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tively sloped. The lines OP, OQ, are called ridge lines and pass, by their
definition, through all those points where isoquants are vertical (such as
points M, D, F), and through all the points where isoquants are horizontal
(such as points, N, C, E).

THE LAWS OF VARIABLE PROPORTIONS
The behavior of output according to the laws of variable proportions
can be examined by considering in the diagram (Figure 8-9) the line GH
drawn parallel to the Ax axis. Points on this line correspond to combina-
tions of the input of a fixed quantity (OG) of factor A2, together with the
input of different quantities of factor Ax. As we move to the right along
1 68 MARKET THEORY AND THE PRICE SYSTEM


the line GH, we are considering the effects of combining greater and greater
quantities of At with the fixed quantity of A2.8 In so doing, of course, we
are decreasing the ratio of the quantity of A2 employed relative to the
quantity of A1 employed. (Thus if straight lines were drawn joining the
origin to points M and E, we would find that the slope of a straight line OE
would be less than that of a straight line OM.)
Now as we move from G toward M (where the line GH is intersected by
the ridge line OP), we cross higher and higher isoquant lines; total output
is steadily increasing. But so long as the point M has not been reached, the
isoquants slope upward since we are outside the ridge line. This means
that at any point between G and M, output could be greater if there were
less of the fixed factor A2. In this range there is too much of the fixed
factor in relation to the variable factor. While the marginal increment of
output corresponding to increases in the input of the variable input is posi-
tive (for all points in this range), that corresponding to increases in the fixed
input is negative. (That is, for any point between G and M the output is
higher than it would have been if the quantity of the fixed input had been
greater.)
As we move further to the right, from the point M to the point E, we
are in the region between the two ridge lines. Within this range, move-
ment to the right still brings us to higher isoquant lines; successive incre-
ments of the variable factor bring about progressively higher levels of
output. Also, in this region, the isoquants slope downwards. Marginal
increments of output corresponding to increases in either factor would be
positive. At any point between M and E, output is lower than it would
have been if the quantity of either input would have been greater.
As we move still further to the right, we reach the region outside the
second ridge line OQ. In this range, every increase in the input of the
variable factor decreases output (shown by the intersection of GH with
lower isoquants). Output is higher than it would be if the input of the
variable factors (Ax) were greater, but lower than it would be if the quantity
of the fixed input (A2) had been greater. There is too much here of the
variable factor A1 in relation to the quantity of fixed factor A2 available.
The fixed factor is being overworked.
From these considerations it is possible to develop a rather complete
description of the effect that different input proportions will have upon
both the per-unit and the incremental effectiveness of the factors. We must

8 When we talk of "a movement to the right" along a line, we do not, of course, mean
a temporal succession of cases (each one of which is more to the right than the ones
actually earlier in time). Different points on an insoquant map refer to alternative situa-
tions possible at one moment in time. A "movement to the right" means, then, that
we proceed to consider successively the situations more to the right as alternatives to
those more to the left, which we consider first.
169
PRODUCTION THEORY



remember that for the case of constant returns to scale, which we are con-
sidering, points on an isoquant map that lie on the same straight line
through the origin correspond to situations where the per-unit output of
any one of the factors is the same for both points, and where the marginal
effectiveness of any one of the factors is the same for both points. 9 This
means that these measures of factor effectiveness depend only on the ratio




˜n˜ f¯f




w
Figure 8-10

of input proportions, not on scale. Thus in Figure 8-10, the diagram (which
selects certain features of Figure 8-9 for emphasis) shows (besides the line
GH) the line WZ drawn parallel to the A2 axis, so that the situation at
V on GH is the same (with respect to the per-unit and marginal effective-
ness of the factors) as at the point V on WZ; the situation at B on GH is the
same as at B' on WZ; and so on.
Now as we moved to the right along GH, total output rose steadily until
point E (on the ridge line OQ) and then declined. Since the quantity of
Ao did not change during this movement, it follows that the output attrib-
utable to one unit of A2 rose steadily until E and then declined. This is
an important result. We have seen that movement to the right along GH
is equivalent (insofar as the effectiveness of units of the factors is concerned)
to a movement downward along WZ. We are thus able to state that a move-
ment downward along WZ increases the output per unit of A2 until point Ef,
after which the output per unit of A2 falls. (With constant returns to scale
9
For proofs of these mathematical propositions, see Allen, R. G. D., Mathematical
Analysis for Economists, The Macmillan Co., London, 1938, pp. 317-322.
170 MARKET THEORY AND THE PRICE SYSTEM


the ridge lines are straight lines through the origin; thus, E, E' are both points
on the ridge line.) Said another way, a movement upward along WZ first
increases the per-unit output attributable to A2 and then decreases it. This
is an even more important result. It tells us that with one factor constant
(here Alt held fixed at an input of OW), successive increments of a second
factor bring about first a steady increase and then a steady decrease in the
per-unit output attributable to this second (variable) factor. Similarly, the
output per unit of A1 steadily increases with movement upward along WZ
until M' (on the ridge line OP), after which it declines (since Axh constant
along WZ, and total output rises till M' and then falls). Hence for move-
ment to the right along GH the output per unit of A1 rises until M and then
declines steadily thereafter.
We can restate the results of the previous paragraph in the following
terms. As the ratio of the employment of one factor to that of a second
is steadily increased from very low values to very high values, the follow-
ing changes appear in the output per unit of each of the factors.
1. At first, for each of the factors being used, the per-unit output in-
creases. This is seen for the factor used relatively freely in this stage, from
the behavior of the output per unit of A2, during the movement to the right
along GH from G to M. The same is seen for the factor used relatively
sparingly in this stage, from the behavior of the output per unit of Alt dur-
ing the movement to the right along GH from G to M.
2. A range follows during which the output per unit of the factor whose
relative employment is being decreased rises steadily (this is seen from the
behavior of the output of A2 during the movement to the right along GH,
from M to E); while the output per unit of the factor whose relative employ-
ment is being increased falls steadily (this is seen from the behavior of the
output of A1 during the movement to the right along GH, from M to E).
3. Then there is a final stage where, for each of the factors, the per-unit
output decreases (this is seen for both factors”the one being used sparingly
in this stage, A2', and the one being used relatively freely in this stage, A1”
by the behavior of the per-unit output of each in a movement to the right
along GH, to the right of E).
We are also in a position to set forth the consequences of altered input
proportions upon the effectiveness at the margin of units of the factors.
We have seen that a movement to the right along GH (that is, the addition
of successive increments of input A1 to a fixed input of A2) brought about
a rise in the output per unit of Ax until the ridge line at M, after which it
fell. In other words, so long as the input of Ax (for the given quantity of
A2) is less than indicated by the point M, each additional unit of Ax brought
about such an addition to total output that the output per unit of A± was
raised. This means that in this range the marginal effectiveness of Ax was
PRODUCTION THEORY 1 71


greater than the average effectiveness of Ax. Moreover, in the range along
GH moving from M to E, the effect of adding a unit of Ax brought about so
small an addition to output that the output per unit of Ax was lowered.
This means that in this range the marginal effectiveness of A1 was lower
than the average effectiveness of Av Finally, moving along GH to the
right of E, we found that each additional unit of A1 actually reduced total
output; the marginal effectiveness of A± in this range is therefore negative.
Similarly, for a movement upward along WZ it can be seen that until
the ridge line at Ef, the marginal effectiveness of A2 (added to a fixed input
of Ar) is greater than the average effectiveness of A2; that above E' the mar-
ginal effectiveness is lower than the average effectiveness, and that above M'
the marginal effectiveness is actually negative. Translating the movement
up WZ into the equivalent but reversed movement to the right along GH,
we see that until the point M, the marginal effectiveness of A2 is negative;
that between M and E the marginal effectiveness of A2 is positive but below
the average effectiveness of A2, while to the right of E the marginal effective-
ness is greater than the average effectiveness of A2.
We can restate the results of the preceding paragraphs as follows. As
the ratio of the employment of one factor to that of a second is steadily
increased from very low values to very high values, the following changes
occur in the effectiveness at the margin of additional units of input of each
of the factors.
1. At first the factor that is being used relatively freely in this stage
is negatively effective at the margin”this is seen in the negative marginal
effectiveness of A2 in the movement along GH to the right until M; while
the factor being used relatively sparingly in this stage is positively effective at
the margin (and has a marginal effectiveness greater than its average effec-
tiveness in this stage)”this is seen in the marginal effectiveness of A1 in the
movement to the right along GH to M.
2. A range follows where the factor xohose relative employment is being
decreased is positively and increasingly effective at the margin (although not
as effective as the factor as a whole is, per unit, in this range)”this is seen in
the effectiveness at the margin of A2 along GH from M to E; while the factor
whose relative employment is being increased has an effectiveness at the
margin that is positive but steadily declining (so that it is below the over-all
per-unit effectiveness of the factor in this range)”this is seen in the effective-
ness at the margin of A1 along GH from M to E.
3. There is a final stage where the factor whose relative employment has
been decreased has an effectiveness at the margin that has risen higher than
the over-all per-unit effectiveness of the factor in this range, while the factor
whose relative employment has been increased is negatively effective at the
margin.
172 MARKET THEORY AND THE PRICE SYSTEM

The laws of variable proportions can now be expressed compactly in the
form of a table.

