Capital

The stationary economy

Nonstationary models

BIBLIOGRAPHY

Capital is necessary because production takes time (Smith 1776; Ricardo 1817; Fisher 1907). The inputs have to be put in and paid for over an interval before they result in outputs available for sale. This is true whether the input consists of equipment that is needed right at the beginning (fixed capital) or of materials that have to be put in continuously during the process of production (working capital). A producer therefore needs a stock of money capital out of which to pay for input over this interval. Only after the interval, during which he will have turned his money capital into real capital (the stock of goods in process from input to output), can he begin to use the inflow of proceeds from output to cover the outflow of payments for input, and he will therefore not need any more capital.

The existence of the interval is obscured by the continuous flows of input and output in “sausage machine” types of production. (We are leaving for later consideration the need for acquiring the machine itself and, for the moment, are concentrating on the working capital alone.) The interval between the input of a particular piece of “meat” into the machine and the output of the “sausage” containing that piece of meat may seem insignificant, and the quantity of real capital (the meat that is at any moment on the way from the input point to the output point of the production process) may seem negligible. The two flows may even be said to be “synchronized,” or “simultaneous,” which suggests that there is no interval between them at all (Stigler 1941, chapter 11).

”Width” and “depth” of capital. The quantity of capital needed for a productive process depends, of course, on the volume of production. Two factories instead of one, working in exactly the same way, with twice the input and twice the output, will naturally require twice as much capital as well. This has been called the “width” of capital. But the quantity of capital needed is also directly related to the length of the interval between input and output. This has been called “depth” of capital (Hawtrey 1937). If it takes five minutes for the meat put into the machine to come out as sausage, the “meat capital” will correspond to the quantity of meat put in during five minutes. If the interval is ten minutes, twice as much meat capital is required for the same rate of input and output. This may seem negligible, but if the meat has to be brought to the factory each morning and the sausages produced are taken away the next morning, the interval for the factory is 24 hours and the meat capital corresponds to a day’s input of meat.

The relationship between the length of the interval and the quantity of capital needed is seen most easily in imaginary cases of “point input–point output” production (of which our sausage machine is an example if we consider only the meat input). If we suppose that the making of wine requires nothing more than one day’s work in making the barrel and squeezing the (freely available) grapes and one year of waiting for the juice to turn into wine, then an established winery will consist of a capital stock of 365 barrels of maturing wine for each barrel in the daily input of grape juice or output of one-year-old wine. The depth of capital corresponds to the length of the interval or, its equivalent, the ratio of the stock of capital to the flow of input or output.

The average period of production. There may also be many different intervals between input and output. If the meat is brought to our sausage factory every morning but the sausages are collected and paid for only on Monday mornings (and the factory works a continuous seven-day week), then the capital needed corresponds to the average interval. For the meat brought in on Sunday morning the interval is one day; Saturday’s meat has a twoday interval and Monday’s meat a seven-day interval until it is taken away as sausage the following Monday. The average interval is four days, and the quantity of meat capital needed will be equal to four units (four days’ input of meat), since that will be the average stock of meat in the factory. On Mondays there will be just one unit, on Tuesdays two units, and on Sundays seven units.

It might seem that seven units of capital are needed, corresponding to the total period of seven days, since the producer has to buy meat for seven days before he gets any proceeds from the sale of sausages. But this is true only if he has to have on hand every Monday morning all the money to pay for the whole week’s purchases of meat. In that case the appropriate input is not the daily input of meat but the input of the money for a whole week’s meat every Monday morning. The interval from input to output is then from Monday morning to Monday morning, or seven days. But if the producer does not need to hold any money idle, he needs only the four units of capital Corresponding to the average interval of four days. In the first three days of the week he needs as capital only one, two, and three units, respectively, and he can lend to others the difference between this and his four units of capital: namely three, two, and one units. During the last three days of the week, when he needs five, six, and seven units, he can borrow the difference of one, two, and three units from others—an exactly equivalent amount.

Another way of seeing this is to suppose that a producer sets up seven such factories, each selling its sausages on a different day of the week. For this he would need one unit of capital the first day for the first factory, two more units on the second day (one for the second day of the first factory and one for starting the second factory), three more units on the third day (one for starting the third factory and two for the first two factories), and so on: one unit more each day than the previous day until the seventh day when he would need seven more units. On the eighth day the first factory’s weekly output of seven units becomes available, and its proceeds can pay for the daily input of all seven; every day after that another factory’s output becomes available. The total amount of capital required is therefore 1 + 2 + 3 + 4 + 5 + 6 + 7, or 28, which is just four units per factory and equal to four times the daily input of the seven factories.

