The Discount Versus the Cost-of-Production
Theory of Capital Valuation
Harry Gunnison Brown
[Reprinted from the American Economic Review,
Vol. 4, No. 2 (June, 1914), pp. 340-349]
In recent years there has arisen and gained strength in the world of
economic theory, a school of writers who find the proximate
explanation of interest solely in the preference of individuals for
present or early enjoyment over future or later enjoyment.
Consistently with this view, these writers find the value of capital
to be determined by discounting its future benefits and to have no
direct dependence upon the cost-of-production. To every suggestion
that interest may be directly determined, in large part, by the
productivity of capital, the answer is made that the value of this
productive capital is itself arrived at only by discounting, at some
rate of interest or time-preference, its future products, and that,
therefore, whatever interest is arrived at in the conclusion as due to
productivity, was assumed in the premises. So certain is the advocate
of the time-preference theory that the productivity theorist must
necessarily be thus reasoning in a circle, that no care on the part of
the latter to avoid doing so suffices to free him from suspicion of
it.
I have myself very lately experienced the effects of this suspicion,
as shown in Professor Fetter's criticism, in this REVIEW,[1] of a
recent article by me regarding theories of interest.[2] Thus,
Professor Fetter says[3] of the article in question:
The explanation is hardly begun until the productivity is
assumed to be a five per cent, a ten per cent, or a twenty per cent
productivity. Per cent of what? Of the capital valuation, or the
prices at which the borrower can buy the agents. Productivity in
what way? In that the present prices, being the discounted value of
the incomes that are expected, emerge at their maturing value as
time elapses. The discount-rate involved in the capitalization
is the "rate of productivity" which appears again and
again in the argument.
Now I had taken particular pains not to state the rate of
productivity as la per cent of capital value, for I knew perfectly
well that if I did so I might be accused of reasoning in a circle. To
begin with, I had no capitalization and, therefore, no discount rate
involved in capitalization. In order to avoid all such difficulties, I
dealt with quantities of goods instead of with values, intending to
compare the quantity or the number of units of certain goods, which
relatively direct production would yield this year, with the quantity
of the same goods, which exactly the same amount and intensity of this
year's labor would yield in a later year if the production process
were more roundabout. I assumed that a given amount of productive
effort would yield 100 this year by direct production and 110 a year
later by a more roundabout method, and then tried to show that the
rate at which the present goods would be offered for the future, or
vice versa, might be directly determined, at least in part, by this
difference in the productivity of the two methods. I did not value
either the 100 units of present goods or the 110 units of future goods
in terms of money or in terms of anything else exchangeable for them.
I did not, at the start, even value either in terms of the other. I
simply asked, given the assumptions as to direct and roundabout
productivity, at what rate the present goods would exchange for the
future, and tried to arrive at a conclusion. I had, at one time,
myself been a believer in the pure psychological theory, and had
thought that the productivity theory necessarily contained somewhere a
discount-value assumption, either as to the capital which was said to
be productive, or as to the wages of laborers, an assumption which
rendered it untenable. I was, in consequence, especially careful, when
I came to feel that productivity acts directly, so to state myself as
to avoid any semblance of petitio principii. I am, therefore,
compelled to believe that Professor Fetter's firm conviction of the
impossibility of showing interest to depend on productivity, without
reasoning in a circle, caused him to take for granted that I had done
this, instead of attempting to prove that I had.
It is this same conviction that the productivity theorist must assume
a rate of interest to prove one, which has led to Professor Fetter's
second misunderstanding of my argument. He says:[4]
"Here, as always, the productivity theorist looks
at the proximate influence, not at that one step removed; examines
the middleman's motive, land ignores the ultimate consumer."
And of both Professor Seager and me he says,[5]
"their conception of productivity goes little
farther than the personal enterpriser."
It is true that in one or two paragraphs of the article which
Professor Fetter criticises, I made allusion to the enterpriser who
borrows, and employs labor. This I did in the fear that I might be
criticised for dealing with too simple a community and ignoring the
complications of modern industry. But, for the most part, I wrote as
if assuming a community where each person employed only himself and
could engage in roundabout production if he had the accumulated means,
where each person might directly borrow of or lend to another, and
where each person was at the same time an active producer and an
ultimate consumer. If the theory of interest as I presented it in the
article in question, has, therefore, any significance at all, it has
significance as explaining the fundamental problem, and is not a mere
explanation of the relation of middleman-enterpriser's interest to
other interest.