Effectiveness of Factor (AJ Effectiveness of Factor (A2)
Being Used in Smaller and
Being Used in Greater and
Smaller Proportion.
Greater Proportion.
Average Average Effectiveness
Effectiveness
Ratio of Ai/Ag
at the
effectiveness effectiveness
at the
margin
Margin
Stage 1 Greater than
Increasing
Increasing Negative
Very low At/A2 average
ratio
Falling (but Positive, increas-
Stage 2
positive) and ing, but less than
Increasing
Intermediate Falling
less than the the average
Ax/A2 ratio
average effectiveness
Greater than
Stage 3
Falling the
Falling Negative
Very high At/A2
ratio average

The interest these laws have held for economists over the past century
and a half, we have noticed, has been largely confined to the special case
where successive increments of a variable factor (such as labor) are added
to a given quantity of a "fixed" factor (such as land). The traditional "law
of diminishing returns" was formulated for this case, either (a) in terms of
the average product of the variable input (that is, its product per unit) or
(b) in terms of the marginal increment of product brought about by unit
additions to the variable input.10 The central point in either formulation
was that eventually the average product and the marginal increment of
product would both diminish. One or two points may be noticed concern-
ing these formulations. First of all, they do not assert that these variables
will always be decreasing. In fact, it will be seen from our analysis that if
there is any point (on a production surface characterized by constant returns
to scale) where the addition of a unit of one factor by itself will diminish
total output, then there is a range where the average product of that factor
is increasing. Marginal increment of product also may be increasing ini-
tially, but the point where it begins to decline will be before the point where
average product begins to decline. (This has sometimes caused unnecessary
confusion as to the point where "diminishing returns set in," due to con-
fusion between the two formulations of the law.)
10 For the proof that these two formulations are not mathematically equivalent (as
economists have sometimes believed), see Menger, K., "The Laws of Returns, A Study in
Meta-Economics," Economic Activity Analysis (edited by Morgenstem, O.), John Wiley
and Sons, Inc., New York, 1954.
173
PRODUCTION THEORY

Most of these considerations can be seen in Figure 8-11, which is a
vertical section of the production surface along the line GH. The curve
shown is thus the curve of total output corresponding to increasing input
of A1 (with a fixed input of A2). The curve that has been drawn is contin-
uous; thus, we can observe the way average output changes for very small
changes in input, and also the way marginal output changes continuously.11

Output
of
X




H Input of 4 ,
IM E
Figure 8-11


The average output of any quantity of input Ax is shown by the slope of the
straight line joining the origin to the total output curve at the relevant
point. Thus for input GI of Alf that output is 7/°, and average output is
therefore II°/GI, which measures the slope of the angle I°GI. Marginal
output at any level of input of A1 is shown by the slope of the total output
curve itself at the relevant point, since this is the limit of the rate per unit
of input at which the curve rises for very small increments of input.
It will be seen that until /°, the output curve rises more and more
steeply (corresponding to rising marginal product of Ax) and thereafter
rises less steeply (corresponding to falling, but positive, marginal product).12
At the point E°, when total output is at a maximum, the slope is zero
(horizontal), corresponding to zero marginal product for Ax\ thereafter the
slope is downward, corresponding to negative marginal product. It will
be seen further that straight lines drawn joining the origin to successive
points on the output curve have steeper and steeper slopes until the point
M° (where the slope of the line GM° is also the slope of the output curve it-
self, GM° being tangent to the output curve at this point); after M° the lines
11 See in this chapter p. 155, ftnt. 3.
12 Concerning whether the output curve passes through the origin (or begins to rise
only to the right of the origin), see Knight, F. H., Risk, Uncertainty and Profit, Univer-
sity of London (Reprint), London, 1957, p. 101”ftnt.
1 74 MARKET THEORY AND THE PRICE SYSTEM


have lower and lower slopes. This corresponds to rising average product of
Ax until the point M and steadily declining average product thereafter.
It will be readily seen that M, E, correspond to the two points in the
isoquant map where the line GH was intersected by the two ridge lines.
The first stage, described in the laws of variable proportions, thus corre-
sponds to the portion of the curve from G to M°. In this region the average
output of Ay is increasing, and its marginal output is positive and greater
than the average output (as seen by comparing the slope of the output
curve at any point in this region, with the slope of the line joining this
point to the origin). In the diagram, since this portion of the output curve
was drawn concave from above, the marginal output also was increasing
during a portion of the range. The second stage described in the laws of
variable proportions corresponds to the portion of the output curve between
M° and E°. In this region the average and the marginal outputs are both
decreasing (but positive). The third stage corresponds to the region to the
right of E°; average output continues to fall and marginal output is nega-
tive. The points M°, and E°, have the special significance that for point
M° average output of Ay is at a maximum, while at point E° total output
is at a maximum (with marginal output of Ax zero).
Taking the more general approach, with the focus upon the ratio
between the inputs of the two factors rather than on the absolute input of
Alt we can easily see the application of the symmetry noticed earlier. The
situation in the first stage with respect to average and marginal output
of AJt with the quantity of Ax increasing, is completely mirrored in the third
section, with respect to average and marginal outputs of A2 considered for
a steadily decreasing input of Ax. In particular it is true that with constant
returns to scale, wherever the ratio of the input of either of the factors to
that of the other is so low that the average output of the first factor rises
with its increased input, then the situation is such that the other factor is
being so used that its marginal product is negative; output could be in-
creased by discarding some of this other factor. Moreover, at M°, where the
average product of A1 is at a maximum, the marginal output of A2 is zero
(that is, the total output yielded with any fixed quantity of Ax is maximized
when A2 is employed in the proportion denoted by the point M in Figure
8-11); and the converse of this proposition is true at the point E°.

ECONOMIC IMPLICATIONS OF THE
LAWS OF VARIABLE PROPORTIONS
The laws of variable proportions describe the pattern of technical condi-
tions that make up the background of the alternatives the producer-en-
trepreneur is able to choose from. In the market place, the precise
PRODUCTION THEORY 175


determination of these alternatives depends on the prices that quantities of
the factors can be bought at in the market.
Several generalizations can be made immediately. No entrepreneur
will under any circumstances employ a unit of a factor whose employment
causes output to decline. Thus, the laws of variable proportions tell us
immediately that there are opportunities open to the entrepreneur that
he will unquestionably reject. The entrepreneur will not employ factors
in a proportion that fits into either stage one or stage three of possible input
proportions. In either of these regions greater output could be obtained
simply by discontinuing the use of some of the factors. Thus, the very
important result is established that the only portion of the production sur`
face ever seriously under consideration is between the ridge lines. This
means that any group of factors employed in production will be in such a
proportion that (a) the per-unit output of each factor would be lower with
increased input, and (b) the marginal increment of product of any factor
would be lower with increased input. 13 (Increasing average or marginal
products can occur only where one of the factors has negative marginal
product; that is, in the regions outside the ridge lines.)
The goal of the entrepreneur is to produce his output at the lowest
possible cost. Of all the available alternative ways of producing a given
output, there will be one, or several, that require a smaller total outlay
than the others. Or, to put the matter the other way around, of all the
possible levels of output that it is possible to attain with a given cost out-
lay, one or several will be higher than the others. The entrepreneur will
seek to combine inputs in that proportion that will squeeze the most output
out of the cost outlay.
If either of the factors is a free good, it is very simple to determine
the optimum factor proportion. Additional units of this factor can be
obtained, for any given cost outlay, without forgoing the employment of
any of the other factor that it might be desirable to employ. The en-
trepreneur, thus, must simply buy as much of the priced factor as the given
cost outlay permits and then combine with it as much of the free factor as
will maximize output. That is, he must choose the proportion of the factors
at which the marginal output of the free good is zero (which is then also
the point where the average output attributable to the priced factor is at
a maximum). This point, of course, is at the boundary of the middle stage
(within which all entrepreneurs will, as we have seen, necessarily operate)
where the free good is employed relatively more freely.

