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this aspect of economic life too much has been usually assumed
as to the harmony of human interests. Nothing is more funda-
mental in economic science than the proposition that there is
an antagonism of human interests. If there were a complete
harmony of interests, labor and capital might be expected to
seek those industries which are most productive from the
social standpoint. But aside from the observable fact that
labor and capital do nothing of the kind, it is a matter of
common observation and experience, confirmed by reflective
analysis, that there is no such harmony of human interests.
One man's interest is served by having the labor and capital
of the community directed in one line, another's by having
them directed in quite a different line. More than that, there
is great inequality among individuals in the power of giving
direction to the industry of the community. The one who
owns land or capital in addition to his own labor power is in
better position, other things being equal, to determine the
direction of business activity than is the one who owns only
his labor power. We therefore not only have the certainty
that each individual will try to direct business activity in
the line most conducive to his own interests, and that in
many cases his interests will not harmonize with the interests
of the community, but also the certainty that the power to
give this direction differs greatly among different individuals.
If we did not know it as a matter of direct observation and
experience, we might predict from these premises that the
business activity of the community would not, in all cases,
be directed in the most productive lines, and that therefore
it would be possible, by some form of discrimination, to
attract labor and capital from the less productive to the more
productive industries.



360 PRINCIPLES OF POLITICAL ECONOMY

The following illustration may add something to the con-
creteness of this conclusion. Let us suppose that a certain
tract of land had been devoted to cultivation of a fairly inten-
sive kind, and had been producing enough to pay the wages
of twenty laborers, with something left over for rent. Through
some change of circumstances the price of wool rises, and it is
found more profitable to use the land for wool-growing. By
turning the land into a sheep run, nineteen of the laborers
may be dispensed with, and the saving in wages would more
than measure the difference between the value of the wool
crop and that of the present crop, so that a larger surplus
would be left over as rent. There is little doubt that the land
would then be devoted to the growing of wool. That would
be to the interest of the landlord and against the interests of
the nineteen laborers, but the landlord is in a better position
than they to determine the form of cultivation. There is
also little doubt that this would be contrary to the interest of
the community. Less wealth would be produced either for
consumption or for international trade. Fewer people could
be supported, or the same number would not be as well
supported as formerly.

If the nineteen men thrown out of employment cannot find
places elsewhere, they will probably, since they want to live,
offer their labor at lower wages, enough lower to enable the
landlord to get as much rent from the more intensive form of
cultivation as he might get by the less intensive form. Here
we have the somewhat anomalous situation of an increase in
price of one of the products of industry causing a fall in the
price of labor. The key to this anomaly is found in the fact
that what is cost to one man is frequently gain to another.
Now in this supposed case (which is not altogether a supposed
case) there is little doubt that some form of discrimination in
favor of the present crop and against wool would increase
not only the relative share of the produce going to labor, but
the absolute amount of the produce of the land.



PROTECTIONISM 361

And this is a rule which works both ways. In a community
where land is extensively cultivated, it is presumably because
extensive cultivation produces the best results from the stand-
point of the landowner. Any one of the following conditions
may induce him to change to intensive cultivation : (i) a fall in
the price of labor ; (2) a fall in the price of the products of
extensive cultivation ; (3) a rise in the price of the products of
intensive cultivation. There lies the opportunity for the pro-
tectionist. By some discrimination which will tend to increase
the profitableness of the intensive product, or decrease, rela-
tively at least, the profitableness of the extensive product, an
absolutely larger and more valuable product might be created.
This would support a larger number of people, or support
them better. They would have a larger number of products
either for consumption or for international trade. Labor and
capital would have been attracted from the less productive to
the more productive industry. Since a protective tariff is one
means by which the relative profitableness of different indus-
tries may be changed, it follows that a protective tariff may
be a means of increasing the total product of the industry of
the community.