All this of course refers only to the “meat capital,” which stands for the raw materials and other inputs involved in current production and in the maintenance of the factory—the labor, the raw materials, the electricity, the window cleaning, and all such things. There remains the capital needed for equipment, which usually comes to a much greater amount. It corresponds to the average interval between the input (elsewhere) of resources into the production of the equipment and the output (in our factory) of the services of the equipment.

Capital and ownership. It would be possible for an individual producer to manage without any capital if he could buy the services yielded by all the capital items involved in his line of production without owning any of them (or, what comes to the same thing, if he could rent the capital items from their owners). He would then be paying out a current flow of money for the current flow of input to his factory, and he would be receiving a current flow of money from the current flow of his output, earning the excess of the money inflow over the outflow (or losing the deficiency).

But to manage in this way without any capital he would have to find others who own all the capital items, including the working capital or goods in process—the “meat capital.” Such arrangements are unusual. Normally the producer finds it more convenient and more economical to acquire ownership of most of the capital goods—at the very least, the working capital—even if he has to borrow money capital for this. He needs capital to the extent that he finds it more convenient, more efficient, or more economical to own the sources of services involved in his productive activity than to buy the services or to rent the sources.

Capital and accumulation. This difference between owning the sources and renting them (or buying their services) from someone else is crucial to the individual producer. But it is of no use whatever from the social point of view, because from the social point of view there is no someone else. Society can acquire additional productive services only by bringing into existence additional sources of such services. This involves the slow process of accumulation, or net investment, which is the production of more than is being used up during a period—that is, a period in which input exceeds (final consumption) output.

The social average period of production. It is obvious that society must have accumulated in previous periods all the capital in existence at any point in time. This includes both the “meat,” or “working,” capital and the fixed capital involved in the equipment, which may come to many times the working capital. Not quite as obvious is the fixed capital that normally has to be sunk in learning how to operate the factory smoothly and efficiently.

Nor is this all. From the social point of view it is also necessary to consider the capital that must have been accumulated for industries that produce the sausage-making equipment, including their working capital, their equipment, and their initial growing pains. These industries in turn depend on more generalized industries such as transportation, electricity, fuel, and so on. A similar proliferation appears when we consider what is necessary for the provision of the current input. The “meat” producers need both capital and current input, and their providers depend on yet other industries whose capital must have been accumulated, and so on.

Still another set of proliferations appears if we look in the other direction—that in which the output of our factory goes. In some cases our “sausages” are in turn the raw material of other industries, which cannot take our supply until they have built up their own stock of capital. Even then these industries cannot be our regular customers until their own customers have themselves built up capital and made connections with suppliers and customers and so on.

However, this seemingly endless proliferation does not make our problem unmanageable. We are saved by two considerations. First, the different proliferations overlap. Many of them involve links to the same industries, and their total number is no greater than the finite number of industries in the economy as a whole. Second, the social point of view cannot limit itself to the input and the output from our sausage factory. The social output is the net product of all the final goods and services that constitute consumption and accumulation in the economy as a whole—those products that are consumed by the citizens and those that are not consumed but are added to the capital stock of the economy. The social input is the total of productive services available to the economy from its labor force, its natural resources, and its accumulated stock of capital. The social capital corresponds to the average interval between the application of the productive services and their emergence (as either consumption or accumulation) after passing through the different industries that are the stages in the production of the final social output. (We stipulate net and final to avoid double, or rather multiple, counting. We do not want to count the meat, the sausage that contains it, and the restaurant meal that includes the sausage.) This average interval for the economy as a whole, to which the social capital stock corresponds, is called the social average period of production (BöhmBawerk 1884–1912; Dorfman 1959).

“Corresponds” is a deliberately ambiguous expression. Under certain assumed special conditions the ambiguity disappears. One then can say that the value of the net flow of input is equal to the value of the net flow of output and that the average period of production is equal to the ratio of the value of the capital stock to the value of each of these flows—namely, to both the capital–input ratio and the capital–output ratio. If the average period of production is three years then the capital–input ratio and the capital–output ratio will each be 3:1 (the input and the output flows being measured at annual rates).

The assumptions under which these relationships hold are indeed abstract and unreal, but they help us to see the nature of more complicated, but more realistic, conditions. The special assumptions are a stationary economy and a zero rate of interest.