13 One conceivable exception to these generalizations may result from a producer's
knowledge that the market price of his inputs and outputs depends very sensitively upon
his own production decisions. For the remainder of this chapter wTe ignore this possi-
bility.
1 76 MARKET THEORY AND THE PRICE SYSTEM



THE LEAST-COST COMBINATION
Where, as is the usual case, both factors can be had only at a price, the
problem of determining the least-cost combination of factors for a given
output is very similar to the problem that the consumer faces in allocating
his income among several goods. In both cases the goal will be to ensure
that expenditure is distributed in such a way that were any sum of money
to be withdrawn at the margin from one good in favor of another, the
economizing individual would rank the sacrificed commodities higher on
his value scale than the additional commodities. In the case of the con-
sumer, the comparison involved the marginal utilities of the relevant com-
modities. For the producer the comparison can be made more objectively
in terms of the output given up, and the additional output gained. Thus
the least-cost factor combination, which the entrepreneur will consciously
seek to achieve, will be attained when the marginal increment of product
corresponding to the last "dollar's" worth of expenditure upon any one
factor is greater than the marginal increment of product corresponding to
a prospective additional expenditure of a dollar upon any other factor. If
this situation does not prevail, there is room to gain output, on balance, by
withdrawing money spent at the margin on one factor and expanding by
this amount the sum spent on other factors. This transfer will go on with
the consequence that the marginal increment of output corresponding to
the factor from which expenditure is being withdrawn will steadily rise
(because according to the law of variable proportions the relevant stage is
always that where the marginal output falls with greater inputs), while that
of the factors whose use is being expanded will fall, until the least-cost
combination is attained.
It is easy to see that with small-sized marginal units of factor (with
which the difference between the marginal increments of output corre-
sponding to two successively acquired units of factor can be ignored), this
least-cost combination condition can be stated as follows. The marginal
increments of product corresponding to units of any two factors must be
in the same proportion to one another as are their prices (MIPAl/MIP„2 =
price of ^j/price of A2). A given sum of money (S) being spent at the
margin on A2 (buying the quantity S/PAo, with P„9 the price of A2) makes a
difference to output responsible for S x MIPAo/PA(¬ output (approximately);
whereas the same amount of money spent on additional units of A1 could buy
V^¿i units > which could add (approximately) S X MIPAi/PAi in additional
output. But if, say, MIPAJM1PA2 > PAl/P„2 then MlPAJPAl > MIP„2/P„2
so that the transfer of expenditure at the margin from A2 to Ax would be
worthwhile. Thus, only equality between the two fractions describes the
situation where the least-cost combination has been attained.
177
PRODUCTION THEORY


GRAPHIC ILLUSTRATION OF THE LEAST-COST COMBINATION
The isoquant map provides, once again, a useful means for visualizing
the particular choice of input proportions that an entrepreneur will make
under given cost conditions. It is necessary to introduce once more a
graphic device that we have already met in the theory of consumer income
allocation”the constant expenditure curve. It will be recalled that if any
two goods, Ax and A2, can be obtained in any amount at constant prices per
unit (PAl and P¿2 respectively), then a line (BC in Figure 8-12) can be drawn




Figure 8-12

tracing out all the different packages of the two goods that a given sum of
money (say, S) can buy. For such a line, OB = S/P„2, and OC = S/PAl, so
that the slope BC with respect to the A1 axis is equal to P±JPA^` I*1 t n e
case of production, such a line passes through all the different factor com-
binations that can be bought for a given cost outlay and is given the name
isocost line.
When the isocost line is superimposed on an isoquant map, the points
where the isocost line is intersected by successive isoquants rank the differ-
ent factor combinations in order of their productive efficiency. The
particular choice of input proportions the entrepreneur seeks to achieve
corresponds to the point on an isocost line where it meets the highest of
these attainable isoquant levels.
In Figure 8-13 the isocost line BC (corresponding to a ratio of PAJPA» ”
OB/OC) is superimposed upon an isoquant map. It is evident that the
point P on the isocost corresponds to the particular factor combination that
yields highest output. It is at this point that the isocost is just tangent to an
isoquant. An any other point (for example, at T) the isocost can only
cut an isoquant; thus, there is a higher level of output that can be obtained
by giving up some of one input (for example, A2) and employing instead
additional units of the other (AA). At P, a transfer in either direction
178 MARKET THEORY AND THE PRICE SYSTEM

would be disadvantageous because it could result only in lower output.
Any level of output higher than at P is simply out of reach with this outlay.
It will be observed that at the point of tangency, the slope of the
isoquant line is the same as that of the isocost; thus, this point fulfills the
(approximate) condition that the additional quantity of any one factor
necessary to offset the withdrawal from production of one unit of the




Figure 8-13

other factor be equal to the ratio of the price per unit of the second factor
to the price per unit of the first. This, of course, is simply the same
condition developed in the previous section, that the ratio between the
marginal increments of product corresponding to units of the two factors
be equal to the ratio of their prices.14
This graphic derivation of the least-cost condition provides an inter-
esting illustration of several of the principles developed in earlier sections
of this chapter. Thus the significance of the fact that the factors are not
perfect substitutes for one another is clearly brought out. If factors were
perfect substitutes so that the isoquants were straight lines, then, if the
slope of these isoquants were different from that of the isocost, there would
be no point of tangency at all. Substitution of one factor for another
would continue until only the one factor would be used. If the slope of

14 It may be observed at this point that much of the isoquant geometry developed in
this chapter has, in the literature, a counterpart in consumer theory. In the literature
the formal and diagrammatic analogy between consumer theory and production theory
has been carried forward very extensively. Corresponding to the isoquant map in produc-
tion theory, economists discuss the indißerence curve map in the theory of the consumer.
An indifference curve is a line drawn through all those different possible combinations
of two commodities between which a consumer feels indifferent. The approach to
consumer theory adopted in Chs. 4 and 5 made it unnecessary to resort to the use of
indifference curves (concerning which there are some rather serious theoretical problems).
The detailed discussion of isoquant maps in the present chapter, however, may be
applied to consumer theory without significant alteration if it is desired to employ the
indifference curve technique.
179
PRODUCTION THEORY

the isocost was that of the isoquants, then the isocost would coincide with
an isoquant throughout its length; thus, no particular proportion between
the two factors can be pronounced the most economic. (This, in fact,
would be the case where, as we saw, the two factors make up one homo-
geneous group. The equality in isocost and isoquant slopes simply means
that different prices are not being charged for economically identical units
of factors.)




FC
Figure 8-14

Movement along an isoquant corresponds to an alteration of input
proportions. The fact that one such proportion is better than the others
is the corollary of the fact that the factors are not perfect substitutes for
each other. A change in the slope of the isocost (corresponding to a
relative cheapening of one of the factors, compared with the other) will
alter the point of tangency, either making a higher output possible for
the same outlay or bringing down the possible level of output. In any
event such a change will alter the optimum proportions of input in favor
of the factor that has become relatively cheaper.15
With a given relation between factor prices, it is possible to draw a
series of isocost lines, as BC, DE, FG . . . (in Figure 8-15). The respective

15 By an extension of the analysis of the least-cost combination, an insight can be
obtained into the notion of the demand curve for a factor of production. Such a curve,
for any one producer, reflects the different quantities of the factor that he asks to buy
at respectively different prices (all other things remaining unchanged). The lower the
price of a factor, the larger will be the quantity that a producer will generally wish to
buy. Our analysis explains part of the reason for this: the lower the price of a factor,
the more it pays to substitute it in place of other factors. The lower the price of a
factor, the greater becomes the marginal product derived from the last dollar spent on
it. Consequently the producer must (even if he were not to expand his output as the
result of the lower costs) switch expenditure at the margin from other resources to the
now cheaper resource, in order to achieve the (new) least-cost combination. (See also
Ch. 9, p. 200, ftnt. 10.)
MARKET THEORY AND THE PRICE SYSTEM
180

points of tangency on these lines correspond to the different factor com-
binations that are optimum for successively higher levels of cost outlay.
Each such point makes the most of the relevant cost outlay; the entrepre-
neur has to select that level of outlay, which, taken in conjunction with
the price he can expect to get for his output, maximizes profits. The
path joining these points of tangency is appropriately named the expansion
path.




0 C£ G I A%
Figure 8-15

We can refer graphically, finally, to the special case where one of the
factors is a free good, costing nothing to obtain. In this case, the isocost
line will be a straight line parallel to the axis of the free input. It will
show that a fixed quantity of the non-free input can be employed, with no
limit on the free input. The point of tangency with the isoquants will
be where the isoquants are vertical or horizontal; that is, on the ridge line.




(o)
PRODUCTION THEORY 1 81


At this point, as much of the free input is being used as can be employed
without diminishing possible output.

