Search

IN CLASSICAL economic theory, the firm's stock of physical capital is adjusted toward the optimum as capital productivity is greater or less than cost. A thread of this thinking is woven into the investment equations of most of the major econometric models by inserting, in independent variable(s) form, the stock-adjustment idea. In modern (Keynesian) macroeconomic theory, optimum investment is where the marginal effciency of capital just equals "the" interest rate. The marginal efficiency of capital is the rate of discount that equates expected dollar flow to the present cost of the investment. Since the expected dollar flow is a function of effective demand and the stock of capital, investment again is seen to be an adjustment as the stock of capital is either more or less than optimal. Thus, both classical and modern investment theories contain the stock-adjustment idea. But in addition, modern investment theory places heavy emphasis on "the" interest rate, expected dollar returns, and dollar cost of investments, all financial variables. Therefore, in the typical econometric investment function, the classical "real" variables are synthesized with the modern financial variables. For example, in the basic investment equation (4a) of the Wharton model, investment in manufacturing plant and equipment is a function of the "real" variables: capacity utilization, gross output, the stock of manufacturing capital; two financial variables; and anticipations. Distributed lag weights are applied to those variables where required. Equation 4a is

During the period of the late fifties and early sixties there was a considerable amount of discussion in the literature on the usefulness of the concept of the marginal efficiency of capital in the evaluation of alternative investment projects; see, for example, Masse (1962) and Merrett and Sykes (1962). There are basically two problems: multiplicity of roots for the solution of the marginal efficiency of capital, given in income stream and capital cost, and the different results obtained in ranking projects according to marginal efficiencies of capital and according to net present values. With respect to the former problem, some thought has been given to the economic meaning of the multiple roots and to the choice of root for ranking projects. The objectives of this paper are to show that the marginal efficiency of capital is not appropriate for ranking investment projects, as it is essentially an equilibrium concept; that the "internal rate of return" and the marginal efficiency of capital must be distinguished; and that, when the internal rate of return is appropriately defined, the ranking of projects by the internal rate of return and by net present value for projects with equal time spans is identical. Further, it is shown that the internal rate of return can always be calculated and has a unique value relative to the market interest rate. Finally, an economic interpretation is given to the multiple roots for the solution of the marginal efficiency of capital and to the case where there are no real roots.

SUMMARY The author makes net investment an increasing function of the marginal efficiency of capital affected by the corporate tax and accelerated depreciation, and then lets that investment enter the growth equation as an independent variable. Thus he shows that the corporate tax rate or the length of the period of accelerated depreciation will have to be reduced if the rate of growth of productive capacity is to be increased in a capital-scarce market economy. Further the author brings out two implications. First, considering the tax-afforded depreciation reserves as a definite fraction of national income, the resulting ratio is added to the private saving ratio so as to increase capacity growth. This first implication is thought important to a developing economy whose personal saving is insufficient to finance the net investment required for capacity expansion. The second of the implications is brought out by making externally raised capital funds an increasing function of tax-influenced dividend payments. Considering such capital funds as a fraction of national income on a par with the personal saving ratio, the author demonstrates the theoretical possibility of the low corporate tax favorable influencing capacity expansion. He points out that this second implication is especially important to an economy whose securities market is highly developed but whose long-term bank financing is relatively underdeveloped. He alludes to some relevant empirical evidence as supporting his theoretical arguments.

Professors Frost and Schall have quite rightly criticized my attempt to redefine the "internal rate of return" and to distinguish such a definition from the current synonym "marginal efficiency of capital." Accordingly, in this reply I will use the phrases "internal rate of return" and "marginal efficiency of capital" as exact synonyms and will use "Ramsey rate of return" for the concept defined in equation (4) in Ramsey (1970, p. 1020). The Ramsey rate of return can be usefully interpreted as a weighted average of the firm's own rate of return, which may vary from period to period. Thus, if in each period i the net return is Ri, then the firm's own rate of return in the ith period is R C, where C is the capital cost of the investment. For example, if on a capital expenditure C the firm obtains the income stream R1, R., . . . Rn, then the firm's rate of return may vary from period to period and the Ramsey rate of return is a weighted average of the varying rates of return given by

According to the Keynesian theory of Investment, the firm determines the optimal amount of Investment by taking into consideration the marginal efficiency of capital and the rate of Interest. In order words, It asserts that the firm determines Investment so as to equate the demand price to the market price of capital goods.1) This Investment behavior implies that a firm determines its optimal stock of capital by maximizing its present value with respect to its capital stock and labor input.2) That is, the Keynesian theory of Investment is nothing more than the neo-classical theory of firm’s behavior.