The stationary economy

Implicit in a stationary economy are an unchanging technology, a constant supply of labor services, a given stock of land yielding a constant flow of land services, and an unchanging stock of capital goods.

The constant supply of labor services implies not only a constant population but in addition the absence of changes in skills, education, training levels, and the proportion of workers in the total population. The given supply of land constitutes the “original and indestructible properties of the soil” of the classical economists, where “original” means that land can never be produced (by men) and where “indestructible” means that in the normal course of events the supply and the fertility of land never diminishes.

The unchanging stock of capital goods existing at any moment has been produced by labor and land services in the past and is contributing to the production of consumption goods and services that will become available only in the future. It is unchanging in its composition because each item, as it gets a day older, takes the place of a similar item one day older and is replaced by a similar item one day younger. The very oldest item of each kind is completely used up and disappears, while the one-day-old item is replaced by a newly created one. The stock of capital goods may thus be viewed as consisting of congealed past labor and land serv-ices waiting to be turned into future consumption goods or services.

The existing stock of capital goods, of course, has been produced by land and labor services, working not by themselves but in cooperation with other capital goods that existed in the past; but this does not change the essence of the matter. We need only go back further into the past to the land and labor services that went into the making of the other capital goods, then to those that went into the still more remote capital goods that contributed to the production of these later goods, and so on. Similarly the currently existing capital goods will be used not only to produce future consumption goods and services but also to make further capital goods in the future. This again means only that we must go still further into the future to the consumption goods and services that will be produced by these capital goods, then to those that will be produced by the capital goods that these future capital goods will help to produce, and so on. The longer the interval between the original application of land and labor services and their final emergence in consumption goods and services, the larger the capital stock constituting the volume of congealed past services that at any moment in time are still on their way to their final transformation into future consumption goods.

This stationary economy is essentially a very simple model, but many find it very difficult to use because they tend to forget that it is only a model of an imaginary economy that has been in exactly the same condition since time immemorial and that is expected to remain so for ever. They are therefore disturbed at its being nothing like a true account of the actual past and nothing like a plausible prognosis of the future.

This model contains the essence of the theory of capital as developed by Eugen von Böhm-Bawerk (1884−1912). Since the 1930s there has been a tendency to neglect Böhm-Bawerk because without the implausible assumption of a zero-interest rate (which would induce the owners of capital and of land to consume more than their possibly very small incomes and, thus, to disrupt the stationary economy) it seemed impossible to maintain his basic tenet—the equality of the capital–input ratio, the capital–output ratio, and the average period of production. [SeeBÖhm-bawerk.]

A zero-interest model

The assumption of a zero rate of interest in the model is what gives us the equality between the value of the present capital stock and of the past flow of land and labor services congealed in it. Unless these values are just equal, it would be profitable to increase or decrease the stock of capita] goods, rather than maintain the stationary economy by merely replacing them when they wear out. Similarly, the zero rate of interest is what makes the value of the present capital stock just equal to the value of the future flow of consumption into which the capital stock will be transformed. Thus, it is only at a zero rate of interest, when the date on which goods or services exist or are performed does not matter, that the capital–input ratio, the capital–output ratio, and the average period of production are equal to one another.

A positive-interest model

It is possible to construct a slightly less implausible model of a stationary economy with a positive, instead of a zero, rate of interest. At a sufficiently high rate of interest, the owners of property would on the average want to keep it for the sake of its yield and not consume any of it. The stationary economy could then persist. The capital stock would still incorporate a quantity of past land and labor services equal to their rate of flow of input over the average period of production and would still be the source of an aggregate future consumption equal to the rate of flow of output over the same average period of production. But the values would no longer coincide.

In this model the value of the current stock of capital goods must exceed the value of the incorporated land and labor services by the interest that can be earned on them during the interval between their input and the current date. Otherwise it would pay to increase or to decrease the capital stock. The capital–input ratio is greater than the average period of production. At the same time the value of the future consumption output from the capital stock must exceed the value of the current capital stock by the interest that can be earned on this stock from the present until the appearance of the future consumption output. The capital–output ratio is therefore less than the average period of production.

These apparent departures from the average-period-of-production theory of capital are however only the result of an incomplete introduction of interest into the theory. If there is a positive rate of interest the services of the capital stock cannot be disregarded (as they quite properly were disregarded in the zero-interest model, in which such services are free goods and not economic goods). They must be treated as input on a par with land services and labor services. Bringing these into the model removes the excess of the value of the flow of output over the value of the flow of input, since that excess is precisely equal to the missing value of the flow of the uncounted input of capital services and thus restores the equalities of Böhm Bawerkian capital theory.

