce a given output.

Output
of
Product
X




H N Input of Az

Figure 8-2

In Figure 8-2 the diagram shows a vertical section of the production
surface parallel to the XA2 plane through the point C (or better, it can
be considered as the projection of this section onto the XA2 plane so that
O is at the origin). The curve thus represents the quantities of product
3 The notion of a surface presupposes continuity in the production function. This
implies divisibility of the inputs and outputs. Production theory, while simplified by
such assumptions, does not depend on them for the validity of its general theorems.
1 56 MARKET THEORY AND THE PRICE SYSTEM


that can be obtained by employing alternative quantities of one factor, A2,
in combination with a fixed quantity (OD) of the other factor Ax. Thus
(always keeping this quantity of Ax unchanged), the employment of OH
of factor A2 yields HL of output, and the employment of the quantity ON
yields NC. The increment of factor A2, in the quantity HN, thus yields
an additional output of BC (other things, especially the quantity of factor
Alf remaining unchanged). The quantity BC is termed the marginal in-
crement of product corresponding to the input increment HN.á This
quantity, as we shall see, has considerable significance for entrepreneurial
decision making. An entrepreneur is always faced with the alternative
of purchasing an additional quantity of a particular factor. To assess
the attractiveness of any such alternative, it is first necessary for the en-
trepreneur to judge what difference this increment of factor will make
to output. This difference is the marginal increment of product generated
by the additional quantity of factor.

Output
of
X




0 J N Input of As
Figure 8-3


In Figure 8-3 an analogous diagram is drawn to show the alternative
outputs that can be produced with different quantities of input of the
factor Alt the quantity of factor A2, this time, being held unchanged at
OE. The curve OC is thus the projection, onto the XAX plane, of the
vertical section through the production surface at C parallel to this plane.
The quantity BC is the marginal increment of output associated with
the input increment JN of factor Ax.
4 For continuous total product curves (such as in Figure 8-2), the slope of the curve
at any point (such as at C) measures the rale output increases at with increasing input
(of A2) when the input level is shown by the abscissa of the point (such as the quantity
ON). In the literature this rate of output increase is known as the marginal product of
A2 (when it is employed in volume ON). The notion of a marginal increment of prod-
uct corresponding to specific increments of input, used in the text, does not require the
postulation of perfectly divisible inputs or outputs. The marginal increment of product
has the dimensions of products; marginal product has the dimensions of product per
unit of input. For small input increments, marginal increment of product is thus ap-
proximately equal to marginal product times the increment in input.
PRODUCTION THEORY 1 57


At any point on the production surface, the relationships between the
marginal increments of output corresponding to the various variable
factors spell out the alternatives open to the entrepreneur. As we shall
see the first question asked by an entrepreneur concerning a given process
of production is whether it is the cheapest method of producing the given
quantity of output. This is the question of whether the process, corre-
sponding to a point on the production surface, is cheaper than any other
point on the same isoquant. This question resolves itself into two com-
ponents. The one component asks which other physical combinations of
factors are able to yield the same output; the second component concerns
the money costs of these different input combinations. Leaving aside the
latter problem at this stage, it is clear that the first part of the question
asks about the various additional quantities of, say, factor Ar required to
keep the level of output unchanged when various quantities of the other
factor, A2, are withdrawn from the productive process.




The relationships can be visualized with the aid of Figure 8-4. Here
MKL is an (enlarged) portion of the production surface bounded by (a)
the solid line KL, a small portion of an isoquant line; (b) KM, the line
of intersection of the production surface through …7 by a vertical plane
perpendicular to one of the factor axes, say, At (so that the line MQ is
horizontal, and is indicating increasing input of A2, toward Q); and (c)
LM, the line of intersection of the production surface through L by a
vertical plane perpendicular to the other factor axis (so that the line MS
is horizontal, perpendicular to MQ, and is indicating increasing input of
A¬ toward S). The curved line QS is the projection of the isoquant seg-
ment KL onto the horizontal plane through M. To an entrepreneur weigh-
ing a productive process corresponding to the point K} the answer to the
question considered in the previous paragraph, insofar as it concerns the
possibility of point L, is that in order to offset a loss of the quantity MQ of
input of factor A2, it is necessary to expand the input of Ax by the increment
MS. An entrepreneur producing the quantity of output shown by the
point K can maintain the same level of output by withdrawing MQ of factor
A2 and adding MS of factor Al·. The relation between MQ and MS thus
1 58 MARKET THEORY AND THE PRICE SYSTEM