In choosing a group of topics out of the multitude covered in Keynes’ General Theory, I have sought one to which Keynes himself attributed great importance, one which is theoretically interesting and which has not been fully explored already. I have been attracted to the group concerned with the links between the economic future and the present, because Keynes clearly believed that it was in the treatment of these links that orthodox theory was particularly defective. He wrote: “The fact that the assumptions of the static state often underlie present-day economic theory, imports into it a large element of unreality. But the introduction of the concepts of user cost and of the marginal efficiency of capital, as defined above, will have the effect, I think, of bringing it back to reality, whilst reducing to a minimum the necessary degree of adaptation. It is by means of the existence of durable equipment that the economic future is linked to the present.”1

“Those who are strongly wedded to what I shall call ‘the classical theory’ will fluctuate, I expect, between a belief that I am quite wrong and a belief that I am saying nothing new.”1 Did Keynes actually say something new? He certainly said something quite different as compared with what most other economists were saying at the time, but it is not difficult to find in the literature of economics many of the same ideas earlier expressed. In fact, somewhere in literature every element of the Keynesian system was at some time discussed. But no single theorist ever worked out a complete and determinate model based on (1) the propensity to consume (save), (2) the marginal efficiency of capital, and (3) liquidity preference.† All the predecessors of Keynes to be discussed in this chapter failed to make use of one or more of the Keynesian ideas. Furthermore, many of these forerunners had not clearly in their minds the theoretical formulations, and it is often necessary to read between the lines in order to reconcile their views with those of today. We shall make no attempt to consider every author in history who discussed economic problems along the lines of Keynesian analysis, but shall merely select some of the better known cranks, heretics, and respectable economists who have concerned themselves with the problem of unemployment.

as being equal to that rate of discount which would make the present value of the series of annuities given by the returns expected from the capital-asset during its life just equal to its supply price. This gives us the marginal efficiencies of particular types of capital-assets. The greatest of these marginal efficiencies can then be regarded as the marginal efficiency of capital in general [2, pp. 135-36].

Applications of capital theory refer to a world of changing population, institutional processes, technology, and innovation. For example, an investment decision may be affected by some expected repetitive patterns of circumstances or by some seemingly irreversible processes threatened by obsolescence or stagnation. One may assume the principle of an eventually diminishing net returns flow. It seems desirable to treat the marginal efficiency of capital in terms of an initial investment and a net returns flow that varies with time. For a variety of such time dependent net returns flows the treatment of the marginal efficiency of capital is simplified by the Laplace transform technique illustrated in this article.

In his recent article in this Journal,' Mr. Tsiang has declared that the emphasis placed on acceleration-induced investment by Messrs. Harrod and Hicks,2 among others, is incorrect. Instead, following the lead of others, Mr. Tsiang would have the emphasis shifted to investment which is made a function of the level of national income rather than its rate of change. Mathematically, the relation I = f(Y) would be substituted for the relation I = f(AY), the latter standing for the acceleration effect.3 Different reasons have been offered for preferring systems which relate investment to the income level. One reason concerns the effect current sales will have on profit expectations relating to investment outlays which will bear fruit in the distant and uncertain future. Because of the uncertainty associated with the future, there is a tendency to extrapolate, to a certain extent, what is knowable and certain, namely, the events of the immediate past and present. This tendency to use current sales and income as a barometer of the future results in the marginal efficiency of capital varying directly with the level of income and profits. Moreover, in the face of capital rationing, an important part of the supply of investment funds available to industry will tend to be related directly to the level of income and profits, too. In the first place, since savings, in the short run at least, tend to rise with the level of income, there will be some tendency for the supply of equity capital to rise also as national income rises. More important perhaps, profits will, of course, vary directly with the level of income, as will