PART FOUR



Which has to do with the shares into which the products of industry are
divided and the awarding of these shares to different groups and classes



363



CHAPTER XXX
THE LAW OF VARIABLE PROPORTIONS

The problem of the distribution of wealth is the problem of
dividing the products of the industry of the community among
the various classes. The claim of each class to a share of the
wealth is usually based upon the claim that each has contrib-
uted something to its production. The contribution may be
labor, either mental or physical ; it may be capital, or the results
of foresight or investing ; or it may be land which the owner
has appropriated or otherwise come into possession of.

The market value of services. The market value of what
each has to offer determines his share in the product. If the
market value of labor is high, the laborer gets a large share ; if
it is low, he gets a small share. The same is true of that which
each has to offer. Our first problem must be, therefore, to
study the market value of each factor, or agent, of production
in order to find out why the seller of each factor gets a large,
or a small, share.

The income of each class, however, is a flow rather than a
fund or a lump sum. The laborer sells not himself but the
flow of productive energy which he can exert during a given
period of time. The capitalist sells not his capital but the flow
of utilities which come from his capital during a given period
of time. If the laborer were a slave, he might be sold bodily,
and in that case he would bring a price. The capitalist and
the landlord may sell their capital or their land. This involves
a question of exchange and market price. When they sell the
flow of utilities which their properties yield, we have interest
and rent, which are questions of distribution. The following
outline will indicate the relation of these various problems to

365



366 PRINCIPLES OF POLITICAL ECONOMY

the general problem of valuation. 1 For convenience the flow
of utilities yielded by the various factors of production are
called services.

f Consumers' goods
Of goods -1 f Land

[ Producers' goods < Capital



VALUATION



[ Laborers (under slavery)



f Of land, yielding rent
Of services Of capital, yielding interest
[ Of laborers, earning wages

Why productive agents are desired. The reason for pay-
ing for an agent of production is that it helps to produce
something which is desirable. Its value is derived from that
of its product. The greater its product, or the greater its con-
tribution to the joint product of a group of factors, the greater
its value. It is therefore of the utmost importance that we find
out, if such a thing is possible, how to determine the contri-
bution of each factor. This is one of the most elusive problems
in the whole field of economics. The student is requested to
study this problem as carefully and intensely as he would an
intricate problem in physics or chemistry.

A combination of the factors of production not a chemical
combination. In Chapter XV we saw the necessity of a proper
balance, not only among the factors of production but also
among all the factors of national life. But some variation
among the factors of production must always be allowed.
What constitutes the perfect balance depends upon a number
of considerations which have not yet been discussed. A number
of factors of production, when used in combination, are not
like the elements in a chemical reaction or the colors in a pic-
ture. These probably permit of no variation. The factors of
production may always be combined in different proportions
without destroying the result. One can grow a hundred bushels

1 Compare note by the author on " The Place of the Theory of Value in
Economics," in the Quarterly Journal of Economics, November, 1902.



THE LAW OF VARIABLE PROPORTIONS 367

of wheat in a year by using little land and much labor or by
using much land and little labor. Which is the more economi-
cal combination will depend upon the relative cost of land
and labor. Where land is cheap and labor dear, it pays to use
much land and little labor ; where land is dear and labor
cheap, it pays to use little land and much labor.

In an actual chemical combination the various elements have
to be combined, apparently, in fixed proportions, without any
variation whatever. This is known as the law of definite pro-
portions. But in order to induce a given chemical combination,
different substances have sometimes to be mixed in considerable
masses. This gives rise to another law, which is as definite and
as well understood as the law of definite proportions.

The law of variable proportions. Take, for instance, the
juvenile experiment of mixing vinegar and baking soda for
the purpose of producing a fizz. The actual combination of mole-
cules which produces the gas that makes the bubbles doubt-
less follows the law of definite proportions. But not all the
materials in the mixture will be thus instantly combined. At
the end of a definite period of time, say a minute, some of
the acid and some of the soda will remain uncombined, probably
because a certain number of molecules of each never happened
to come in chemical contact with the requisite molecules of the
other. The greater the quantity of vinegar in proportion to
the soda, the greater the probability that each molecule of the
soda will come in chemical contact with a molecule of acid.
Therefore, the greater the proportion of vinegar to soda, the
greater the proportion of the molecules of soda that will be
used in the formation of gas, and, conversely, for the same
reason, the smaller the proportion of the molecules of acid that
will be used.