Not only do the time-preference theorists explain the value of all
capital by the discount process, but they explain cost-of-production
in the same way. The expense of hiring labor to construct capital is
said to be fixed by the discounted value of the future benefits
constructed. The cost of raw material and machinery and, further back,
the wages of the labor employed to produce these, likewise depend,
directly, only upon the far future benefits to be yielded. The
enterpriser, it is asserted, pays for capital and for labor force the
discounted value of future benefits and gets the maturing value.
Hence, he can afford to borrow and pay interest. But the real interest
problem is said to be the problem of valuation of capital and,
therefore, of the labor services required to produce capital, at less
than the realized future value of the benefits which capital yields.
It is, then, precisely at this point, on the problem of the valuation
of capital, that the time-preference theory may be most profitably
analyzed. In order to avoid confusing complications and, also, in
order to protect ourselves against any possible charge of confining
attention to the middleman-enterpriser, let us assume producer and
consumer, buyer and seller, employer and employee, lender and
borrower, to deal with each other directly.
To picture concretely such a condition of affairs, we may betake
ourselves to Crusoe's island after the addition to the island's
population of the group of Spaniards. The unimproved land is
valueless. It is all "marginal" or "no-rent" land.
One acre is as good as another and the supply is more than ample for
all who live on the island.
But on part of the land, Crusoe has made valuable improvements. Among
other things there are some trees of a certain sort, which yield
nutritious fruit once, a year after being planted, and then die.6 On
an average there are 110 of the fruit to a tree. Young trees, suitable
for planting, grow on a neighboring island, as does also the fruit.
This other island is not a suitable place for a permanent habitation.
But it can be availed of for its products, land can be reached from
Crusoe's island, except at high tide, by fording. At first, Crusoe
went to the neighboring island, at picking time, for the fruit of
these trees. But he soon found that it took him 10 trips to bring
over, with considerable effort, 1,000 of the fruit, because of his
limited carrying capacity; while 10 trips or, all things considered,
an amount of labor equivalent to that required to bring 1,000 of the
fruit, would enable him to bring over and plant 10 young trees. The
next year these would yield, altogether, 1,100 of the fruit.
Conditions of moisture, fertility, etc., are such that the trees have
to get their start, as seedlings, on the neighboring island. Hence a
new supply has to be secured each year. But, though it involves a year
of waiting, the same amount of labor yields Crusoe 10 per cent more by
this roundabout method than by the direct.
Enter now one of the Spaniards. Crusoe has just planted his year's
crop of 10 trees. The Spaniard, who, in order to accumulate some
capital of his own, is doing more work than is necessary to satisfy
his present needs, would like to buy. Crusoe demands payment in terms
of the kind of fruit the trees yield. One year hence the trees will
yield 1,100 of the fruit without appreciable further labor. How much
of the fruit are they now worth? How much will the Spaniard give? How
little will Crusoe take? Is the question solely one of time-preference
with each, or is something else involved in this valuation of capital?