W RORK in economics can proceed on a variety of levels. The writers of "The Scale of Operations in Agriculture" were attempting nothing more than to breathe a modicum of scientific rigor into the handling of a subject which has suffered badly in the hands of those who work hunches and prejudices to death and yet fail to advance economic analysis. Mr. Cavert takes his stand with this group. With respect to the questions at issue Mr. Cavert's stand seems hardly defensible-except insofar as he objects to abstraction. On this methodological aspect the writers merely state their case, and let it rest on its merits. They assert that economics is an abstracting science, despite the literature which testifies volubly to the contrary. They fully realize what must be sacrificed as a necessary consequence of abstraction. With the foregoing statement of what the writers were attempting, and the limitations involved in their method, the objections which Mr. Cavert raises can be dealt with briefly: 1. The fundamental objection is that the writers have overlooked the fact that the real difficulties in conducting a large scale agricultural undertaking are those of standardizing jobs and those of supervision of workers. The truth is not that these hoary, but not particularly venerable, notions were neglected in the paper being discussed, but rather that they are stated in economic terms. They were described as "management proper, composed in turn, of supervision and coordination or decision making." Further, they are certainly included in Keynes' delightful concept of the marginal efficiency of capital which occupies a central place in the paper being discussed.

I. Why the marginal efficiency of capital tends to be low in "mature" economies, according to the stagnation doctrine: less room for extensive growth, 638; institutional rigidities, 639; technological and organizational factors, 640.—II. "Deepening" vs. "widening" of capital during the 'twenties, 642. — Grounds for holding that innovations during the nineteenth century led to a considerable "deepening" of capital, 646. — Further criticism of the technological argument, 648. — Conclusions, 651.

I appreciate the preceding comments. Beyond pointing out that careful reading of my note will show that I did not pretend to explain fully Argentina's postwar rate of capital formation, I would like to remark briefly on three matters. First, I seem to have been misunderstood. Since I did not mean to imply that the proportion of private saving, in the national income declined. I merely stated that, while certain conditions favored the use of savings for purposes other than fixed capital formation, it is also probable that the investment equivalent of the propensity to save declined. This could occur while the propensity to save out of current income remained constant or even increased. I based my conclusion on the rise in the share of wages in the national income1 and on a change in the price structure favoring lower income consumers in particular. Second, I do not think that conclusions regarding the marginal efficiency of capital can be drawn from the information given by Schwartz. His calculations, based solely on the capitalization of companies registered with the Buenos Aires stock exchange, suggest that the profitability of some companies increased. Yet, it may well have declined for the economy as a whole. Indeed, prices on the Buenos Aires stock exchange, after rising sharply until 1948, fell and, notwithstanding the violent inflation, had not reattained their 1948 level by 1958.2 Nor can pressure to import machinery be taken as evidence that the marginal efficiency of capital in general was high. Actually, imports of capital goodsbut not of raw material and intermediate partsaveraged less in the 1950's (1950-1958) than during 1935-1939 and 19461949, and investors had to be satisfied to a greater extent than they may have wished with locally produced capital goods.3 Third, Schwartz suggests that the investment consumption goods price ratio declined after 1949. This is correct, but the ratio by no means returned to the prewar level. Furthermore, following the 1955 and subsequent devaluations, import and investment prices rose substantially in relation to domestic and consumption prices respectively.4 In Table 1 of the note which is the subject of this discussion, I merely showed two averages one for 1946-1949, the other for 1950-1958-of the relationship between investment and consumption goods prices. I felt that this was enough to point out the new price relationships established during the 1940's and essentially maintained during the 1950's. In my judgment, the movement of the indices is of such magnitude that, notwithstanding the limitations inherent in them, they point to a substantial change in the price relationships between economic sectors. Interestingly, recent studies tend to confirm this conclusion. In 1960 and 1962, investment prices were higher in relation to consumption prices in Argentina than in other Latin American countries.5 I feel that such developments merit attention because of the effects they may have, not only on resource allocation, but on saving and capital formation in general. * The writer is a member of the United Nations Secretariat. Neither the opinions expressed here nor in the original article-written before he joined the United Nationsnecessarily reflect those of that organization. 1 Schwartz's point concerning social security taxes is correct. However, data excluding social security taxes also show an increase in the wage share for all sectors for the years 1946 to 1955 inclusive, for which the data are available to me. See United Nations, Economic Commission for Latin America, El Desarrollo Econo'mico de la Argentina, Anexo (mimeographed, 1958), 190, 191. 2 Bolsa de Comercio de Buenos Aires, Anuario Estadistico. 'R. Hayn, "Inflaci6n, Formaci6n de Capital y Balance de Pagos de la Argentina, 1940-1958," Revista de Economia y Estadistica (Cordoba, Argentina, 1962), No. 2 (esp. Table 4). 'Ibid., (esp. Table 9). 5See footnote 1 in the note under discussion and United Nations, Economic Commission for Latin America, A Measurement of Price Levels and the Purchasing Power of Currencies in Latin America, 1960-1962 (mimeographed, March, 1963).