SUMMARY
Chapter 8 commences the analysis of the activity of the individual
market participant in the role of producer. This analysis serves as the
foundation for the examination of the supply side of the market. The
economist sees the producer as making choices among alternatives of a
special kind. These alternatives involve the various productive uses that
the resources available to him might be put to. The rejected productive
uses constitute the economic costs of production of any adopted process
of production involving scarce resources. In society the efficiency of pro-
duction is advanced through specialization and division of labor. The
producer's alternatives are rigidly controlled by the market prices of the
resources he must purchase for a given production process.
Production is carried on with factors of production. A unit of factor
may possibly be related to a second unit of factor in a substitute relation-
ship, or possibly in a complementary relationship. A unit of factor may be
specific to the production of a certain product; it may be specialized for
this particular production; or, on the other hand, it may be versatile in
production.
Analysis of production decisions is formalized by the use of several
mathematical and graphical concepts. Production possibilities are ex-
pressed in the production function, expressed graphically as the produc-
tion surface. Contour lines on this surface are isoquants. The slope of
the isoquants measure the substitutability between the cooperating factors.
Extreme cases are those where either no substitution at all is possible
(technically rigid proportions being required), or where the one factor may
be substituted completely for the second. Typical production processes
permit substitution between the complementary factors to a limited degree.
The isoquant geometry points up clearly the distinction between al-
terations in the proportions in which factors are combined, and alterations
in the scale in which factors (combined in a given proportion) are applied.
Alterations in scale yield alterations in output that may be characterized
by increasing returns to scale, decreasing returns to scale, or constant re-
turns to scale. Alterations in factor proportions yield alterations in out-
put that are governed by the laws of variable proportions. Detailed anal-
ysis of the various possible cases throws light on the alternative possible
ways of expressing these laws.
The economic implications of the laws of variable proportions include
the delimitation of the best input combination a producer will employ
1 82 MARKET THEORY AND THE PRICE SYSTEM


under given technical and market conditions. The attainment of this
"least-cost combination" may be analyzed both logically and graphically.


Suggested Readings
Knight, F. H., Risk, Uncertainty and Profit, University of London (Reprint), Lon-
don, 1957, Ch. 4.
Carlson, S., A Study on the Pure Theory of Production, Kelley and Millman Inc.,
New York, 1956.
Stonier, A. W.”Hague, W. C , A Textbook of Economic Theory, Longmans Green,
London, 1953, Ch. 10.
Costs and Supply



A, of the operation
.N UNDERSTANDING
of the full market process must include, we have seen, the understanding
of the forces acting to supply the market with the various produced goods
and services. These forces determine the arrays of alternatives offered to
prospective consumers. But we have seen that these forces are themselves
conditioned by the circumstances under which entrepreneurs are able to
engage in production. In particular the entrepreneur operates in a situ-
ation where his choice of product, his choice of production method, and
his choice of volume of production must be made on the basis of the
market facts relating to the prices of both products and factors. In order
to produce any particular quantity of a particular product in a particular
way, the entrepreneur must pay definite costs of production. The quantity
of any one product that an entrepreneur will contribute to the market
supply, thus, will depend partly on the costs incurred for this output. The
quantity that the market as a whole will supply of any one product will
in turn depend partly on the costs of production that must be incurred
individually by entrepreneurs for the various possible levels of output.
In this chapter we carry further the analysis of the forces of supply.
Leaning heavily on the principles of production discussed in the previous
chapter, we examine especially the way costs of production of firms in a
particular industry are likely to change with output. The chapter carries
through the analysis to include the way the entrepreneur reacts to these
alternative production opportunities and the way is thus cleared to the
understanding of the forces of supply as they finally impinge on the market.
The focus of attention in this chapter is thus rather different from
that of the previous chapter. There we studied production, examining
the way output depended on the particular input combination employed.
Here we adopt a point of view corollary to that of the previous chapter;
183
1 84 MARKET THEORY AND THE PRICE SYSTEM


here we are principally concerned with the way the costs of the firm depend
on the level of output. Unless otherwise specified, it may be assumed
throughout the chapter that for each output level, the least-cost combina-
tion problem has been solved. We turn first to a review of the ultimate
meaning of cost and its place in production theory.

COSTS AND RENTS
The cost concept is bound up inseparably with the concept of human
action. Action consists in choosing between alternatives. The adoption
of any one specific alternative implicitly involves the rejection of other
alternatives; in particular it involves the rejection of the "second-best"
alternative”namely, that alternative that would have been adopted had
the alternative that was actually adopted been unavailable. It is this
rejected alternative that the economizing individual recognizes as the cost
of the adopted alternative simply because both opportunities cannot be
simultaneously adopted. A man may have to choose between the chance
of opening a certain kind of store on the one hand, and retaining the
friendship of a man engaged in the same line of business, on the other
hand. If he adopts the former alternative, then he recognizes that his
business has cost him his neighbor's friendship. Should he value the
friendship more highly, then the cultivation and preservation of this friend-
ship has cost him a possible lucrative business opening. Cost is made up
of the conscious sacrifice of an available opportunity. This is the most
general conception of the cost category.
For the isolated individual, the act of production involves a particular
aspect of cost. The employment of a unit of a non-specific resource for
the production of one particular product necessarily withholds it from
making any contribution to the production of other products. A decision
to make any particular use of a resource thus involves the sacrifice of other
potential uses. This sacrifice constitutes the cost of production of a pro-
duced good. Every product is produced at the cost of some other product.
This is the idea of opportunity cost.
Where production takes place within the framework of a market econ-
omy, the conception of cost of production is not quite so simple. While it
is true that a firm owning a fleet of taxicabs might conceivably use the
services of the cab drivers whom it employs to drive transcontinental freight
trucks, this opportunity may not be an alternative normally taken into
serious consideration. With effective division of labor, we have seen that
an entrepreneur finds himself able”and called upon”to decide on the
kind of product he is to produce only at relatively infrequent intervals.
A taxicab firm does not ordinarily weigh the relative usefulness of its
employees as cab or truck drivers. When it sends men into the streets
COSTS AND SUPPLY ] 85


with its cabs, the firm has immediately rejected, not the opportunity to
send them into the highways with trucks, but the opportunity to refrain
from hiring the men altogether. The rejected opportunity is normally
thus the chance to save money costs paid to its cab drivers”including, of
course, the chance to use the money saved to improve the quality of other
inputs”perhaps to buy new cabs more frequently, perhaps to install a
radio-dispatch system. In a market economy the individual entrepreneur
considers as his costs of production the sums of money he is required to
pay for factors in the market. A product is produced with the sacrifice of
these sums of money. The alternative that is rejected is the opportunity
to avoid both the act of production and the expenditure of money that it
entails.
But the concept of opportunity cost, which we found in the case of
the isolated individual producer, plays an important role in costs of pro-
duction as they emerge in a market economy as well. There is an im-
portant sense in which the cost of production of any product is in fact the
sacrificed opportunity of producing either some other product or the same
product elsewhere. While it is true that the notion of cost pertains
essentially to the alternatives forgone by an individual in his act of choice,
a secondary connotation also is attached to it. The term "cost" is applied
somewhat loosely to the effects of a given act of choice even where these
are felt by an outsider. The decision of a man not to open up a particular
business, in order to preserve a friendship with a potential competitor,
may be said to have "cost" the consumers the advantages that would have
ensued from their competition. In the same way, while the employment
of drivers in one branch of industry costs the individual employers only
definite sums of money, this employment, in a very real sense, "costs"
other branches of industry the opportunity to use the services of these
drivers. And, similarly, one can say that the employment of drivers by
a particular employer "costs" other employers in the same industry the
services of these drivers.
From this opportunity cost point of view, the "cost" of a particular
decision may take on a number of quite different dimensions, depending
on the point in the economic system upon which the effects of the decision
are being assessed. From the point of view of taxicab firms, the employ-
ment of a driver by taxicab fleet A has the effect of withdrawing a potential
driver from each of fleets B, C, and so on. From the point of view of
consumers, however, such an employment has hardly any effect at all on
cab service; but it has an effect on consumers insofar as other branches
of industry are concerned. The cab driver's employment costs the con-
sumer virtually nothing in terms of cab service, but it does cost them the use
of the drivers in other kinds of service.
These considerations are not merely a questionably ingenious way of
1 86 MARKET THEORY AND THE PRICE SYSTEM