In such a model, properly corrected for a positive rate of interest, we have stocks of land, labor, and capital yielding flows of land services, labor services, and capital services. Every capital good begins to yield capital services from the moment of its creation and continues to do so until the moment of its complete disappearance into consumption. The average interval between the application of land, labor, and capital services and the emergence of the final output of consumption goods is shorter than the average period of production, in terms of the “original” factors of production (land and labor) alone, because the capital services continue to be applied later in the productive process by the stock of congealed past labor, land, and capital services. The value of the capital stock is just equal to the value of the current flow of input (or the value of the current flow of output) multiplied by the corrected average period of production, which in turn is just equal to the corrected capital–input ratio as well as to the corrected capital–output ratio (Lerner 1965).

Private capital and social investment. So far we have been following the traditional simplifying assumption that every nonhuman source of productive services is either both producible and consumable, in which case we called it capital, or is neither producible nor consumable (“original and indestructible”), in which case we called it land. But there are also sources of productive services that are producible but not consumable, such as tunnels through hard rock or land reclaimed from the sea, and there are sources that are consumable but not producible, such as fossil fuels or ore deposits, which are used up when they are used. Such phenomena do not fit into the classical average-period-of-production theory of capital. We also touched on a somewhat disturbing difference between the individual and the social aspects of capital when we noted that the individual producer is concerned with the extent to which he should own sources of productive services, while society is concerned with the extent to which it is possible and desirable to produce (or to refrain from consuming) such sources. Both of these difficulties can be settled at the same time by a clarification of the relationships between capital and investment.

For the individual it does not matter whether the sources of productive services are producible or consumable or both or neither. If he does not want to own the sources, preferring to buy the services (or rent the sources) from someone else, he needs no capital. But if he wants to own any source of productive services he needs capital funds to enable him to buy it.

For society as a whole, which cannot buy productive services (or rent their sources) from someone else, the only problem is how much to produce of producible sources and how much to consume (or refrain from consuming) of consumable sources. This is another way of saying that society is never faced with problems of acquisition or disposal of stocks of capital goods against money or credit. It can only decide on the rates at which it invests in the production of producible sources and disinvests by consuming consumable sources.

The productivity of capital and the return on investment. The theory of capital is necessary to explain why investment yields a positive return. The explanation is that a period in which input exceeds output, which is the essence of investment, increases the quantity of sources of capital services (and therefore the supply of these services also) in relation to other services. If the economy had all the capital goods that could be of any use, then investment could not increase productive capacity and would not yield any positive return. But as long as a longer average period of production (which means having a larger stock of producible and consumable sources of productive services) or a larger stock of other nonhuman sources of productive services permits a larger total output, capital is productive. The increase in total output due to the existence of a larger stock of capital (with its larger flow of productive services) constitutes the marginal productivity of capital.

The marginal productivity of capital is denied by the labor theory of value, which says that only labor produces value. But in recognizing that the total product is greater when there is more capital (or more land), the supporters of the labor theory of value in essence confess their failure to provide a tenable theory of exchange value (as distinct from postulating an ethical judgment as to how the product ought to be distributed). The marginal productivity of labor means only that a larger quantity of labor (used together with the same amount of other productive services) results in a larger product, which is true as long as labor is not a free good but is “scarce.” But a larger quantity of capital also results in a larger product, as long as capital is not a free good but is “scarce.” To say that only labor is productive and that an increase in capital merely increases the productivity of labor makes no more sense than to say that only capital (or only land) is productive and that an increase in the quantity of labor merely increases the productivity of capital (or of land). [SeeProductionandValue, labor theory of.]

It is possible for the marginal productivity of labor to fall to zero (in countries that prevent extreme poverty), because of a natural tendency for population to increase indefinitely. But it is not possible for the marginal productivity of capital to fall to zero, because there seems to be no natural tendency for capital to increase indefinitely. The preference for current, over future, consumption and the expectation that technical progress will make future consumption levels higher than present levels will stop any net investment, and there-fore any increase, in the capital stock as soon as the rate of return on investment falls below that required to offset these considerations.

