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Why Do Capitalists Earn Interest Income? / Artikel mises.org

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Why Do Capitalists Earn Interest Income?
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by Robert P. Murphy

[Posted July 10, 2003]

THE INTEREST PROBLEM

<img alt="Eugen von Bohm-Bawerk" src="http://www.mises.org/images/bawerkc.gif" align="right" border="0" width="152" height="218">

Eugen von Böhm-Bawerk's three-volume work, Capital
and Interest,<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftn1" name="_ftnref1">[1]</a>
is a classic, both because of its brilliant analysis and its witty exposition.  The
first volume provides a history and critique of all preceding explanations of
the"interest problem."  For Böhm-Bawerk, the task of the
interest theorist was to explain why a capitalist could regularly earn a net
return on his financial assets, even though (unlike laborers) he apparently
did nothing to"earn" this interest income.<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftn2" name="_ftnref2">[2]</a>

BÃ-HM-BAWERK'S"AGIO THEORY"

Böhm-Bawerk's solution consisted of two steps.  First,
he framed the phenomenon of interest, not as a return to financial investments,
but rather as a premium, or agio, in intertemporal exchanges.  For
example, take the case of a tractor.  Typically, a capitalist who
invests in a tractor (either directly or by lending funds to a farmer) can
earn an interest return on his investment; that is, he will have more real
wealth after the tractor has been used to harvest crops than before.  What
Böhm-Bawerk realized was that this phenomenon—the growth in real financial
wealth through investment in the tractor—relies on an apparent undervaluation
of the tractor.

To see this, suppose that the tractor is expected to yield
an additional $1,000 worth of revenue every year, and that it will last ten
years (before being junked).  Böhm-Bawerk argued that the only
reason a capitalist could earn money through ownership of the tractor is that
its initial purchase price is less than $10,000.  Only in
that case could an investor use an initial amount of financial wealth and turn
it into a greater subsequent amount (ten years later).

Thus, Böhm-Bawerk had transformed his original question.  Rather
than asking,"Why do capitalists earn an effortless flow of interest
income?" he could instead wonder,"Why is it that the initial
purchase prices of capital goods systematically fall short of the future
revenues they are expected to yield?"

The second step in Böhm-Bawerk's solution was to make the
claim that present goods are preferred to future goods.  Generally
speaking, a person values present apples, houses, etc. more than he values claims
to such goods that cannot be redeemed until the future.  In the case
of our hypothetical tractor, its purchase price is denominated in present dollars,
while it only offers the hope of a stream of future dividends (of
$1,000 each year for ten years).  Since no one would be willing to
give $10,000 now in exchange for a promise of $1,000 payments for each of the
next ten years, it naturally follows that no one would pay $10,000 for our
hypothetical tractor.  Because of this fact—that present goods are
worth more than future goods—the tractor can be purchased for less than
$10,000, and a capitalist can increase the market value of his wealth by
investing in tractors (and waiting ten years).

THE"NAÏVE PRODUCTIVITY THEORY"

Of particular interest to modern Austrians is Böhm-Bawerk's
refutation of a popular, rival explanation for the phenomenon of interest.  Many
economists would argue that, in the case of our tractor, the reason a
capitalist earns a net return on his wealth is that the tractor is productive:  After
all, a farmer can harvest more crops, year after year, with a tractor than
without one, and so naturally (these economists believe) someone who buys a
tractor can earn an income over time.  More generally, such
economists argue that borrowers are willing and able to pay interest because
of the"productivity of capital."

Böhm-Bawerk brilliantly refuted this line of reasoning,
which he referred to as the"naïve productivity theory" of interest:

<blockquote dir="ltr" style="MARGIN-RIGHT: 0px">

I grant without ado that capital actually possesses the
physical productivity ascribed to it, that is to say, that more goods can
actually be produced with its help than without.  I will also
grant…that the greater amount of goods produced with the help of capital
has higher value than the smaller amount of goods produced without it.
 But there is not one single feature in the whole set of circumstances
to indicate that this greater amount of goods must be worth more than the
capital consumed in its production.  And that is the feature
of the phenomenon of excess value which has to be explained.  (I,
p. 93, italics original)

[/i]

We can understand Böhm-Bawerk's argument in terms of our
tractor example.  The"naïve productivity" theorist
claims that the owner of a tractor earns a net return on his investment
because the tractor yields $1,000 in marginal revenue each year of its life.  So
this explains (so thinks the naïve productivity theorist) the annual
percentage return reaped by the capitalist.

