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In partial response to Mat Forrester's question, here is my summary of
the Knight-Boulding debate on capital theory. This was only one of
many such debates Knight was having at the time -- others were with
Hayek, Machlup, Kaldor, and Lange.
CHRONOLOGY
Boulding, K. (1934)
The Application of the Pure Theory of Population Change to the Theory of Capital
Boulding, K. (1935)
The Theory of a Single Investment
Knight, F.H. (1935a)
The Theory of Investment Once More: Mr. Boulding and the Austrians.
Boulding, K.E. (1936a)
Professor Knight's Capital Theory: A Note in Reply
Boulding, K.E. (1936b)
Time and Investment
SUMMARY
Boulding and Knight find agreement on many issues, but disagree over
fundamental conceptions of capital. Boulding conceives of capital as
heterogeneous physical inputs while Knight's capital consists of a
perpetual fund of value. Knight (1935, 57) summarizes the debate by
saying
<Thus the basic issue is the old and familiar one of choice between two
conceptions of capital. In one view, it consists of "things" of limited
life which are periodically worn out or used up and reproduced; in the
other, it is a "fund" which is maintained intact though the things in
which it is invested may come and go to any extent.>
Boulding develops his conception of capital within a physical process
of production in two articles. In the first, Boulding (1934) uses
population theory to construct an analog for the average period of
production. He treats the aggregate of goods as a heterogeneous
population that is aggregated in dollars, then applies population theory
where value of all goods is the stock, or population; inputs correspond
to flow of births into the population; outputs correspond to flow of
deaths out of population; and average period of production
corresponds to average length of life. APP = total value capital/total
money income per year.
In the second, Boulding (1935), extends the profit-maximizing
condition of marginal revenue equals marginal cost to incorporate <the
element of time as an explicit variable of the problem>. Assuming
perfect foresight, Boulding examines the complete history (revenues,
costs, net revenues) of a single investment, <from the day of its
inception to the day of its final liquidation> Given a physical
production function which includes the period of production as a
variable, the investor maximizes the internal rate of return over the life
of the investment by choosing the optimal rates of input and period of
production. The maximum rate of return is the rate of interest which
makes, at any date, the present values of revenues (outputs) equal to
the present value of costs (inputs).
Knight agrees with much of what Boulding says [1], and makes no
substantive rebuttal of the logic or details of the models. In a letter to
Taussig (editor of the QJE), Knight (22 August 1935; B62 F7) says <I
do think these articles of Boulding contain about the only really
significant discussion of the capital problem I have seen in print which
looks in the general direction of a production period theory, and that
they ought to be discussed seriously>. Knight (1935, 57) accepts
Boulding's model of a single investment as <mathematically correct>
and < valid for a single investment if it is built up from zero and then
completely disinvested in accord with know function of time>
But Knight rejects the assumption of Boulding's models -- that capital
goods have finite, physical life spans. With Knight's (1935, 57) belief in
the perpetual or immortal nature of capital, he asserts that Boulding's
<argument is not valid ... for ... capital which is not fully consumed at
the end of some definite period, but is continuously maintained> This
belief in the perpetual maintenance capital also leads Knight to reject
Boulding's population analogy -- <Apart from concrete capital goods
with a know life history, there is no possibility of finding any
correspondence between "births" and "deaths," and no motive for
attempting to do so> (1935, 59).
Boulding (1936, 527) summarizes the debate, focusing on the same
disagreement over fundamental conceptions of capital that Knight
identified.
<For the "Austrian," capital is something which arises out of the
physical productive process, because inputs ... precede outputs ...
Capital is the fund necessary to bridge this gap in time ... and ... total
capital depends directly on ... some "average period of production."
Professor Knight, on the other hand, in rejecting the concept of a
physical process of production, is forced to consider capital as a kind
of self-subsistent factor of production, "essentially perpetual" in its
nature ... This view of capital seems to be possible as an abstraction,
particularly in the theory of the stationary state, but it abstracts too
much from the real peculiarities of capital to be wholly satisfactory as a
general theory.>
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[1] Knight and Boulding both reject the Austrian distinction between
primary and secondary factors of production, and both recognize that
compound interest complicates the measurement of the period of
production so that there exists no simple relation between r and
roundaboutness. Boulding is forthright about the limitations of the
period of production -- that it is limited to stationary or steady-state
equilibrium models, that it is <difficult or virtually impossible to
measure> (1934, 664), and that the intertemporal aggregation of
heterogeneous physical inputs in value terms is <makeshift>, <a device
to express as a single figure what in fact has too many dimensions to
be so expressed> (1936, 526-7). But he defends the concept as useful
for providing an order of magnitude and points out that <We have
exactly the same difficulties in connection with the concept of a price
level; and though all measurements of price level are to some extent
arbitrary, that fact does not prevent us from finding the concept useful
within certain limits> (1935, 527-8).
REFERENCES
Boulding, K. (1934) The Application of the Pure Theory of Population
Change to the Theory of Capital. QJE 48 (August): 645-666.
Boulding, K. (1935) The Theory of a Single Investment. QJE 49 (May):
475-494.
Knight, F.H. (1935a) The Theory of Investment Once More: Mr.
Boulding and the Austrians. Quarterly Journal of Economics. 50
(November): 36-67.
Knight, F.H. (1935b) Letter of 22 August 1935 to F. Taussig. In Frank
Knight Papers at the University of Chicago, B62, F7.
Boulding, K.E. (1936a) Professor Knight's Capital Theory: A Note in
Reply. Quarterly Journal of Economics. 50 (May): 524-31
Boulding, K.E. (1936b) Time and Investment. Economica (new
supplement) 3 (May): 196-220.
Avi J. Cohen
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