Many factors at work in combination. There are, of course,
other factors in the problem, such as the size and shape of the
receptacle in which the mixture is placed, the temperature of
the mixture, the amount of shaking or stirring to which it is



368 PRINCIPLES OF POLITICAL ECONOMY

subjected, as well as the time allowed for the combination to
take place. Leaving all the other factors unchanged except
the one selected for experimentation, we get a result similar to
that which we obtain in some of the larger economic combina-
tions, such as the application of labor to land. In fact, we are
here in contact with a universal law which applies to mixtures
of chemicals, as distinct from chemical combinations, through
the mixture of fertilizers in the soil, up to the combination of
various forms of human talent in the promotion of national
greatness.

The manufacture of ether. In the manufacture of ethers,
alcohol is combined with acids much as soda is combined with
vinegar in the experiment referred to above. After the mixing
has taken place, only a limited proportion of the original in-
gredients is actually combined. Since alcohol is expensive and
the acids cheap, it is found economical to use large quantities
of acids in order to force as much of the alcohol as possible to
combine. The acid is literally massed in its attack upon the
alcohol, in order that no molecule of the latter may escape.
In fact, this phenomenon is explained by the so-called mass
law. If alcohol were cheap and acid expensive, it would then
be desirable to force every molecule of the acid to combine.
In order that as few as possible might escape, it would be neces-
sary to mass the alcohol in its attack upon the acid. An econo-
mist might not improperly call this an intensive use of acid and
an extensive use of alcohol. Conversely, the rule actually
followed of massing the acid upon the alcohol might be called
an intensive use of alcohol and an extensive use of acid.

The results of massing one ingredient upon another may be
illustrated by the diagram which is familiar to all students
of economics.

With a given quantity of alcohol let us mix varying quanti-
ties of acid, which we shall represent on the line OX. The
quantity of the product, ether, we shall represent on the line
OY. When a quantity of acid represented by the line OC is



THE LAW OF VARIABLE PROPORTIONS 369

put into the mixture, let us assume that we get a quantity of
ether represented by the rectangle OABC. Twice that quan-
tity of acid with the same quantity of alcohol will increase the
product, ether, but will not double it. That is, the product
increases but does not increase in proportion to the acid.
Let us suppose that a quantity of acid represented by the line
OF produces, with the other ingredients, a quantity of ether
represented by the rectangle ODEF. A third increment and
a fourth would still result in some additions to the product, as
long, perhaps, as any of the original quantity of alcohol was
able to escape the mass action of the acid. Eventually the
point would be reached when further increases of the acid
would add nothing
to the product.



It will be observed,
however, that the
addition of the in-
crement CF to the
acid did not add
the rectangle CIEF Diagram A

to the product. The

addition to the product is the difference between the rectangle
OA B C and the rectangle ODEF. That difference is represented
by the rectangle CGHF.

The marginal product. This is technically known as the
marginal product of the acid. This technical term does not
mean, however, that even the product CGfiFwas produced by
the acid alone ; it merely means that whatever value there is
in the added product CGHF would be the outside limit of the
value of the added ingredient CF.

Air and gasoline in a carburetor. A problem something like
this presents itself in practical form in the use of air and gaso-
line in an internal-combustion engine. Both are necessary,
but they may be mixed in somewhat variable proportions. One
may use a rich or a lean mixture. A rich mixture is one rich



K



370 PRINCIPLES OF POLITICAL ECONOMY

in gasoline and lean in air. A lean mixture is one lean in gaso-
line and rich in air. Combustion itself is a chemical process
and presumably follows the law of definite proportions rather
than the law of variable proportions. But the mixture of air
and gasoline which has to precede combustion is not a chemical
combination and follows the law of variable proportions ; that
is to say, not all of both ingredients actually burn, any more
than all of the ingredients in the manufacture of ether are
actually combined . A lean mixture masses air on the gasoline
and enables more of the latter to burn, though much of the

air is unburned ; a
rich mixture does not
mass so much air,
does not burn so
much of the gasoline,
but burns a larger
proportion of the air.
If air were expensive
and gasoline cheap,
L V x a rich mixture would
Dia e ram B be more economical.