But Böhm-Bawerk points out that this is only looking at one
side of the matter.  Yes, the productivity of the tractor explains
why its owner enjoys $1,000 per year in extra income; if he wished, the owner
could rent out the tractor and charge up to $1,000 per year for its services.

However, this flow of income will only represent a net
return on the original investment if the original purchase price is less
than $10,000.  For suppose that the tractor initially cost
$10,000.  In that case, its owner would still receive $1,000 per
year for the ten years of the tractor's life, but at the end of the decade the
capitalist would be left with his initial principal, $10,000.  In
other words, the depreciation of the tractor would exactly offset the flow of
dividends, so that the net rate of interest on the investment would be zero.  Note
that this is perfectly consistent with the fact that the tractor is productive,
and so the tractor's productivity as such cannot be the explanation for
a positive rate of interest.

THE NEOCLASSICAL APPROACH

Modern mathematical economists, who explain
economic phenomena through systems of simultaneous equations, are often
bewildered by the Austrian stress on subjective intertemporal preferences—rather
than capital productivity—when it comes to interest theory.  Indeed,
a standard condition in a typical mainstream model is

r = f '(k),

which denotes the fact that in equilibrium, the real rate of
interest is equal to the marginal product of capital, i.e. the increment in
output produced by an increment in the capital stock k.

On the face of it, the neoclassical approach seems to commit
the very fallacy that Böhm-Bawerk pointed out over one hundred years ago:  The
mainstream economists seem to argue that the real rate of interest is directly
proportional to (and in a sense"caused by") the extra output
yielded by additional units of capital.  So what's going on here?  Do
the mainstream models contain a logical error?

Actually, they do not.  What has happened is that,
because of their need for analytical simplicity, the mainstream models assume
that the world has only one good.  Consequently, capital goods
and consumption goods are the same thing, and all of the difficulties in
"Austrian" capital theory are assumed away.

We can see this most clearly by a simple example.  In
order to motivate their assumption of a single good serving as both capital
and consumption, the neoclassicals might adopt a model in which sheep are the
only good.  In this fictitious world, people own stocks of sheep.  They
can choose to consume their sheep in the present, enjoying the current
marginal utility of consumption, or they can postpone consumption (i.e. save
their sheep) for a future period.  If they choose the latter course,
their stock of sheep will multiply (because of natural reproduction).  If,
say, the number of sheep doubles every year, then (the neoclassical would
argue) the equilibrium real rate of interest in this fictitious world must be
100 percent.<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftn3" name="_ftnref3">[3]</a>  It
is through reasoning such as this that the mainstream economist believes that
the"marginal product of capital" is linked to the equilibrium real
rate of interest.

However, as I claimed above, this type of model assumes away
the thorny issues in capital theory, which only the more sophisticated
Austrian analysis attempts to handle.  Recall that in our tractor
example, the fatal flaw in the naïve productivity explanation was that it did
not explain the initial purchase price, or market valuation, of the tractor, in
terms of dollars.  The tractor represents a claim on future
dollars, but we cannot know the implicit interest rate on the investment until
we know the present market value of the tractor in terms of
dollars.

In contrast, consider the sheep example.  In a
fictitious world where sheep are the only good, the only measure of a person's
real financial wealth is the number of sheep that he owns.  In this
simplified scenario, yes, if someone's stock of sheep physically doubles every
year, then the market-clearing (real) interest rate must be 100 percent.

To put it another way:  One sheep now represents a
claim on an endless stream of future sheep.  But unlike the tractor
example, we do not here run into the Böhm-Bawerkian problem:  The
current market value of one present sheep, in terms of sheep, is always
one!  In the tractor case, physical facts alone could not tell us
how many dollars would exchange for the capital good; the tractor might cost
$5,000, or $10,000, or $15,000.  But in the case of the sheep, we can
say what the real price of the capital good (sheep) in terms of its future
consumption good (sheep) has to be:  One sheep trades for one sheep.  Thus,
the incidental use of a one-good model has allowed the neoclassical to
completely sidestep the"Austrian" problem<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftn4" name="_ftnref4">[4]</a>
of valuing the capital stock in terms of its eventual output of consumption
goods.