stretching the meaning of the word "cost." They point, in fact, to sig-
nificant relationships in the operation of the market system. The key to
the matter is that the sums of money that the individual producer con-
siders as his costs of production tend to depend in a sensitive fashion upon
these other opportunity costs of production. For a cab driver to be em-
ployed by any one employer, it is necessary that he be paid a wage (which
are money costs of production from the employer's point of view) at least
high enough to keep him from selling his services either to employers in
other industries or to other employers in the taxicab industry itself. The
employment of a driver at one point in the economy means the withdrawal
of his potential services from other points in the economy. The values
of these potential services to employers at these respective points are the
measures of the relevant "costs" of the employment. At the same time
these values set the amounts of money that these other employers will be
willing to bid for these services. The wage actually paid must be at least
high enough to outbid these amounts. Thus, an entrepreneur's money
costs of production reflect in part also the value of the opportunity costs
of production as felt by other employers and other industries.
The sums of money paid by the entrepreneur for a factor of production
(and thus entering into his costs of production) can thus be analyzed into
a number of distinct amounts. First, one part of the sum paid to a factor
by a producer of a given product was necessary to attract and keep the
factor in the industry producing this product. This amount would have
to have been paid by any employer producing this product to prevent
the factor from being successfully bid for by entrepreneurs producing other
products. The size of this amount thus depends on the value placed by
the entrepreneurs in these other industries, on the usefulness of the factor
to them in their production activities. This element in the money costs
of production paid out by the eventual employer of the factor, thus meas-
ures that cost to consumers”often loosely termed the "social cost" of
production”which takes the form of the lost products that might have
been produced by entrepreneurs in other industries (the measurement
being made by the appraisals of these entrepreneurs). This element is
frequently termed the transfer cost of the factor, the amount that must
be paid to the factor to keep it from being used by another industry. Any
amount of money paid to a factor over and above its transfer cost cannot
be considered as "costs," from the point of vieiu of the consumers choosing
between products. The assignment of a factor to the production of a
particular product has not implied any loss of other possible products to
consumers that can be valued above the transfer costs of the factor.
From this point of view, sums of money paid for a factor above transfer
costs are termed economic rent to the factor owner. The importance
of the recognition of this second element, in the sums of money paid for
COSTS AND SUPPLY 1 87


factor services, lies in the realization that any payment of rent in this
sense involves no exercise of influence upon the allocation of factors be-
tween industries.
Although from the point of view of consumers only transfer costs are
true costs, insofar as the choice of product is concerned, there may be
valid points of view from which the cost element in the payments to fac-
tors is considerably larger. What is rent from one point of view may
well be true cost from another point of view. The amount of money
that a particular employer must pay to ensure that the services of a factor
are not snapped up by a rival producer of the same product is a true
cost, in the sense that this sum is the decisive factor in the allocation of
productive factors between producers of the same product. And even
from the point of view of the consumer this kind of allocation is not a
matter of indifference, since different producers may have different degrees
of ability in efficiency of production. What is a rent, viewing the industry
as a single unit, may be a cost, when the industry is viewed as consisting of
producers of different entrepreneurial skills. An oilfield being exploited
by a particular oil company commands a price a small part of which is
necessary to withstand the competition of farmers for the land, the rest
being necessary to outstrip the competition of other oil companies. This
second portion of the price is rent from the viewpoint of the oil industry
as a whole, but cost from the viewpoint of any one oil company.1

OPPORTUNITY COSTS AND SUPPLY THEORY
When it is realized that in a market economy as well, the costs that a
producer's accountant reports to him are to be seen as reflecting opportun-
ity costs in a real sense, then the dependency of the supply of particular
products upon costs of production becomes visible in its proper context.
It is apparent, for example, that the reason why all the resources of an
economy are not channeled into the production of a single product is that
the costs are too high, in tivo senses that are ultimately equivalent to one
another. First, after a point the price that must be paid for the necessary
factors would become very high indeed, far higher than could be justified
by the value of the product produced. Second, the channeling of all re-
sources into a single product means the complete cessation of the supply
of any other goods; this sacrifice is too great. Both interpretations are
ultimately equivalent in that the intolerable magnitude of the sacrifice
of all other products manifests itself in the high prices that will be offered
in the market for the other products, and hence for the resources required
for their production.

l Sec p. 230, ftnt. 12.
1 88 MARKET THEORY AND THE PRICE SYSTEM


These considerations point up a general tendency operating upon
the supply of any one product.
The per-unit costs of production of any particular product tend in
general to rise as the margin of output of this product is advanced.
Economic analysis of the conditions of supply of particular commodities
hinges ultimately upon the degree to which this tendency is actually ful-
filled as against the degree to which this tendency is thwarted by special
circumstances. As more and more of a particular commodity is produced
during a given period of time, fewrer and fewer other commodities can
be produced. By the principle of diminishing marginal utility, this means
that the advancement, by successive units, of the margin of output of a
particular product would involve the simultaneous reduction in impor-
tance of each additional unit of this product, and increase in importance
of the units at the respective margins of output of other products. But
this can only mean that the expansion of any one kind of production tends
to entail, for each additional unit to be produced, the rejection of alterna-
tives that are more and more difficult to ignore; a tendency toward in-
creasing costs prevails. For the isolated individual, as for the market,
the tendency toward increasing costs determines the margin of production
for each good. The market process strives, as do the actions of the isolated
individual, for a production pattern that strikes a balance between goods
so that the opportunity costs of the production of each good be minimized.
The output margin for each good tends to be at the point where an ad-
ditional unit of it (whose utility falls with increased output) would no
longer justify the opportunity cost of its production (which rises with
increased output).
Ultimately, this is a general tendency that can hardly be escaped. The
competitive market process may in fact be viewed as enforcing that or-
ganization of production that is enjoined by this principle of increasing
cost. Nevertheless, this process is complicated by the different ways the
tendency toward increasing cost actually makes itself felt in the cost data
facing the individual entrepreneur. It is vastly complicated further by the
possibility of ranges of production where there is no apparent tendency to-
ward increasing costs. Most of this chapter is concerned with these com-
plications. Our task will be to understand the selection by the entrepreneur
(who produces one commodity) of that quantity of output that he will seek
to supply to the market, out of the alternative output levels available to him.
As was the case in the analysis of consumer demand, understanding the way
the individual producer makes his output decisions will clarify the nature
of the forces acting upon the market supply of particular products.
COSTS AND SUPPLY 1 89


PROSPECTIVE AND RETROSPECTIVE COSTS
The insights afforded by viewing production costs as sacrificed op-
portunities are of particular value in distinguishing sharply between the
costs of production concerning which the accountant informs the entre-
preneur after a process of production has been completed on the one hand,
and those costs of production that are, on the other hand, involved in the
entrepreneur's decision making before embarking on a production process.
We are directly concerned only with the latter in the analysis of supply
(although, of course, the entrepreneur's anticipations of future costs are
built on his experiences in previously completed production ventures).
An entrepreneur has produced a quantity of goods and wishes to de-
termine in retrospect the total costs of his production. His financial rec-
ords provide information concerning a large number of outlays that had
to be incurred in order for the production to take place. First of all, far
in advance of the actual production, the entrepreneur built or bought
some kind of manufacturing plant. The books record both the sum paid
for the plant and the interest the entrepreneur has had to pay (and which
he may still be paying) on the capital raised to make the initial investment
in the factory. These sums were incurred, it is true, in order to engage
in production over a long period of time; they were not paid solely in
order to produce the particular batch of goods whose costs of production
the entrepreneur is now examining. Nevertheless, if these sums had not
been paid, these particular goods could not have been produced. The
entrepreneur is immediately conscious, in retrospect, of the difficulty in
stating precisely what portion of these initially incurred sums of money
are to be included in the costs of production of any particular batch of
produced goods.
In addition, the entrepreneur's records mention sums paid, both in
the past and during the period the goods were being manufactured, for
maintenance and repairs to the plant and equipment. These sums also
were incurred not only to produce one particular batch of goods. All these
sums were more or less necessary in order that the particular batch of goods
be produced, but the amounts thus paid seem to have little relation to the
size of this batch of products. These sums, too, do not vary in any simple
manner, in relation to the size of the batch of products whose costs of
production are under examination.
But the entrepreneur's accounts may show further sums that do relate
very precisely to this batch of goods. It may be possible to calculate, for
example, the amount of money paid for the raw material used up in the
production of these goods; it is possible to calculate the amount of money
paid for the labor directly employed in their manufacture. These sums
depend very plainly on the size of the batch of products under considera-
1 90 MARKET THEORY AND THE PRICE SYSTEM