The rate of return on investment measures the extent to which a sacrifice of (potential) current consumption permits future consumption to be increased by more than the current sacrifice. If the sacrifice of 100 units of consumption goods this year permits an increase of 110 units in next year’s consumption (all other future outputs remaining the same), then the rate of return is 10 per cent per annum. Consumption of the 110 units available next year can be postponed for another year. If there is no change in the general situation, this will again yield 10 per cent for a combined total of 121 units from a two-year postponement of 100 units. It is also possible to consume 10 of the 110 and to reinvest the remaining 100, which would yield 110 again the following year. Each successive year the same procedure can be repeated. In this way there can be a permanent return of 10 per cent per annum on the investment.

Investment and interest

The marginal rate of return on investment will vary inversely with the volume of investment, since at a higher rate of return (required, say, to pay interest at a higher rate on the money borrowed for the investment) fewer investments will qualify.

For the individual, perfectly competitive firm this tendency would not show itself as a downward sloping investment curve with respect to the rate of interest. A fall in the rate of interest would cause the firm to reconsider the technique it was using and to buy (or rent) more capital goods at once so as to have the greater ratio of capital (and of capital services) relative to other productive services that is appropriate at the lower interest rate. But for the economy as a whole (unless there are unemployed productive resources freely available, in which case all of the economics that deals with scarcity is irrelevant) additional capital goods can be provided only by the slow process of shifting resources from the production of consumption goods and services to the production (or preservation) of sources of productive services. This is investing.

Investing by the economy as a whole comes about through the attempts of firms to increase their capital. Suppose that increased thriftiness causes the monetary authorities to lower the rate of interest in order to prevent unemployment. The reduction of the rate of interest makes it worth while for the competitive firms to try to buy more capital. They cannot succeed in increasing the total of the capital stock owned by all of them together, since they can only buy capital goods from one another. But their attempt has the effect of raising the prices of the capital goods. This induces the manufacturers of capital goods to increase their output, drawing the needed extra resources from a reduction in the output of consumption goods. The increase in the rate of output of capital goods raises their costs of production. An equilibrium is reached at that increase in the rate of output of capital goods which makes marginal costs equal to the higher prices. This determines the increase in the rate of investment, for the economy as a whole, that goes with a reduction in the rate of interest (and conversely, of course, for a decrease in thriftiness).

If the process starts from a stationary equilibrium, with zero net investment, the rate of net investment becomes positive. As this proceeds the stock of capital goods increases, while their prices fall, and the rate of investment begins to move down again. Meanwhile, the firms can succeed in increasing the ratio of capital services to other productive services. When the stock of capital goods has increased enough to satisfy the greater thriftiness, consumption will have increased enough to absorb the whole net output of the economy once more and investment will have fallen to zero again in a new stationary equilibrium with a lower rate of interest.

Nonstationary models

To make the analysis “dynamic,” let us substitute for the implausible assumption that the future is unchanging and known the much more implausible assumption that the future is continually changing but is still known. We may then imagine that each firm, given a known time shape (i.e., the value at every future date) of all prices (including interest rates), will fix on that dynamic time shape of all planned future inputs and outputs which maximizes the present value of the firm. The time shape of net investment, instead of being constant at zero (with gross investment just enough to offset the constant depreciation and depletion of capital), will be changing over time (and will be equal to the changing difference between input and output). But in both cases this time shape will be different for different expectations. In both cases a change in expectations would make the firms want to revise their (static or dynamic) plans, beginning with an immediate adjustment of their stock of capital. In both cases there will be a determinate limit to the change in the social rate of investment, as a result of increasing costs in the capital goods industries as their rate of production increases. In both cases we see that from the social point of view changes in prices (including interest rates) are not exogenous data (as they appear to be to the perfectly competitive firm) but are part of the mechanism through which changes in the basic conditions (including expectations) work themselves out on the firms’ demand for capital goods, on the prices of these goods, and thus on their net supply, which constitutes the social investment (Stigler 1941).

Marginal productivities and efficiencies

A country, industry, or firm will be interested in both capital and investment if it is not so small as to have no significant effect on the prices at which it buys or sells or if it has internal resistances to changes in the proportion between the factors of production (so that any change is more difficult if it is done more rapidly). To deal with this difficulty we must define four concepts: the marginal productivity of investing (mpI), the marginal productivity of capital (mpK), the marginal efficiency of investing (meI), and the marginal efficiency of capital (meK).