We may begin with the Spaniard. His position is analogous to that of
a lender. If he buys the trees, he will be giving up present fruit for
future fruit. What is the most he will give? He will be guided in his
decision by two considerations. One of these is his impatience or
time-preference. The other is the cost-of- production (in the place
desired) of the trees. If he dislikes to sacrifice present goods for
future unless he gets a return of (say) 5 per cent, he certainly will
not give 1,100 of the fruit now for 1,100 a year from now. Even after
he has gathered enough fruit, from the neighboring island, to buy the
trees, he will refuse to buy them at any price above 1,048, and this
refusal may be due to his time-preference. But will he give 1,048 if
and because his impatience is only 5 per cent? By no means. For he has
to deal with the fact that the same number of trips to the neighboring
island and the same amount of labor, which will yield him 1,000 pieces
of fruit, would get him 10 trees and plant them. If he has to pay
Crusoe 1,048 pieces of fruit, he must work harder and make more trips,
to get the means of buying the trees from Crusoe, than to get trees
directly. He, therefore, however low his rates of time- preference,
will refuse to pay more than 1,000 fruit for 10 trees, so long as he
can get and plant 10 trees for himself with the same labor as is
required to get the 1,000 fruit. His refusal to give more than 1,000
is not due to high time-preference for present goods but to his desire
to get future goods in the cheapest way possible. It is not
time-preference at all, but a choice between two different amounts of
present labor, yielding the same future result. This is the sense in
which the value of capital depends upon cost- of-production. The value
of the trees cannot go above that amount of other goods which requires
the same labor to get directly, as the trees do. The goods which could
be got directly with the same labor and which must be sacrificed for
the present if the trees are directly got instead, may be regarded, in
an entirely proper sense, as the cost-of-production of the trees. The
essential fact is, then, that the prospective purchaser of capital has
a choice among not less than three lines of action and not between two
only. He is not, as the time-preference theorist would have us
believe, restricted to a choice between the present fruit and the
future fruit. Instead, he can have the present (i.e., the early or
this year's) fruit, or he can have next year's fruit from the
purchased trees, or he can have next year's fruit from trees which his
own labor procures. Not only the preference for present (or early)
consumption will cause him to refuse to pay a too high price for
Crusoe's trees; but also his other alternative of producing (in the
economic sense of producing-in this illustration, place utilities) the
trees by his own labor, will cause him to refuse to pay a too high
price in the other possible products of such labor. Would Professor
Fetter say that this option, the possibility of producing, more
directly, the same kind of capital which the Spaniard contemplates
buying with other products, exercises no influence at all,
immediately, on the price in present goods, which will be paid for
durable capital yielding future goods? Would he say that this option
can influence capital value only through first influencing
time-preference and, therefor, determining a discount rate? Unless he
is prepared to make such assertions, his theory of time-preference
ceases to be a universal, all-inclusive explanation of capital value.
We reach a parallel conclusion if we suppose that the Spaniard,
instead of buying trees of Crusoe the capitalist, employs Crusoe as a
laborer to get the trees, paying him in present fruit. The Spaniard
will not be willing to pay Crusoe more than 1,000 fruit for the labor
of getting or planting 10 trees. Rather than pay wages appreciably
higher, he would himself get and plant the trees desired. To be an
employer of labor, advancing present consumable goods for durable
capital, he must produce present goods in excess of his own present
needs. But he has the alternative of devoting his surplus time,
instead, to the production of durable capital which will serve his
future needs. This possible alternative will make him unwilling,
however low his time-preference, to accumulate present goods for the
payment of wages, unless his future return from so doing is equally
large.
Likewise, if we suppose him to lend to Crusoe, the rate at which he
will lend is influenced directly by his other alternative, and not
merely by his time-preference or by his other alternative acting
through the intermediation of time-preference. He will not lend Crusoe
1,000 fruit this year for much less than 1,100 next year, however low
may be his time-preference, because the labor necessary to secure him
the surplus 1,000 this year above present needs will, if turned to
more roundabout production, yield him a return next year of 1,100. He
would rather get 1,100 next year as a result of this year's labor in
roundabout production, than to get less than 1,100 next year as a
result of this year's labor in supplying Crusoe's present needs. There
is no intention to deny that the surplus productivity of roundabout
production also influences time-preference, by influencing the
relative endowments of present and future.[7] Neither is there any
intention to deny that the rate of time-preference, by influencing the
extent to which roundabout production is carried, affects the marginal
gain from such production. In the article8 which Professor Fetter
criticises, I distinctly asserted both of these facts. The rate of
interest fixed by market competition will also be the rate of time-
preference and the rate of surplus productivity of roundabout
production. But to assert this is not to assert that time-preference
is the sole proximate cause and that all other causes must act through
it. As we have just seen, the rate of productivity influences directly
the supplier of present goods; and the cost-of- production of capital,
in the sense here used, has a direct influence on the demander of such
capital.