measures the rate at which factors can be substituted for one another at the
margin. From the diagram it is clear that the required relationship between
the increments of factor MQ and MS is defined by the condition that each
is associated with the same marginal increment of product (in our case shown
as being the quantity KQ, equal to LS). If one unit of factor Ax has a higher
marginal increment of product (at the relevant margin) than one unit of
factor A2, then the increment of A2 required to offset the withdrawal of a
unit of Ax will of course have to be larger than one unit.

THE SHAPE OF THE ISOQUANT
AND THE SUBSTITUTABILITY OF FACTORS
Thus, the shape of the isoquants is the graphical expression of the
degree of substitutability between the two factors used in production. The
slope of a straight line drawn connecting two points on an isoquant
measures the degree of substitutability over this range. Thus, if in Figure
8-4 the straight line KL had been drawn, its slope with respect to the A2
axis (like the slope of the straight line QS) would be MS/MÇ¿, showing
the quantity of the one factor required to offset a withdrawal of a given
quantity of the other. The steeper the slope of KL, the greater would be
MS in relation to MQ, showing that A± would be less good a substitute for
A2 at the margin. For a continuous isoquant line, with the points drawn
closer and closer together, the slope of the line joining them becomes
very nearly the slope of the isoquant itself at a point. This slope measures
the marginal rate of substitution of factor Ax for the factor A2; that is,
the increment of factor Ax necessary to keep output level unchanged when
a small reduction is made in the employment of factor A2.5
The importance of the slope of the isoquants in this regard can be
spotlighted by contemplating two extreme theoretical situations, one where
no substitution at all is possible between the factors, the second where the
factors are perfect substitutes for one another (so that there is no economic
justification for distinguishing between them).
In Figure 8-5(a) isoquants are drawn that require the cooperation of two
factors Au A2, in a fixed proportion. Thus the point K, for example,
yields a level of output 1, using OR of Ax and OS of A2. The point L,
corresponding to a level of output twice that of K, requires OT (which
is twice OR) of Alf and OU (which is twice OS) of A2. An increase in
the quantity of factor A± used, without the required proportional rise in
factor A2 used, yields no additional output whatsoever. This is indicated
by the shape of the isoquant family. At K, for example, increases in
either Alt or A2, separately, yield no increase in output so that the isoquant
3 For a continuous isoquant line, this marginal rate of substitution of At for A2 is
then mathematically equal to the ratio of the marginal product of A2 to that of Ax.
59
PRODUCTION THEORY


• > 2\
9




M
L
u
K
s
R T


(b)
(a)
Figure 8-5

is perfectly horizontal to the right of K (showing that an increase in Al9
by itself, does not lift output at all) and is on the other hand perfectly
vertical above K (showing that an increase in A2, by itself, does not raise
output at all). A higher output is achieved only when both factors are
raised proportionately. An example of such a process inight be the bottling
of a beverage that can be sold only in a given-size bottle. Each additional
unit of output requires the employment of one additional bottle, plus
one additional unit of the beverage. Use of two or more empty bottles
does not yield any product; neither does the use of additional beverage”
in any amount”without bottles.
Such a case is one where there is no substitutability between factors.
This is expressed in the L-shaped pattern of the isoquant family. The
marginal rate of substitution of Ax for A2 in the vertical portion of the
isoquants is zero, since the slope of the isoquant with respect to the A2
axis is zero. No additional units at all of Ax are needed to offset the with-
drawal of units of A2 (because the quantity of A2 available, compared with
that of Alf had been greater than that required by the fixed proportion).
On the other hand, in the horizontal portion of the isoquants, the marginal
rate of substitution of A1 for A2 is infinitely large (as is the slope of the
isoquant with respect to the A2 axis) showing that no matter how much
additional A-± might be used, it would be insufficient to offset the loss
of even a small quantity of A,· The level of output depends, not on the
quantity of either input by itself, but on the number of "units" each of
which is compounded of a fixed quantity of the one factor together with
a fixed quantity of the other factor. An entrepreneur, in making his
decisions as to the quantities of input that he should purchase, will in
fact treat units of the two inputs as component parts of a single unit of a
composite factor”in the same way as he would treat the two blades of
a pair of scissors.
The diagram in Figure 8-5(b), on the other hand, depicts the diametri-
160 MARKET THEORY AND THE PRICE SYSTEM