We define mpI as the additional quantity of investment goods (i.e., capital goods or sources of productive services) that can be produced by the sacrifice of an additional unit of current consumption goods. (For consumable, but nonproducible, sources of productive services it is the additional quantity that remains as the result of sacrificing an additional unit of consumption.)

We define mpK as the additional flow of output due to the use of an additional unit of sources of productive services.

The product of these two is meI—the additional flow of future output from that addition to the stock of productive sources that results from the reduction of current consumption by one unit. The rate of investment will be in equilibrium when meI is equal to the rate of interest. This will be the case when expected additions to future output, discounted at the appropriate rates of interest, are equal in value to the unit of current consumption sacrificed. The meI is what Keynes called “the marginal efficiency of capital” (Keynes 1936).

Every firm will have a planned time shape of its future activities and, consequently, of its capital stock, in which the size of the latter will at each point in time be such as to make the marginal rate of return on owning it—the value of the marginal (flows of) output plus the expected increase in its price—equal to the expected rate of interest for the corresponding period; otherwise the firm would want to have a larger or a smaller stock of capital goods. The firm’s marginal rate of return on the capital goods it owns might therefore be called the meK. However, we have seen that the attempts by firms to change the size of their capital stocks does not directly affect the total quantities–only the prices. It is therefore better to keep mek to describe a condition where not only the rate of investment but the stock of capital in the economy is in equilibrium.

Steady growth models

One situation of equilibrium is that in which there is a constant rate of growth for the economy as a whole with no changes in the ratio between any two of its elements. The ratio of net investment to capital stock constitutes the rate of growth of capital and must therefore be equal to the rate of growth of the entire economy. The quantity of capital can then be said to be in a moving equilibrium.

Therefore meK is best defined as the mel when the quantity of capital is in equilibrium. Only then will meK and meI both be equal to the rate of interest (Lerner 1965).

A special case of the steady-growth model, which was at the center of most capital theory until the “post-Keynesian” developments in economic theory (mainly in Cambridge, England), is the stationary state, in which the absolute quantity of capital has reached equilibrium and in which the ratio of investment to the capital stock is not merely constant but zero (i.e., equal to the zero rate of growth). The actual world is seen as one of disequilibrium, in which the quantity of capital has not reached the equilibrium level, so that meK is above meI and above the rate of interest. This is why investment takes place. The rate of investment is that which brings meI into equality with the rate of interest. The continuing positive investment is, however, continually increasing the stock of capital and using up the opportunities for investment. The rate of investment asymptotically falls to zero as meK asymptotically falls to equality with both meI and the rate of interest.

A satisfactory level of employment therefore depends on the maintenance of investment sufficient to absorb all the saving that would be undertaken at such an employment level. This could be attained by any of the following factors in sufficient strength: reduction of total saving through government dissaving; encouragement of private investment through reduction of the rate of interest; an excess of capital-using, over capital-saving, inventions; investments or grants from rich countries for the development of poor countries; the destruction of capital in wars or in natural catastrophes; or some combination of such factors. [SeeEconomic growth, article onMathematical theory.]

Modern mathematical models

The foregoing is becoming an old-fashioned approach. Modern capital theory tends more to the development of mathematical models of growth that attempt to deal with many kinds of capital goods and consumption goods; with independent changes in population, given the stock of land (which in the constant-rate-of-growth models was supposed to have grown in step with capital in efficiency terms); with technical progress, both neutral (on various definitions) and biased, as between being capital saving or capital using; and with the introduction of uncertainty about the future. It is hoped by these means to arrive at growth models that will be more directly related to the actual world than are the traditional disequilibrium models that were assumed to be moving toward imaginary stationary states. If these efforts are successful, some light may be thrown on the still unsolved problems of how to bring more rapid economic growth to the poorer countries, whose apparent falling further and further behind the richer countries threatens the future of all.

Abba P. Lerner

[See alsoInterestandLand.]

BIBLIOGRAPHY

Blaug, Mark 1962 Economic Theory in Retrospect. Homewood, 111.: Irwin. → See especially Chapter 12. Also contains useful notes on the literature.

BÖhm-Bawerk, Eugen von (1884–1912) 1959 Capital and Interest. 3 vols. South Holland, 111.: Libertarian Press. → First published in German.

Dorfman, Robert 1959 Waiting and the Period of Production. Quarterly Journal of Economics 73:351–372.

Edelberg, Victor 1933 The Ricardian Theory of Profit. Economica 13:51–74.

Fisher, Irving 1907 The Rate of Interest: Its Nature, Determination and Relation to Economic Phenomena. New York: Macmillan.

