----------------- HES POSTING ----------------- 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.> ------------------------ [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 ------------ FOOTER TO HES POSTING ------------ For information, send the message "info HES" to [log in to unmask]