cally opposed situation where the factors used in production are perfect
substitutes. Here the isoquants are downward-sloping parallel straight-
lines throughout their extensions, showing that the same additional quan-
tity of any one of the factors can always be used instead of a given quantity
of the other factor. The marginal rate of substitution of one factor for
the other is thus constant at all points on the diagram and is neither zero
nor infinite.
However, the two cases shown in Figure 8-5(a) and in Figure 8-5(b) are
extreme, limiting cases. In the real world the proportions between inputs
seldom are technologically completely fixed. Usually there is room for
some alteration in input proportions without altogether wasting any input.
On the other hand, we have already seen that if two factors were perfect
substitutes in production, then they would be classed together as units
of an economically homogeneous group of goods. Typical isoquants, there-
fore, will be neither parallel to the factor axis nor straight lines throughout
their length. They will express the fact that inputs are partial substitutes
for one another; that within limits, a withdrawal of one input can be
offset by additional use of the other input, but that such substitution be-
comes more and more impractical. The marginal rate of substitution of
one factor for the other becomes greater and greater as the substitution is
carried forward. Greater and greater quantities of a factor are needed
to replace given withdrawn quantities of the other factor as the replace-
ment goes on. The typical situation is thus one where the proportion
in which the factors will be used, while not fixed absolutely by technological
considerations, is yet by no means a matter of complete indifference.6
These possibilities are sometimes described with the assistance of the
concept of the elasticity of substitution. The elasticity of substitution
between two factors measures the degree to which it is possible to substitute
one of the factors for the other, without bringing about more than a given
increase in the marginal rate of substitution of the first factor for the
second.7 A high elasticity of substitution characterizes two factors sub-
stitution can take place freely between, without causing more than a mod-
6 These considerations governing the substitutability of factors have their counterparts
(in the theory of consumer demand) with respect to substitutability between commodities
in consumption. We saw in earlier chapters that as a consumer gives up quantities of
one good in order to acquire additional units of a second, he tends to be willing to
continue such exchange only on increasingly attractive terms.
7 Mathematically the elasticity of substitution between two factors Ax and A., is defined
— MRS ÁlAs/”> w h e r e MRS
as d(”¬/d(MRS AlA2) ^A2 is the marginal rate of substitution of
` ….n' . . A%
/ ¿l \
At tor A2. The di ” ) term denotes the change in the use of Ax as compared to that
of A2. The d(MRS AlAi,) term denotes the change in the marginal rate of substitution.
The remaining terms are introduced to make the result independent of the size of units
used.
61
PRODUCTION THEORY

erate worsening of the rate further substitution can be made at. In the
special case of perfect substitutes, the elasticity of substitution is infinite.
No matter how far substitution has been carried, it is always possible to
carry it still further at the same rate of substitution. There is in such
a case no "optimal" proportion, deviation from which makes further
substitution more and more disadvantageous.
A low elasticity of substitution, on the other hand, characterizes two
factors from which best results can be obtained only by combining them
in rather definite proportions. A significant deviation from these pro-
portions brings about a very sharp drop in efficiency, so that the more the
one factor has been substituted for the other (thereby departing from the
best proportions) the more disadvantageous are the terms on which still
further units of the first factor can be substituted for the second. In the
special case of factors, the proportions between which are technologically
fixed with complete rigidity, the elasticity of substitution is zero at the
point of fixed proportions. When the quantity used of one of the factors,
relative to the quantity used of the second factor, is slightly less than is
required by the fixed proportion, then its marginal rate of substitution for
the second is, we have seen, zero. As soon as the quantity of the first
factor has been raised to meet the required proportion, its marginal rate
of substitution for the second has risen to infinity (no amount of it can
offset the slightest reduction in the amount used of the second factor).
Such an abrupt rise in the marginal rate of substitution, brought about
by only the slightest alteration in the relative employments of the factors,
constitutes zero elasticity of substitution.