tion. If a smaller batch had been produced, less raw material would have
been bought and less labor would have been hired. It is quite possible,
however, that some expenses, incurred for raw materials, labor, power, and
other factors used up entirely in the production of this batch of goods, were
undertaken in advance and would have required payment regardless of
the quantity of goods produced. It is possible, for example, that some
of the labor employed in the production is engaged under a contract pro-
viding for an annual salary, or that certain raw materials were already
bought (or agreements for their purchase completed) well before the actual
production decisions were made.
This wide variety of circumstances surrounding the expenses incurred
in connection with the production of the goods may not altogether frus-
trate the entrepreneur who is trying to discover ex post facto what total
figure to assign to the payments made for all the factors of production
employed.2 But this variety does point clearly to the fact that the costs
of production involved in the decisions to produce may be quite different
from the costs of production used to calculate the profit or loss relating
to a completed venture. The key point is that a process of production
takes time;3 thus, there are typically a number of opportunities to make
production decisions, to revise them, to carry them forward, or to abandon
them. At each such opportunity the entrepreneur makes his decision,
based partly on the anticipated costs of production of the process. For
each such decision the relevant costs of production are different.
When a process of production is being contemplated from the very
beginning, the entrepreneur must try to anticipate all the expenses that
the process will necessitate. These "full costs" are identical, in the en-
trepreneur's mind, with the costs that he expects to use at the end of the
process in calculating the final profit or loss of the entire venture. But as
the plan of production is put into operation, the entrepreneur again and
again is called upon to decide whether the process should be continued as
planned, continued with changes, or simply be abandoned. In making
2
It will be remembered throughout the chapter that costs of production must, from
the opportunity cost viewpoint, include not only the actual money expenditures that
the producer makes to buy resources, but also those values of his own resources that
he employs in production. The latter values are known as i?nplicit costs and must be
included in any economic tally of costs of production both prospectively and retrospec-
tively. A producer who devotes his own labor to production is obviously sacrificing what
he could earn in the market by his labor. (The accountant will, in this respect especially,
frequently furnish records or estimates of "costs" that are different from those relevant
to economic theory.) It should be observed that from the theoretical point of view,
which sees production carried on by "pure" entrepreneurs who own no resources, all
costs will be explicit. Implicit costs arise only in a real world where different market
functions are performed in combination by a single market participant.
3 For further analysis of the time-consuming aspect of all production, see pp. 316 ff
in the Appendix on multi-period planning.
COSTS AND SUPPLY 191


these decisions, the entrepreneur must still consider the costs of production
necessary for a continuation of production. He must, as in all entrepre-
neurial decision-making, balance expected revenue against expected costs.
But in making this calculation,
he pays no attention whatsoever to the expenses of production that he
has already paid out (or that he has irrevocably committed himself
to pay).
What has been paid has been paid. To be sure the entrepreneur will be
conscious that his past actions and commitments have determined, in
part, the circumstances under which future activity must be carried on.
(He will be aware, for example, that a past commitment to pay annual
interest sums on capital sunk into a plant will limit his future cash posi-
tion.) But in comparing anticipated costs with anticipated revenues, the
entrepreneur pays no heed to those amounts that do not depend on his
present decisions. These past amounts may have been wisely or unwisely
incurred, but there is nothing that can be done to alter the past. The
aim must be to exploit now the favorable position the entrepreneur may
find himself in (as a result of the past decisions that now appear to have
been wise ones); or to make the best of a poor situation he may find himself
in (as a result of past decisions that now appear to have been unwise ones).
In either event, the way to achieve this aim is to make that decision, with
respect to the continuation of the production process, that promises the
widest margin between the revenue anticipated on the one hand, and the
costs of production yet to be incurred through continuation of production,
on the other hand.
When the statement is made that the quantity supplied to the market
by the individual entrepreneur depends on his costs of production, the
proposition may thus refer to many different situations in each of which
it is valid, mutatis mutandis. It is true that the quantity supplied by an
entrepreneur depends on his decisions as to the size of factory to build,
and it is equally true that the quantity supplied depends on entrepreneurial
decisions as to how heavily to utilize a given plant once it has been built:
on the decisions as to how many machines to install; and, again, on sub-
sequent decisions as to how fully to employ the available machines once
they have been installed; and so on. For each of these decisions the rele-
vant "costs of production" are different; yet there is clearly a sense where
supply depends on each of these different conceptions of costs of produc-
tion. The crucial point is obviously the time factor. There are forces
acting upon supply which make themselves felt both frequently and rapidly;
there are other forces, no less powerful, which influence supply less fre-
quently and less rapidly.
In the economic literature it is sometimes convenient to group together
the short-run influences upon supply, as distinct from the long-run forces.
1 92 MARKET THEORY AND THE PRICE SYSTEM


The latter are conceived as being felt only over those periods of time long
enough to warrant reconsideration of the size of the firm's fixed plant.
The "short-run" forces are felt whenever there is room for decisions as
to the level of output to be achieved with given plant. While this dichot-
omy is of considerable convenience (as will be seen in later chapters), it
must not be regarded as more than a simplification. The truth is that a
decision that an entrepreneur is called upon to make may vary, in respect
to the permanence of its impact on production, through a wide spectrum.
A sudden change in market conditions may influence the entrepreneur to
step up production sharply. The immediately felt consequences, possibly,
will be overtime employment of the labor force and intensive utilization
of existing machinery. Should the change in conditions persist, the en-
trepreneur might initiate more frequent replacement of machines, recruit-
ment of a larger permanent work-force, and so on. Finally, the entre-
preneur might be called upon to decide whether or not to expand the
size of the factory, whether or not to build an additional factory, and so
on. Supply depends, in a different sense, upon each of these kinds of
decisions. Each such decision is based on the relevant costs of production.
In each case the entrepreneur is aware that the total relevant costs of pro-
duction will vary with the size of the output concerning which the decision
is to be made. Costs that do not vary in total amount with production
are simply not relevant costs of production. They are sums that have
already been incurred in past production decisions and therefore do not
depend on, and cannot influence decisions concerning, the level of output
now to be undertaken.4


CAPITAL GOODS AND COST THEORY
The foregoing discussion indicates the role played by capital goods
in a theory of costs and supply. We have seen that the forces influencing
the supply of a particular product are as numerous, and as different in their
impact, as are the opportunities available to the entrepreneur to alter the
progress of production. The main reason for the differences between the

4 The distinction between long-run and short-run forces is responsible for the
corresponding distinction, current in economic literature, between fixed costs and variable
costs. Fixed costs are unchanging for the duration of the short run; variable costs are
those that do change with changes in output even in the short run. From the long-run
viewpoint there are no fixed costs; all are variable. The discussion in the text will have
made it clear (a) that from the short-run point of view, expenditures that do not fall
under the heading of variable costs are best considered, not as "fixed," but as not being
costs at all; (b) that there may be a number of degrees of "fixity" in costs corresponding
to the numerous junctures at which a producer may be forced to make decisions (and
at which the expenditures previously irrevocably incurred are no longer weighed as cost
factors in arriving at decisions).
COSTS AND SUPPLY 1 93


impacts of these various forces lies fundamentally in the specificity of the
capital goods introduced at various stages of the process of production.
The concept of specificity in a factor of production refers, we have
already seen, to the limitation of the usefulness of the factor to a narrow
range of purposes. A specific factor is either used for these definite pur-
poses, or it can be of no use at all. Factors of production, we saw in the
previous chapter, are more specific or less specific, depending on their degree
of versatility in production.
Any produced factor of production capable of yielding productive serv-
ices over a period of time is a durable capital goody Capital goods emerge
as a result of past production of goods that were not consumed. Men pro-
duced, sacrificed labor and the services of other factors, in order to obtain
goods that should yield their services in later production. Where the
capital good is a durable one, the past production and utilization of produc-
tive services were undertaken in order to obtain a stream of such productive
services in the future.
Now it is in the nature of things that capital goods are (at least to some
degree) specific. When labor and raw materials have been combined to
produce any material object, this object is more suitable for some purposes
than for others. The labor applied in its manufacture might have been
used to produce something else; but it happened to be used up in the pro-
duction of this object. While it is sometimes said that capital goods repre-
sent "saved-up" labor (along with other productive services), the capital
good cannot serve, in general, as a store of the versatility of the invested
labor. A man may be able to dig holes in the ground with his bare hands.
Instead he uses them to fashion a spade. The production of this capital
good enables him to "save" his original labor for later use. When he uses
his spade later to dig holes, he reaps (with more or less "profit") the fruits
of his originally invested labor. But the spade, which serves as the "store"
of labor, has stored it in a form that is specific; the original labor services
(which might have been used to chop down trees) can be exploited, in their
stored-up form, only to dig holes.
This necessarily specific character of capital goods is responsible for the
heterogeneous nature of the cost forces acting upon supply. If capital
goods were completely versatile, then the fact that past decisions have been
made would in no way interfere with the necessity to weigh the full costs
of production in making later decisions. Complete versatility in capital
goods (conceived broadly as the capacity of a good to serve equally valuably
in any productive process”and thus including complete mobility and ease
of transfer ability between firms and industries) would mean that expenses
paid out as a result of past decisions are completely retrievable. A new
5 For additional remarks on the nature of capital goods and their role in production
and in market theory, see in the Appendix on multi-period planning, pp. 317-320.
194 MARKET THEORY AND THE PRICE SYSTEM