AUSTRIAN ANALYSIS STILL RELEVANT

I would like to conclude with a personal anecdote that
illustrates the relevance of Böhm-Bawerk's critique.  After I had
reconciled the verbal logic of Böhm-Bawerk with the mathematical models of
the mainstream, I wrote a first draft of one of my dissertation essays in
which I explained away the apparent conflict by pointing out the tremendous
importance of the mainstream's assumption of a single-good world.  I
handed in my draft to a renowned mainstream economist, just to make sure that
I hadn't misunderstood neoclassical theory.

When I got my draft back, I was quite surprised to find that
the professor had clipped a single piece of paper to the front.  On
it he had written something like,"This is the only interest theory that
I, and just about everyone else, understand."  Below he had
drawn a simple diagram, with C(t) (i.e. consumption in period t) on the x-axis,
and C(t+1) on the y-axis.  There was a semicircle connecting the two
axes, which denoted the production possibilities frontier (PPF) for present
and future consumption through tractors.

The professor had drawn two dots on the PPF.  The
dot that was higher on the circle represented the tradeoff that was available
through saving:  By moving to the left on the x-axis, a person
reduced current consumption in order to invest in tractors.  By
moving up on the y-axis, a person increased future consumption because of the
marginal output of the tractors.

And now the crucial step:  Because of the shape of
the PPF, and because he had chosen points on the right side of the curve, it
turned out that the leftward shift in present consumption was smaller than the
upward shift in future consumption.  Therefore, my professor thought
that this simple diagram had shown a technological cause of interest:  Because
of the productivity of tractors, my professor was claiming that a small
reduction in present consumption would cause a great increase in future
consumption, i.e. a positive rate of interest.

What was so frustrating about this diagram was not that it
was wrong per se, but that it completely overlooked Böhm-Bawerk's critique!  My
professor had completely overlooked the problem of pricing the tractors!  Yes,
the technological facts allow us to say that a given increment in future
consumption (i.e. the gap on the y-axis) will require the present investment
in a definite number of tractors; this is an engineering problem that does not
involve subjective preferences.

However, just because we know how many tractors we need to
buy in the present, we do not know how much such an investment will
reduce our present consumption.  In order to know this, we need to
know the market price of tractors in terms of present consumption.  By
drawing the gap on the x-axis, my professor had just assumed that the tractors
would cost less in terms of present consumption than their future output.  In
other words, my professor had assumed a positive rate of interest.

After several minutes of discussion, I finally got the
professor to realize that he had been assuming away this difficulty.  But
he still refused to concede that physical facts alone could not explain a
positive interest rate.  No, instead he proclaimed:  "Assume
we can turn tractors into bananas one-for-one."

In conclusion, Böhm-Bawerk's critique of the naïve
productivity theory was a brilliant leap forward for subjectivist economics.  Unfortunately,
its lessons are as relevant today as they were in the 1880s.

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Robert Murphy is a summer fellow of the Mises Institute. robert_p_murphy@yahoo.com

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<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftnref1" name="_ftn1">[1]</a>
Böhm-Bawerk, Eugen von. (1959 [1881]) Capital and Interest (3 vols.
in 1), South Holland, IL: Libertarian Press.

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<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftnref2" name="_ftn2">[2]</a>
Specifically, Böhm-Bawerk wondered, “Whence and why does the capitalist
receive this endless and effortless flow of wealth?” (I, p. 1, italics
removed).

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<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftnref3" name="_ftn3">[3]</a>
No one would lend out 10 sheep today in exchange for 15 sheep next year,
because the owner could simply hold on to his 10 sheep and allow them to
double into 20 sheep next year through reproduction.

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<a title href="http://www.mises.org/fullstory.asp?control=1263#_ftnref4" name="_ftn4">[4]</a>
Actually, one does not need to use verbal logic to see the problem.  In
the mathematical appendix to my dissertation (available here http://homepages.nyu.edu/~rpm213/files/Dissertation.pdf),
I develop a few general equilibrium models with two goods to illustrate Böhm-Bawerk’s
insight.


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