O Rs Ax

Figure 8-6

The typical processes of production lie somewhere in between these
two extremes. The isoquant family will show a pattern that is exem-
plified, at least for a portion of the production surface, in Figure 8-6. In
the diagram the isoquants are drawn convex to the origin. An entre-
preneur who has been operating at point K can maintain the same level
1 62 MARKET THEORY AND THE PRICE SYSTEM


of output by withdrawing the quantity KT of input A2 and increasing by
quantity TL· the input of factor At. By moving from the production
situation at K to that at L, the entrepreneur increases the proportion in
which input Ax is employed relatively to A2, from the proportion RO/KR
to SO/LS. This is shown graphically by the reduction in slope from that
of the line OK to that of the line OL·. The convexity of the isoquant
means that a further withdrawal ofL·V(drawn to be equal to KT) from the
quantity employed of factor A2 will require, for the maintenance of the
output level, an additional quantity VM of A1 that is greater than TL·
(which had been previously required). The extension of a straight line
joining KL· to N (that is, continued substitution on the same terms), would
bring it into the neighborhood of lower isoquants. The convexity of the
isoquant means that substitution of either factor for the other, if carried
on at a constant rate of substitution, would bring about progressively lower
output yields.
The elasticity of substitution at any point on one of these "typical"
isoquants depends on the convexity of the curves. If the isoquants are
only slightly convex (or, at any rate, in that portion of an isoquant where
the curvature is slight), the marginal rate of substitution (shown by the
slope of the isoquant) changes only slowly so that the elasticity of substitu-
tion over the relevant range is high. This is the case for the central por-
tion of the isoquants. Thus, in the region of KL· in the diagram, a given
percentage change in the ratio of Ax/A2 used does not alter the slope of
the isoquant as considerably, for example, as it does in the neighborhood
of MC. The elasticity of substitution is thus quite high in the central
portion of an isoquant (corresponding to efficiently proportioned combina-
tions of factors) but drops rapidly at the outer portions of the isoquants
where a small amount of substitution brings about a rather sharp deteri-
oration in the terms on which further substitution can take place. Thus,
at the point C, the isoquant is parallel to the Ax axis. This means that
the marginal rate of substitution of A1 for A2 has reached an infinite level:
no amount of additional A1 can maintain output should the input of A2
be cut slightly. From a point slightly to the left of C, to the point C, this
marginal rate of substitution has jumped from a finite (high) level to a
level greater than any assignable value”this corresponds to an elasticity
of substitution very close indeed to zero.
It is now quite easy to perceive the relation between what we have
called the "typical" isoquant, and the two special cases between which it
is intermediate. The case of rigid, technically fixed proportions is one
where the central portion of the typical isoquant has become shrunk to
a single point. It is as if points C and D coincided; the range where some
substitution is possible (and where the elasticity of substitution is not zero)
has become narrowed to the vanishing point. On the other hand, the
163
PRODUCTION THEORY

case of perfectly substitutable factors is one where the central portion of
the typical isoquant extends throughout the production surface. The
range of high (in fact, infinite) elasticity of substitution is not bounded
by any limits whatsoever.

CHANGES IN FACTOR PROPORTIONS,
AND CHANGES IN THE SCALE OF FACTOR EMPLOYMENT
The insights gained in the preceding section should make it easy to
distinguish between the effects of two quite different kinds of changes that
can be made in the input of productive factors. The first kind of change is
alteration in the proportions in which the various factors are combined.
The second kind of change is alteration in the scale in which inputs com-
bined in a given proportion are applied. Here too the isoquant map
provides useful graphic aid in showing the two kinds of input changes.