decision to continue a particular process of production will thus have taken
into account the fact that this course of action means abandoning for the
time being the possibility of recovering all the sums already sunk into the
productive venture. Each decision made during the production process
would then be made by comparing expected revenues with expected total
costs”the latter including all sums, those already spent as well as those
expected to be paid. The level of output will be determined on the basis of
the same cost at each state of decision making (assuming no change in the
market data concerning costs). Changes in the market prices of finished
products would set up forces influencing supply that would not depend for
their impact upon the time available for the impact to be felt. Forces able
to exert a certain long-range impact would not exert any different pressure
on supply than that exerted by forces felt within a very short time.
Capital goods, however, are not completely versatile. Once a decision
has been made to invest in a certain machine, it is a commonplace that the
sum invested can be recovered only at considerable loss, should the original
production plans be abandoned later on. The machine will hardly be able
to be used in other productive processes; and its value as scrap will be far
less than the price paid for it. Moreover, even where the machine can be of
use to similar firms, or to firms in other industries, the cost of transfer is
likely to be such as to make full recovery of its purchase price impossible.
Later decisions concerning the use to be made of the machines will therefore
disregard a large part of the sums originally paid for the machines. The
determination of supply in periods short enough to warrant no purchase of
new machines will therefore be governed by cost considerations different
from those influencing supply when longer periods (during which the costs
of machines may be a pivotal factor) are under consideration.
The more durable the capital goods involved, the longer will be the
time periods during which it may be possible, and wise, to ignore the cost
of the capital goods. The more durable the capital goods, the longer it
will be possible to use their services in production, without having to worry
about their costs”since these services have been paid for already anyway.
A typical situation the entrepreneur finds himself in is where a factory,
more or less well-equipped with certain machinery, has been already con-
structed. The existence of such a complex of durable, immobile, and spe-
cific factors exercises a profound influence on the relative attractiveness of
the various alternatives available to the entrepreneur. The entrepreneur
may be aware of new techniques of production that would enable a modern
factory equipped with up-to-date machines to produce a larger output at a
fraction of his present cost. He may be deterred from embracing this
possibility because the wonderful new factory requires the outlay of money
”new money, while the old factory, inefficient as it is, is available for use
at almost no cost at all. The opportunity costs at this stage of producing a
COSTS AND SUPPLY 1 95


given output with the more "efficient" plant are greater than with the less
"efficient" plant. Both from the point of view of the entrepreneur himself,
and from that of the consumers, the relevant opportunity costs indicate using
up the old plant while it is still worthwhile. Only when the gap between
the technical efficiencies of the new and the old plants has become so wide
as to outweigh the cost disadvantage involved in the initial construction of
the new plant (as compared with the old) will it be economically advanta-
geous to scrap the old factory. Such a gap may occur while the "old" factory
is still quite new; revolutions in technology may render recently constructed
plants completely obsolete. But, more likely, it is necessary for the old
plants to depreciate physically to a greater or lesser extent before it pays to
build a newer and more efficient plant. In the interim period, during
which repeated entrepreneurial deliberations pronounce the old factory the
most advantageous, output levels will depend on the additional costs in-
curred by producing with the existing plant.
These additional costs required to cover the raw materials, labor, and
other productive services used directly in the manufacture of the product
will be found to vary, per unit of output, with the level of output itself.
The existence of a fixed plant, which for the time being is not to be changed,
exerts in itself a powerful influence on the relation between output level
and per-unit production costs. This relationship must now be explored.

FACTOR DIVISIBILITY AND SHORT-RUN PER-UNIT COSTS
Production is carried on, we have seen, with the aid of capital goods.
The more advanced the organization of production in an economy, the
more durable will be the capital goods used in production, and the greater
will be the proportion in which capital goods are combined with other com-
plementary factors of production. The existence in a plant of any given
complex of capital goods has two distinct implications for costs of produc-
tion that the entrepreneur must consider in his daily production decisions.
First, as discussed in the previous sections, the relevant costs in daily deci-
sions will not include sums incurred in the past for the acquisition of the
capital goods, insofar as these involve no current opportunity cost. Second,
and it is this influence that is discussed in this section, a given complex of
capital goods is itself the source of a definite pattern that the entrepreneur
will find to characterize the way his relevant costs of production depend on
the volume of output. This pattern in the costs of production is an inev-
itable consequence of the limited divisibility of capital goods; the pattern
itself is an implication of the laws of variable proportions.
An entrepreneur has at his disposal a fully equipped plant. A decision
to alter output will have the short-run effect, not of a plant being closed
196 MARKET THEORY AND THE PRICE SYSTEM


down (or another erected), but of a different quantity of variable factors
being used complementarily with the given plant.
Any decision to alter production would thus have the immediate effect
of altering the proportions in which the fixed plant and the variable
productive factors are combined.
If capital goods and other factors were highly divisible, then a change
in the volume of output would not necessarily entail an alteration in the
input proportions of the different factors. For each level of output the
optimum combination of factors would be employed. A 10% increase in
the volume of output would call for alteration in the quantity employed
of each of the factors wherever”and only wherever”this would meet the
requirements for the new optimally proportioned input mix. With com-
plete divisibility, there would be no obstacle preventing the exact desired
adjustment in the employment of any factor. Thus, no efficiency in produc-
tion would be gained, nor would any efficiency be lost, by an alteration in
output volume, insofar as efficiency depends on input proportions.
But, of course, capital goods are only imperfectly divisible. An en-
trepreneur who owns one sewing machine can hardly increase or decrease
his employment of sewing machines by 10%. An airline can alter the size
of its fleet of planes only by adding or discarding planes in whole numbers.
Therefore, an entrepreneur who slightly decreases the volume of his output
must do so typically by combining a smaller quantity of variable inputs with
an unchanged quantity of fixed capital equipment. Only if the cutback
in production is considerable will the input of these capital goods be de-
creased. The more elaborate the capital goods involved, the greater the
cutback (or the boost) in production will have to be before any alteration in
the input of this factor is feasible.
The consequence of capital-goods-indivisibility is thus that different
volumes of output are inevitably associated with differently proportioned
input combinations. Thus, the laws of variable proportions clearly become
relevant. Differently proportioned input combinations are in turn asso-
ciated with different efficiencies in production. A change from one level
of production to another means a change in the output that can be obtained
from a given quantity of inputs. Put the other way around, this means
that different volumes of output will be obtained at the cost of respectively
different quantities of input per unit of output. Costs of production must
change, per unit of output, with changing output itself, simply as a conse-
quence of the laws of variable proportions.
We have already seen how the cost forces acting upon the supply of
a product may exert their influence over different time periods. Some
forces will be felt more swiftly, others will be felt only gradually, through-
out longer periods of time. The main reason for this heterogeneity in cost
forces stems, we have seen, from the existence of more or less fixed blocks of
COSTS AND SUPPLY ¬ 97


specific capital goods that are introduced at various stages in the process of
production. Factor indivisibility, in which we are now directly interested,
plays an obvious part in emphasizing this heterogeneity. The costs of
erecting the firm's plant are "fixed," for considerable lengths of time, be-
cause it is only infrequently that it becomes feasible to change the entire
plant. But if plant size were capable of being altered by small percentages,
such alterations would seem profitable at far more frequent intervals. The
fact that items such as heavy machinery and plant are not capable of such
nicely adjusted alterations in size makes their costs relatively fixed over
considerable periods. If plant size were easily variable, then even a rapid
change in output volume might bring about some change in the size of
plant.6
With the imperfect divisibility of capital goods, a fairly well-defined
pattern of per-unit costs of production emerges. An entrepreneur finds
himself with given fixed capital equipment, plant, and machinery. If the
forces of demand were to move him to produce smaller and smaller output
volumes, the immediate consequences would be that the variable inputs
would be combined with the fixed inputs in smaller and smaller propor-
tions. These proportions might be so low that the marginal increment of
product corresponding to a small hypothetical increase in the fixed input
might possibly be negative for low levels of output; in such a situation any
increase in the variable inputs must raise the output per unit of variable
inputs. The proportion of variable to fixed inputs would be less than
optimal: the fixed plant would be greatly underutilized. If, on the other
hand, the entrepreneur were moved by market demand to produce larger
and larger volumes of output, the situation would be reversed. Variable
inputs would be combined with fixed inputs in greater and greater propor-
tions. For one particular volume of output, the input proportions would
be optimal. For greater outputs the fixed plant might be used more inten-
sively than would be optimal; the average efficiency of the variable inputs
would be falling. Although variable inputs would never be added by the
entrepreneur in such volume as to make the corresponding marginal incre-
ments of product negative, nevertheless, the proportion of variable to fixed
inputs may be so high as to render the marginal increment of product very
low.