Suppose, now, we turn to Crusoe's side of the market, the side of the
person who purchases present goods with future. What determines the
price at which Crusoe will dispose of his 10 trees, or rather, since
this is the important question in the long run for capital valuation,
at what price in present fruit will Crusoe be willing to engage in the
business of getting, planting, and selling trees? Crusoe, we may
suppose, is now permanently on the present goods side of the market.
He is no longer accumulating capital and has, perhaps, lost or
dissipated what he had. If he produces durable capital, it is only to
dispose of it for present consumable goods. Let it be understood that
we are not assuming Crusoe to be a middleman. On the contrary, he is
here the "'ultimate consumer." But he is also a producer. He
wants present goods, present fruit. To get this fruit, he must either
go to the neighboring island and bring it over or he must buy it of
somebody else by offering future goods. Once he has produced these
future goods, i.e., secured and planted the 10 trees, time- preference
may alone decide at what rate he will exchange them for present fruit.
But before he turns his labor in that direction, he will consider
whether he can get more present fruit by producing durable capital to
buy it with or by devoting the same labor to getting the present
fruit. Year in and year out Crusoe will not maintain the supply of
more durable capital, i.e., will not produce it for sale, except at a
price which is as satisfactory to him as the yield of direct
production of present goods. The labor necessary to get the 10 trees
is the same, on our hypothesis, as the labor necessary to get 1,000
pieces of the fruit. The 10 trees, planted near by, will yield next
year 1,100 pieces of fruit.
Crusoe's rate of time-preference of course fixes a minimum below
which he will not sell the trees. If his rate of time-preference is 15
per cent, he will not sell them for less than 956 fruit, because he
would rather wait for the 1,100 future fruit. But, in the long run,
his minimum price is fixed by two considerations and not by one only.
The second consideration is his alternative of directly producing the
fruit by going to the neighboring island after it. Year in and year
out, he will not bring, plant, and sell the trees for less than 1,000
of the fruit. If he cannot secure approximately that price for the
trees, he will get the fruit directly instead of trading for it. The
possibility of his doing so will itself tend to keep the trees scarce
enough to yield that price in terms of the fruit. In other words, he
will not sell the trees for less than their cost-of-production
measured by the other goods which the same work would produce.
Our conclusion is no different if we assume him to sell his ser-
vices as a laborer, for wages, instead of selling the trees. He will
not work for the Spaniard at the job of getting and planting trees,
for a less wage in present fruit than the amount of present fruit
which the same labor would give him if applied directly to bringing
the fruit from the other island.
But instead of selling trees for present fruit or working for wages
in present fruit, Crusoe may borrow present fruit to pay it back next
year. Here, also, if he is a productive borrower, he is not simply
comparing present and future benefits. If he has no accumulations and
if, also, it requires all his present labor to provide for his present
needs, Crusoe must needs engage in direct production unless he can
borrow. If he can borrow 1,000 present fruit, he is relieved from the
necessity of getting fruit now for present needs and can get the trees
instead. But more than 1,100 fruit next year for 1,000 fruit this
year, he will not give, since the former represents more present labor
than the latter. Only an unproductive borrower would make such a
contract and he would soon be eliminated from the market. On the other
hand, however low might be his time-preference, Crusoe would still be
willing to borrow at any rate of interest less than 10 per cent. To do
so would leave him as well off in the present and better off in the
future. He would borrow at less than 10 per cent because to do so
would give him a larger future income than not to do so. His
comparison would be between two futures, rather than between a present
and a future.
In this discussion, no middlemen, banks, etc., have been assumed.
Trade has been supposed to take place in kind. The producer of present
goods desired future goods; and the producer of future goods desired
present goods. There was specialization and trade. In spite of the
assumed absence of complicating factors, it is believed that the
essential elements of the problem have been included. The discount
theorist can hardly expect to strengthen his case by making its truth
depend upon the number of middlemen coming between the ultimate
parties concerned, or upon the use of money, or upon the
intermediation of banking.