Figure 8-7

In Figure 8-7 a number of dotted straight lines are superimposed upon
an isoquant map. OP and OQ are straight lines meeting the origin, differ-
ing from one another in their slopes; SR is parallel to the A2 axis, and
TV is parallel to the A1 axis. Any two points on a straight line passing
through the origin (such as W, P on the line OP) represent two combina-
tions of the factors A1 and A2, in both of which the factors are combined
in the same proportions. The difference between inputs at the two points
is one purely of scale. Just as an architect may construct a scale model
of a building (retaining the relative proportions of all lengths while re-
ducing all absolute lengths by a constant scale factor), so too the point W',
for example, is a "model" of the input situation at the point P (retaining
relative proportions but with absolute measurements of factor input mul-
tiplied by the scale factor, in this case OW/OP). An increase in the scale
of input, of course, may take place with any given proportions of factor
164 MARKET THEORY AND THE PRICE SYSTEM

combination; that is, along any straight line passing through the origin.
Points on different straight lines passing through the origin correspond
to combinations of factors between which there is a difference in the pro-
portions of the factors employed. Thus, for example, the point W differs
from the point V, and the point ¾ in that W is characterized by a ratio
of the quantity employed of A2 to that of Aít which is equal to the fraction
WR/OR (the tangent of the angle WOR), while both V and Q have a ratio
of A2 to A1 equal to VR/OR (the tangent of the angle VOR).

RETURNS TO SCALE
The problem of defining the consequences upon output of a change
in the scale of input is the source of the concept of returns to scale. If a
given percentage change in the scale of inputs brings about the same per-
centage change in output, then the production process is said to yield
constant returns to scale. If one hour's employment of a typist's services,
together with the use of given typing facilities, can produce 10 typed pages,
and the employment of two typists, each similarly equipped, yields 20
pages in the same time, then constant returns have prevailed. On the
isoquant map this would be expressed by the condition that intercepts
(marked off along a straight line passing through the origin) between
pairs of isoquants have lengths proportional to the differences between
the output levels represented by the respective isoquants. Equal incre-
ments of output should mark off equal distances along any straight line
passing through the origin.

Output
Output Output
of of of
X X X



/
c Q
QS y /
B B
R/ B
/
A
A A A
/

l\
/
Ai
1. ¿r Inputs 0 MA *\ E Inputs
0 0 Kz £¯lnp
tK
Mz L¯2

(a) (b) (c)
Figure 8-8\

If a vertical section were made of a production surface characterized
by constant returns to scale, along any horizontal straight line passing
through the origin, we would obtain a situation shown in Figure 8-8(a).
Output is measured along the vertical axis; AB, BC represent equal incre-
PRODUCTION THEORY 1 65


ments of output. The section of the production surface shows a straight
line so that the contour lines corresponding to output levels A, B, C, appear
as the points R, Q, P, with RQ=QP. On an isoquant map this is trans-
lated as generating equal distances (ML = LK) between isoquants corre-
sponding to output levels separated by equal output increments (AB=BC).
If a productive process were to be characterized by increasing returns
to scale, the section of the production surface would be convex from below
[as in Figure 8-8(b)] so that equal output increments would correspond to
unequal distances between contour lines; the higher the output level, the
shorter will be the distance between isoquants corresponding to a given
output increment. Thus L1K1 (corresponding to output increment BC)
is shorter than M1LÌ (corresponding to output increment AB, which is
equal to BC). If there were decreasing returns to scale, the situation would
be reversed, as in Figure 8-8(c), with L2K2 (which corresponds to output in-
crement BC) longer than M2L2 (which corresponds to the equal increment
AB at a lower level of output).
While intuitively it might seem almost obvious that constant returns
to scale must prevail universally, with a doubling of all factors in a given
combination yielding a doubled output, and so on, it is impossible to
make any a priori generalizations to this effect. In the real world, moreover,
it is extremely difficult to discover cases where an increase has occurred in
all factors. Usually it is discovered that some important ingredient in a
productive process (for example, managerial skill) has stayed unchanged
during an increase in all other inputs. Where this has been the case,
the changes in output cannot be attributed to a pure change in scale. Along
with the change in scale, in such cases there has occurred also a shift in the
proportions in which the factors, whose input was increased, are combined
with the factor whose input was not increased.