IN the November, 1937, issue of this Journal, Mr. Kalecki endeavours to explain the r6le of increasing risk as a determinant of the size of the single entrepreneur's investment. He argues that the principle of increasing risk is alone sufficient to define the size of the enterprise, and that the two more commonly cited limiting factors-increasing dis-economies of scale and imperfect competition-are either unnecessary for the purpose or of negligible importance. The principle, as formulated, is simply that the marginal risk to the entrepreneur rises as the size of his investment increases. Thus, even though the marginal efficiency of capital and the rate of interest on capital be assumed constant over an indefinite range, the rising risk curve will limit the size of investment. Two reasons are given for this behaviour of risk: (a) the larger the investment the more the wealth position of the entrepreneur is endangered in the event the business is unsuccessful; and (b) the danger and costs of illiquidity: since specific capital goods are illiquid on short notice, a sudden need for liquid capital can be satisfied only by selling the assets at a loss, or borrowing at higher than market rates. Our purpose is to comment briefly on the validity and significance of the principle. i. Let us first examine the stated reasons why the marginal return for risk should increase with the size of the investment. For the entrepreneur the risk is in part determined by the legal form of the enterprise. Mr. Kalecki restricts his analysis to the case of the single entrepreneur who presumably operates as a single proprietor with unlimited liability. The entrepreneur may apply varying proportions of his total wealth within the business. The remainder, we assume, is held in " cash " or other investments. The whole of his wealth, however, may be commanded for

In an earlier article,1 an attempt was made to establish the process by means of which Keynes' equation between the rate of interest and the marginal efficiency of capital (or expected rate of profit) would be brought about. It was established that the conditions under which such an equality could be exactly achieved were somewhat restrictive and various simplifying assumptions had to be employed-rational behaviour by businessmen, perfect foresight, a constant demand for money to hold, interest-elastic investment, perfect shiftability of funds, a single rate of interest, and perfect mobility of resources other than money. Even under these conditions, the level at which this equation would be achieved would certainly vary from time to time. When, however, this framework of simplifying assumptions was removed, there was good reason to believe that " on many occasions the influence of the interest factor is definitely swamped by other more obvious considerations ". If we allow that the businessman does pay heed, even though only to a limited extent, to the costs of raising finance, it is necessary to emphasise, first, that no two entrepreneurs will have access to financial resources on exactly the same terms and, second, even the same entrepreneur will generally find that these costs will be conditioned by the purpose for which he borrows. (In simple terms, rates will usually be different for short-, mediumand long-term borrowings.) Furthermore, not only is there a whole range of interest rates, but also a variety of conditions which may be attached to a loan. Each transaction, therefore, has its unique characteristics. As a result, for each borrowing operation there is one particular rate of interest, which is the Relevant Rate of Interest, and, to the extent that the entrepreneur acts rationally, he will attempt to secure an equation at the margin between this rate and his expected rate of profit. When developing this analysis, no specific mention was made of credit rationing. My attention was drawn to this lacuna in the analysis by my colleague Professor F. W. Paish. I was disposed to believe at the time that the introduction of this complication would require no material modification of the argument. Upon reflection, however, there would seem to be certain peculiarities which do call for further investigation. Sufficient was said in the earlier article about the Relevant Rate of Interest for us to be tolerably clear about its definition. Can we

I. Assumptions, 36. — Five propositions concerning the relationship between short and long rates, 37. — II. Influence of the costs of investment, 41. — Shiftability on the lenders' side, 43. — Two complications: many maturities, 44; the function of banks as changers of maturities, 45. — III. The influence of risk, 46. — IV. Expectations: the rational investor's decisions, 48; possible inconsistencies, 49. Effect of divergent expectations among members of the market, when the majority expect rising interest rates, 51; when "the market" expects rates to fall, 54. — V. Verification: movement of interest rates over time, 55; structure of yields on different maturities, 56. — VI. Bearing of this analysis on: influence of the discount rate on investment, 60; interest and the marginal efficiency of capital, 60; influence of wide gaps between short and long rates, 61; the "liquidity theory of interest," 62.