Haavelmo, Trygve 1960 A Study in the Theory of Investment. Univ. of Chicago Press.

Hahn, F. H.; and Matthews, R. C. O. 1964 The Theory of Economic Growth: A Survey. Economic Journal 74:779–902. → Contains an extensive bibliography.

Hawtrey, RalphG. (1937) 1952 Capital and Employment. 2d ed. London and New York: Longmans. → See especially Chapters 2 and 3.

International Economic Association 1961 The Theory of Capital: Proceedings of a Conference Held by the International Economic Association. Edited by F. A. Lutz and D. C. Hague. New York: St. Martins.

Kaldor, Nicholas (1937) 1960 The Controversy on the Theory of Capital. Pages 153–305 in Nicholas Kaldor, Essays on Value and Distribution. Glencoe, Ill.: Free Press.

Keynes, John Maynard 1936 The General Theory of Employment, Interest and Money. London: Macmillan. → A paperback edition was published in 1965 by Harcourt.

Lerner, Abba P. 1944 The Economics of Control: Principles of Welfare Economics. New York: Macmillan. → See especially Chapters 20 and 25.

Lerner, Abba P. 1965 On Some Recent Developments in Capital Theory. American Economic Review 55, no. 2:284–295.

Ricardo, David (1817) 1962 Principles of Political Economy and Taxation. London: Dent; New York: Dutton. → A paperback edition was published in 1963 by Irwin. See especially Chapter 1, sections 2, 4, and 5.

Smith, Adam (1776) 1952 An Inquiry Into the Nature and Causes of the Wealth of Nations. Great Books of the Western World, Vol. 39. Chicago: Encyclopaedia Britannica. → See especially Book 2, Chapters 1 and 3. A two-volume paperback edition was published in 1963 by Irwin.

Stigler, George J. 1941 Production and Distribution Theories: 1870–1895. New York: Macmillan.

Wicksell, Knut (1901) 1951 Lectures on Political Economy. Volume 1: General Theory. London: Routledge. → First published in Swedish. See especially Part 2.

Wicksell, Knut (1911) 1958 Böhm-Bawerk’s Theory of Capital. Pages 176–185 in Knut Wicksell, Selected Papers on Economic Theory. London: Allen & Unwin. → First published in Ekonomisk tidskrift.

Capital

BIBLIOGRAPHY

Capital can mean many things, including a sum of money, an invested fund, a set of produced means of production, or human skills (“human capital”). In the theory of production, distribution, value, and growth, the term capital refers to capital goods or investment goods and skills. In this perspective, capital is an accumulable factor of production, as opposed to land and simple labor, which are not. The means of production encompass raw materials, tools, and instruments of production, and in the writings of some earlier authors also the means of subsistence enabling workers to perform their tasks. To the extent that natural resources, such as land, first have to be brought into a form that can be used productively, the investment in these resources and the resources themselves become amalgamated into what Karl Marx (1818–1883) referred to as “la terre-capital” (land-capital).

Capital in the sense of capital goods is typically grouped in broad categories, including the following. Circulating or working capital refers to capital goods advanced at the beginning of the period of production that contribute exclusively to the period’s output: they “disappear” from the scene at the same time as their value is transferred to the product. Fixed capital, in contrast, refers to capital goods that are long-lived and cannot be traced on a given unit of output. In their case, the idea of a material-cum-value transmigration into the product seems to lose any foundation. However, as was suggested already at the time of the classical economists and was rigorously shown by the mathematician John von Neumann (1903–1957) and the economist Piero Sraffa (1898–1983), a coherent treatment is possible using a joint-products framework: a fixed capital item that enters production at the beginning of the production period is considered a different commodity from the item that exits at its end. In this way, fixed capital can be reduced to circulating capital.

In Marx we find the distinction between constant and variable capital: the latter refers to raw materials, tools, and instruments of production and represents dead labor; the former refers to wage goods spent in employing living labor, which, according to Marx, is the sole creator of value. American economist John Bates Clark (1847–1938) distinguished between capital and capital goods, the former being a fund of value earning its owner a return, interest, which equals the marginal productivity of capital.