6 Even if plants were perfectly versatile but able to be built only in a limited number
of sizes, this indivisibility would mean that plant alteration is feasible only at fairly wide
intervals. On the other hand, even if plants could be built in any desired size but
were completely specific to one kind of production (or were, at any rate, completely
immobile and thus unable to be transferred to other branches of production), plant
alteration, once again, would be feasible only at long intervals. In the real world, then,
both specificity and indivisibility combine to make expenditures for plant a cost only
from the long-run view, and to bring about the typical pattern of variable costs discussed
in the text.
198 MARKET THEORY AND THE PRICE SYSTEM


Translated into cost terms, our analysis thus yields fairly straight-
forward conclusions insofar as short-run entrepreneurial decisions are con-
cerned. We recall that in day-to-day decision making, the fixed inputs
entail no costs. The entrepreneur is called upon to make pecuniary sacri-
fices in order to obtain product, only through his purchases of variable
factor services. The average efficiency in production of these services has
been seen first to rise and then to fall as output is increased from very low
to very high levels. Thus, the sacrifice of factor services, per unit of out-
put, which the entrepreneur is called to make, would tend to fall, reach
a minimum, and then rise for outputs raised higher and higher from very
low levels. We may assume for the time being that the prices of factor
services, which the entrepreneur is required to pay, do not depend on vol-
ume of output. It is then clear that the per-unit costs of production rele-
vant to short-range entrepreneurial decisions will be high for low outputs,
fall to a minimum for higher outputs, and then rise to higher levels once
again as output is increased to the point where the fixed plant is being over-
utilized, so that decreasing average returns to the variable inputs prevail.

SHORT-RUN COSTS AND THEIR EFFECT ON SUPPLY
We have discovered that per-unit costs of production follow a character-
istic pattern when the volume of production is changed within the frame-
work of a given plant. This pattern suggests the way a producer with a
given plan will make short-run output decisions, and the way these decisions
will change with changes in the market conditions for his product. As we
have seen, once a producer has constructed a plant, changes in market condi-
tions only in fairly exceptional cases will bring him immediately to seek a
different scale of plant. For the most part changes in market conditions
will merely bring about revisions in the decisions concerning how heavily
to utilize the given plant (that is, what quantities of variable inputs should
be combined with the plant). These revisions will be made in the light of
the short-run per-unit cost pattern that we have discovered.
Generally, a producer will seek to produce that volume of output (dur-
ing a given period) that will yield the highest surplus of aggregate revenue
over aggregate (relevant) costs of production. In contemplating any pro-
posed volume of output (per period), an entrepreneur will always ask him-
self whether he could not do better by producing an output volume slightly
larger, or slightly smaller, than that proposed. An output slightly larger
than a proposed level would involve an increase in aggregate (relevant)
costs of production; on the other hand, the increase would bring an increase
in aggregate revenue. If the marginal revenue involved in this way (by
the contemplated expansion of output beyond the level originally proposed)
exceeds the marginal cost involved (the latter, of course, referring to the
199
COSTS AND SUPPLY

increment in short-run costs that are relevant with a given plant), then
clearly the larger output is to be preferred over that originally proposed.
Similarly, in contemplating a contraction of output below a proposed level,
the producer will compare the reduction that this will allow in aggregate
short-run production costs, with the associated reduction in aggregate rev-
enue from product sales. Should the former exceed the latter, then the
smaller output is to be preferred over that originally proposed.
Diagrammatically, therefore, a producer will seek to produce that out-
put (during each period) at which his marginal revenue curve intersects
his marginal cost curve from above. In the diagram [Figure 9-1 (a)] AVC is
the curve of per-unit costs patterned according to the analysis of the pre-
ceding section. It shows that when the plant is combined with only a


$ *
MC
per per
unit unit

A V C
/ ^^
7¯ `<r'
5


MR
Quantity
AC Quantity 0
(b)
(a)
Figure 9-1


small quantity of variable inputs, the costs (of these variable inputs) per
unit of output are high. These costs are shown to fall with increased
utilization of the plant until (at the output OA) variable inputs are com-
bined with the plant in optimum proportions, so that when the plant is
combined with still greater quantities of variable inputs, the average effi-
ciency of the latter fall and result in rising per-unit costs of production.
MC is a curve showing the increments to aggregate variable costs correspond-
ing to each successive unit of output.7 This curve lies below the AVC line
for outputs less that OA, and above the A VC line for larger outputs. For
the output OA (at which per-unit costs are at a minimum), marginal cost
is the same as per-unit cost.8 An average revenue curve (AR) and a mar-
ginal revenue curve (MR) are also drawn in the diagram. The AR line
expresses the producer's expectations respecting the prices at which he can
expect to sell (during each period) the various possible output volumes

7 The cost curves arc drawn continuous. In a real world we might find, of course,
that discontinuous curves would be a more faithful representation.
8 See p. 98.
200 MARKET THEORY AND THE PRICE SYSTEM


under consideration.9 (In drawing this AR line, we make, therefore, the
somewhat questionable assumption that the entrepreneur does in fact possess
definite expectations on these points.) The MR line, then, expresses a set
of implications of the AR line as drawn: it sets down, for each successive
unit of output, the increment to aggregate revenue associated with its pro-
duction and sale. (For any outputs qn, qn+1, which the producer expects to
be able to sell at prices per unit, pn, pn+1, respectively, the marginal revenue
associated with the (n+l) st unit of output, is therefore (qn + 1 * pn + 1) ”
qnPn·)
With the cost and revenue curves shown, the producer will seek to
produce an output volume OC. This he will be able to sell at a price CS.
Any output greater than OC would be less than optimal from his point of
view, since for each unit of output beyond OC the increment in costs exceeds
the increment in revenue. Similarly, any contraction of output below OC
would involve a sacrifice of revenue in excess of the diminution of aggregate
costs of production. With output OC the firm is doing the best it can.10
It is clear, then, that short-run output decisions will depend upon the
expected demand for the producers product, since upon this will depend his
average revenue curve, and, in turn, his marginal revenue curve. Should
expected demand be so weak that the producer can discover no volume of
output where average revenue is greater than the relevant average cost of
the variable inputs, he will produce no output. Thus in the diagram [Fig-
ure 9-1 (b)] were he to produce even the quantity OC (where MR = MC),
while doing better than at any other positive output, he would still be pay-
ing out variable costs for each unit of output that exceeds the correspond-
ing revenue by the amount ST. (In addition, from the long-run point of
view, he would be failing to earn anything toward the recovery of the costs
sunk, in the past, in the fixed plant.) The producer, in this case, finds
himself saddled with a plant that it does not pay to use at all, since nothing

9 On the shape of the demand curve facing an entrepreneur, see pp. 94-96.
!OA word may be added here concerning the quantities of the various factors of
production that the producer will be employing in order to produce the optimal output
OC. These factors, of course, will be employed so as to make up the "least-cost com-
bination" (discussed at the end of Ch. 8). An alteration in the price of a factor of
production will thus affect the quantity a producer will employ (as reflected in his
demand curve for it) in two distinct ways. First, as we have already seen in Ch. 9
(ftnt. 15), an alteration in the price of one factor will induce the producer to substitute
a factor that has become relatively less expensive in place of one that has become
relatively expensive (even if no alteration were to occur also in the scale of production).
Second, an alteration in the price of a factor will change the level of output at which
the marginal cost curve (duly modified to reflect the new least-cost combinations marked
out by the new factor prices) intersects the marginal revenue curve. At all possible
prices of a factor, however, it remains true that a producer will purchase that quantity
of it such that the last dollar spent upon it yields a marginal product worth just more
than a dollar.
201
COSTS AND SUPPLY

that it can be used to produce can be sold for enough to cover even the addi-
tional inputs that would now be required.
Should demand conditions be such that the output, for which marginal
revenue just balances marginal cost, can be sold at a price per unit greater


per
unit
AVC




Quantity
C
Figure 9-2

than the per¯unit cost of variable inputs, then it will pay the producer to
produce this volume of output. As we have seen, this volume of output
(OC in the diagram) is to be preferred over any other positive output level
(since MC = MR); and since for this output AR > AVC, the producer is
better oil with this output than with no output. Even if the excess of aggre-
gate revenue over aggregate cost of variable inputs (that is, the amount
ST — OC in Figure 9-2) is insufficient to cover the current quota of costs sunk
in the fixed plant (so that from the longer-run point of view the decision to
build the plant is seen to have been a mistaken one that has caused losses),
nevertheless, the producer (who now cannot retrieve the past and can only do
the best he can with the plant) can improve his position through producing
OC. By so producing he earns enough revenue on each unit produced to
cover all costs of variable inputs, and, in addition, to leave over the amount
•ST per unit of output (or the aggregate amount ST — OC) toward the re-
covery of the sunk costs. From the short-run point of view this amount
(ST X OC) is "profit": the decision to produce can improve the entrepre-
neur's position by this whole amount. (Should this amount of ST — OC ex-
ceed the entire sum sunk in the fixed plant, then, of course, the operation will
be pronounced a profitable one from the longer-run point of view as well.)
In general, it will be observed that the entrepreneur will in the short
run be prepared to use his plant more intensively as the average and mar-

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