Let us now turn to the distinction between land and capital,
regarding which Professor Fetter has, again, greatly misunderstood my
previous article. The distinction is not, strictly, one between land
and all other capital. It is a distinction rather between reproducible
and non-reproducible goods. The paintings of old masters and business
sites in New York City are in the same category. For all practical
purposes, they cannot be reproduced. I am not at all arguing that
there is no "made land" or that land owes none of its value
to work upon it. But so far as its characteristics cannot be
reproduced, the value of land is not limited by its
cost-of-production. Crusoe could not sell his 10 trees for more than
1,000 pieces of fruit, for that was their equivalent or their
cost-of-production. But if the island were crowded, and there were no
practical possibility of adding to the land, no such definite limit
would determine a minimum price of the land in terms of other goods.
The value of this land could be arrived at only by discounting the
prospective value of its future yield. The value of reproducible
capital is influenced by two considerations; that of capital not
reproducible, by one. Whatever Professor Fetter believes about land or
sites as being similar to or different from other capital, he probably
would not deny that some capital-land, old paintings, original Greek
statuary, etc., is not reproducible in quite the sense to the buyer,
that houses, factories, trees, etc., are. His theory of valuation
(except that the rate of surplus productivity of roundabout production
influences even this discount rate) may serve to explain the value of
such capital as land. But it never has been shown and cannot be shown
that the value of reproducible capital has not as one of its
determinants, the cost of its production, in the sense here explained.
I have tried, in this paper, to meet the issue presented by Professor
Fetter as squarely as possible by showing just what cost-of-
production properly means when it is said that the value of capital
depends upon it. Undoubtedly, productivity theorists have been
careless in this regard and have, by incomplete analysis, laid
themselves open to the charge of taking as cost-of-production
something that itself involved discounting. But it is not necessary to
do so. I do not claim any originality of view in thus defending a
theory long since held, however incompletely stated, by many
economists. Whether for good or ill, a large part of scientific
discussion in every age has to be devoted to reestablishing in current
thought correct doctrines elaborated by earlier thinkers, but
questioned by a few writers of a later date. All possible lines of
attack, even if capable of being easily repulsed, cannot possibly be
anticipated. Consequently, new and ever more intricate processes of
reasoning are invoked against supposedly established principles,
attacking them at points where the forces of defense have not
previously been compelled to rally. Of such a nature is the attack
upon the productivity-theory of interest and the cost-of-production
theory of capital. The earlier economists generally believed that the
value of capital depends, in large part, directly on its cost of
production. This seemed obvious to them as it probably does to most
economists today. They did not foresee that attempts would later be
made to analyze all costs of production into the discounted value of
future services. Hence they did not forestall these at- tempts. Since
these attempts have been made, however, and by economists of note, it
becomes important to show that cost-of- production cannot be entirely
disposed of as a concept arrived at by first assuming a rate of
interest. When this has been shown, even the so-called crude or naive
productivity theorist, who says that interest is a certain per cent
because capital of a certain value yields a certain return, is seen to
have been, however incomplete his analysis, less fundamentally in
error than is sometimes believed.
Professor Fetter ventures to suggest that my treatment of interest is
"eclectic,"[9] because I do not see the explanation of
interest in one cause. If to admit that interest is affected both by
time-preference and by productivity, is to be eclectic, I can hardly
object to the application of the term. Surely there is no special
virtue and no special consistency in holding that a given phenomenon
is explainable by a single cause instead of by two or more causes.
FOOTNOTES AND REFERENCES
- American Economic Review,
March, 1914, in an article on "Interest Theories, Old and
New."
- "The Marginal
Productivity versus the Impatience Theory of Interest," Quarterly
Journal of Economics, August, 1913.
- American Economic Review,
March, 1914, p. 90. The italics are mine.
- American Economic Review,
March, 1914, p. 90.
- Ibid., p. 92.
- This assumption is made only
for simplicity. It is apparent that the principles involved would
be no different on the supposition of (say) a thirty-year life and
a yield each year after the tenth. But so complicated an
illustration of the principle would make the argument more
difficult to follow.
- See Bhhm-Bawerk, Positive
Theorie des Kapitales, Dritte Auflage (Innsbruck, 1912), p.
468.
- Quarterly Journal of
Economics, August, 1913.
- American Economic Review,
March, 1914, p. 92.
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