Since air costs nothing and gasoline is expensive, a lean mix-
ture is the more economical. The leaner the mixture that can
be made to explode, the greater the economy of gasoline. It
wastes air, but that is not bad economy. In short, we try to
adjust our carburetors so as to approximate as nearly as possible
to the conditions represented in diagram B.

Let us assume that a quantity of acid represented by the line
OL results, under certain conditions of manufacture, in a quantity
of ether represented by the rectangle OJKL, while a quantity
represented by the line OQ results, under similar circumstances,
in a quantity represented by the rectangle OMNQ, But these
two rectangles are equal ; that is to say, with a quantity of acid
equal to OL you get precisely the same as with OQ. In short,
the additional acid, LQ, is thrown away. It is of no use whatever



N



THE LAW OF VARIABLE PROPORTIONS 371

in that particular mixture, and yet, the acid being all of uniform
quality, it is as good as any of the rest. The average product,
however, for that quantity of the variable ingredient would be
represented by the rectangle LPNQ. It would be foolish to pay
that much for it, however, or, if it cost as much as that quan-
tity of ether would sell for, it would be foolish to use so much.
If, however, it cost absolutely nothing, it might pay to use that
much, or nearly as much, in order to be sure of getting the
full use of the alcohol, which is expensive.

If we were to reduce the broken lines which form the tops
of the rectangles in the two diagrams, A and B, to smooth
curves, we should get something like the following :

As we increase the
quantity of one ingre-
dient along the line
OX, leaving other
factors unchanged,
the average produc-
tivity, that is, the to-
tal product divided by
the number of units

of the variable ingredient, gradually falls. But as long as there is
any product whatsoever there must be an average productivity
per unit of that ingredient. This is represented by the descend-
ing curve YB. But the marginal productivity falls much more
rapidly and may even become a minus quantity. When so
much of this variable ingredient is used as to yield the maxi-
mum total product, and further additions add nothing to the
total, then these further additions are said to have a marginal
productivity which is nil. In diagram C the marginal product of
varying quantities is represented by the line OA. In some mix-
tures further additions may actually interfere with the work and
reduce the total product. The curve YA C represents the marginal
product under these conditions. In other mixtures the excess
of the variable ingredient does not become positively detrimental




3/2 PRINCIPLES OF POLITICAL ECONOMY

or destructive, but merely neutral. In such cases its marginal
productivity becomes nil but never a minus quantity. The curve
YAC in diagram C, in order to represent this class of cases,
would have to be redrawn. It should never fall below the line OX.

Reversing the experiment gives corresponding results. If now
we change the experiment and introduce varying quantities of
the other ingredient in the mixture with a fixed quantity of
the ingredient which we have been considering as the variable
factor, we shall get results which harmonize perfectly with
those which we have been getting. Returning to the case of
alcohol and acid in the making of ether, let us start with a
quantity of acid represented by the line OL in diagram B.
According to our assumption as explained earlier, that quantity
of acid with the original quantity of alcohol produced no more
ether than a slightly smaller quantity of acid represented by the
line OL. If now we mix a quantity of acid equal to OL with
enough more alcohol to bring the mixture to the same pro-
portions as in the original mixture when OL acid was used,
the product, ether, will increase in exact proportion to the in-
crease in the alcohol, provided, of course, the reaction is not
hindered by the smallness of the receptacle or by some other
extraneous circumstance.