THE LAWS OF VARIABLE PROPORTIONS: THE PROBLEM
We have already noticed some of the consequences of an alteration in
factor proportions. We saw that as the proportion used of one factor
increased (relative to a second factor), substitution of the first for the second
becomes more and more difficult, if a given output level was to be main-
tained. Our focus of attention, in that situation, was a change in factor
proportions under the condition that the level of output be unchanged.
But the problem of changed factor proportions is of importance in several
other aspects. One such problem, for example, is the effect upon output
of changes in factor proportions, under the condition that total cost of
production be unchanged. This will be taken up in a later section of
this chapter.
At this point we are interested in yet another aspect of the problem
166 MARKET THEORY AND THE PRICE SYSTEM


of effects of variations in factor proportions. We are concerned with the
effect exerted by an increase in the ratio of the quantity in which one
factor is employed, relative to the quantity in which a second factor is
employed upon (1) the output per unit (a) of the factor being used rela-
tively more freely, (b) of the factor being used relatively more sparingly;
and (2) the incremental eßect upon output brought about by additional
input (a) of the factor being used relatively more freely, and (b) of the
factor being used relatively more sparingly. Our examination of these mat-
ters will be confined to the simplest case, that of a process of production yield-
ing constant returns to scale. It is clear that as the ratio of employment of
one factor to that of a second is increased from very low values to very high
ones, there is an initial stage where the first is spread very sparsely, so to
speak, over the second factor, and a final stage where the second factor is
spread very sparsely over the first. This symmetry between the initial and
the final stages will be reflected in the above measurements of the efficiency
of the two factors. The behavior, during the initial stage, of the output per
unit of the factor that is being used sparingly in this stage will be mirrored,
during the final stage, in the behavior of the output per unit of the other
factor. And the same will be the case with the incremental effects on output
of additional inputs of the two factors in these two stages.
Inquiries have been made by economists throughout the history of the
science into the effects upon both the per-unit efficiency and the marginal
effectiveness of factors between which the input proportions are under-
going variations. These investigations have tended to focus attention on
one particular way that an alteration in input proportions can be achieved,
the attention paid to this case arising in part from its supposed relevance to
real-world situations. The case most frequently considered involved suc-
cessive increments in the input of one factor to a fixed quantity of another
factor. In the history of economic thought this case has been dealt with
under the name "the law of diminishing returns;" in the real world the case
was exemplified whenever an alteration occurs in the quantity of labor and
capital applied to the cultivation of a given acreage of land.
While we too will investigate the effects on production efficiency of vari-
ations in input proportions, by references to this case, it must be stressed that
the importance of the case lies purely in the change in input proportions
that it exemplifies. The fixed quantity of the one factor is not to be
thought of as one of those "other things" that are so often held unchanged
in economics. It is, on the contrary, the means through which factor pro-
portions can be altered under particular circumstances. For this reason
it is probably better to use the newer term laws of variable proportions in
place of "law of diminishing returns." What these laws describe, once
again, can be visualized with the aid of an isoquant map drawn to express
the results determined by these laws. In the diagram (Figure 8-9), the iso-
167
PRODUCTION THEORY

quants (on a production surface characterized by constant returns to scale)
are drawn convex to the origin (that is, with what we found to be their typi-
cal shape, due to the imperfect substitutability of the factors). However, the
isoquant lines have now been extended to the point where they slope up-
wards in their outer regions.




H




Figure 8-9
This pattern of isoquant map corresponds to a particular set of tech-
nical conditions that, according to the laws of variable proportions, are
typical of production processes. A portion of an isoquant that slopes up-
wards is to be interpreted as the situation where a withdrawal of one of the
factors from the productive process, keeping the input of the other factor
constant (for example, a movement from the point Z in the diagram to the
point E), actually increases the level of output (shown in the diagram by the
fact £ is on a higher isoquant than Z). A positively sloping isoquant thus
corresponds to the case where the marginal increment of product associated
with an increase in the input of one of the factors is negative. The lines
OP, OQ, separate the upward sloping portions of the isoquants from the
other regions. Thus, between the lines OP and OQ, all isoquants are nega-

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