To use, for example, a fixed quantity of air for each explosion,
but a larger quantity of gasoline, would require a larger cylinder.
Making such necessary allowances, we can say that if the
maximum amount of air in a gasoline engine is used with a
given quantity of gasoline, so that more air would be of no
advantage whatever, then a little more gasoline could be intro-
duced and would add considerably to the power. There being
enough air in the mixture to get the maximum combustion of
gasoline, the power would for a time increase in proportion to
the gasoline. As more and more gasoline is introduced, how-
ever, with a fixed quantity of air, making the mixture gradually
richer, a smaller and smaller proportion of gasoline will be
burned because of a scarcity of air. If the mixture is made



THE LAW OF VARIABLE PROPORTIONS 373

rich enough, a point will be reached when further additions of
gasoline will add nothing whatever to the power. The marginal
productivity of gasoline is then nil. When the mixture gets so
rich that it will not explode, it reduces the power, and the
marginal productivity of gasoline becomes a negative quantity.

The marginal product of each factor the complement of
that of the other. The marginal productivity of each factor in
the combination is, it will be observed, the complement of that
of the other factor. When the proportions are such that the
marginal productivity of one is nil, that of the other is one
hundred per cent of the average product ; that is, the total
product increases in exact proportion as this factor is increased.
When the proportions are such that the marginal product of
one factor is low, that of the other is high, the sum of the two
marginal products always equaling the total product.

When there are more than two factors in the compound, the
problem becomes more complicated, but the principle is the
same. In such a case it is better to treat each one separately,
regarding all the others as a bunch, or cluster, and thus
treating them as one. Marshall has suggested the word dose
to designate a group of factors. Thus, if we were considering
nitrogen, phosphorus, potassium, and all other factors in soil
fertility, we could take all the factors except, say, nitrogen and
treat them as constants. By varying the nitrogen in the com-
pound, we get variations in the crop yields.

Rothamsted experiments. Experiments of this kind have
actually been carried on at the Rothamsted Estate, near
London, where the great work inaugurated by Sir John Lawes
has been carried on for many years. In one experiment, for
example, five plots of land of approximately equal fertility were
treated alike in all particulars save one. Different quantities
of nitrogen .were applied in the fertilizer. Forty-three pounds
were applied to one ; 86 pounds to another ; 1 29 pounds to
another; and 172 pounds to another. The following table
shows the results :



374 PRINCIPLES OF POLITICAL ECONOMY

TABLE Ii







AVERAGE YIELD


GAIN FOR


PLOT


FERTILIZER


IN BUSHELS FOR


43 LB. OF






EIGHT YEARS


NITROGEN


No. 5


Mixed minerals alone


19




No. 6


Mixed minerals plus 43 Ib. nitrogen


27i


8*


No. 7


Mixed minerals plus 86 Ib. nitrogen


35i


71


No. 8


Mixed minerals plus 129 Ib. nitrogen


36|


if


No. 1 6


Mixed minerals plus 172 Ib. nitrogen


37 1


1



According to this table the yields show diminishing returns
for each successive dose of 43 pounds of nitrogen. The gain
on Plot No. 1 6 over Plot No. 8 was so slight, being only five
eighths of a bushel, as to be obviously unprofitable. Therefore
this plot was discontinued at the end of eight years, but the
other four were continued for forty-eight years, with the fol-
lowing results : .

TABLE II 1



PLOT


YIELD IN
BUSHELS


GAIN FOR 43 LB.
NITROGEN


No. C .


I c




No. 6


24


q


No. 7 .


3-1




No. 8


^64


il









The number of plots is too small to be finally conclusive,
but so far as they go they show interesting results. The first
two doses of 43 pounds each, on Plot No. 6 and Plot No. 7,
show constant returns, and the third dose, on Plot No. 8,
shows sharply diminishing returns. Allowing $6.50 as a fair
price for 43 pounds of nitrogen, and $i as a fair price for a
bushel of wheat, we get the following results :

1 These tables are presented in the excellent article by Eugene Davenport,
in Bailey's Cyclopedia of American Agriculture, The Macmillan Company,
New York. Compare also the author's volume " Principles of Rural Eco-
nomics," pp. 183-184, Ginn and Company, Boston, 1911.



Online LibraryThomas Nixon CarverPrinciples of political economy → online text (page 30 of 48)