As these examples show, a main issue in capital theory is whether capital is “productive” in the sense that it explains the existence of profits or interest. Critical reviews of early profit theories were put forward by Marx (1905–1910) and the Austrian economist Eugen von Böhm-Bawerk (1884). These authors developed their own approaches against the background of the earlier literature. At the cost of severe simplification, the various traditions in the theory of capital and distribution may be divided into two principal groups, one rooted in the surplus approach of the classical economists, the other in the demand and supply approach of the marginalist authors. Both traditions developed their arguments essentially within a long-period general framework of the analysis centered on the concept of a uniform rate of profit (or interest) and the corresponding set of normal prices.

The classical authors explained profits in terms of the surplus product left after the means of production used up in the course of production of given outputs in the system as a whole and the means of subsistence in the support of workers had been deducted from these outputs. Given wages are thus a characteristic feature of the early classical economists’ approach. (The level of wages was then discussed in another part of the theory, typically by taking into account, for example, whether the society was “improving” or stagnant.) Production was conceived as a circular flow involving a strong degree of interconnectedness of the different industries of the economy. The rate of profits, expressed in material terms, is the ratio between the social surplus and social capital, that is, two aggregates of heterogeneous commodities. A comparison of these two vectors necessitated the development of a theory of value. The classical economists tried to tackle this problem typically by first identifying an “ultimate measure of value,” which was designed to render heterogeneous commodities homogeneous. Several authors, including David Ricardo (1772–1823) and Marx, then reached the conclusion that “labor” was the sought standard and therefore advocated some version of the labor theory of value. By means of this theory, some of these authors, in a first step, determined the rate of profits and afterward, in a second step, used their finding to determine normal competitive prices. Ladislaus von Bortkiewicz (1868–1931) aptly called this approach successivist.

Yet, as Sraffa showed, the successivist approach cannot generally be sustained: “the distribution of the surplus must be determined through the same mechanism and at the same time as are the prices of commodities” (1960, p. 6), that is, simultaneously. The classical authors did not have the instrument of simultaneous equations and the mathematics needed in order to solve them at their disposal. This helps to explain why they had recourse to the labor theory of value. This landed them, in the case of Marx, in the (in)famous problem of the “transformation” of labor values in prices of production. Commodities were produced by means of commodities and there was no way to circumnavigate simultaneous equations. Sraffa showed that a coherent formulation of the classical approach that was independent of the labor theory of value was possible: The rate of profits and competitive prices could be determined consistently in terms of the givens of the problem under consideration: (1) the system of production in use, characterized by the dominant methods of production employed to produce given gross outputs; and (2) the ruling real wage rate(s), or the share of wages.

The alternative marginalist explanation traced profits back to the productivity-enhancing effect of the use of capital goods. It consisted essentially of a generalization of the principle of intensive diminishing returns in agriculture indiscriminately to all industries and all factors of production alike. The older marginalist authors, with the exception of the French economist Léon Walras (1834–1910), were aware of the fact that in order to be consistent with the concept of a long-period equilibrium, the capital endowment of the economy could not be conceived as a set of given physical quantities of heterogeneous capital goods, but had to be expressed as a value magnitude: its commodity composition was seen to be a part and parcel of the equilibrium solution, determined by (1) preferences, (2) the technical alternatives from which cost-minimizing producers can choose, and (3) initial endowments of the economy of labor, land, and “value capital.” The formidable problem for the marginalist approach consisted in the necessity of establishing the concept of a quantity of capital, which could be expressed independently of the price of its service, or the rate of profits, and whose relative scarcity then determined that rate. If such a concept could be shown to exist, profits could be explained analogously to intensive rent on homogeneous land, and a theoretical edifice could be erected on the universal applicability of the principle of demand and supply.

Doubts as to the sustainability of this concept had already surfaced at an early time, and had prompted some authors such as Friedrich August von Hayek (1899–1992), Erik Lindahl (1891–1960), and John R. Hicks (1904–1989) in the late 1920s and early 1930s to abandon the long-period method and adopt instead temporary and intertemporal equilibrium methods (Garegnani 1976). Yet it was only during the so-called Cambridge controversies in the theory of capital in the 1960s and 1970s that the concept was conclusively shown to be untenable in general (see Garegnani 1970; Kurz and Salvadori 1995, chap. 14). The concept can only be used in exceedingly special cases, and it is ironic to see that these are precisely those cases in which the labor theory of value applies. Despite these findings, the concept is still widely employed, in much of macrotheory, for example, with its reliance on the (infamous) aggregate production function. In more recent times, temporary and intertemporal models have also come under attack (see the contributions by Pierangelo Garegnani and Bertram Schefold in Kurz [2000]).

With the process of globalization going on, there is a tendency toward an internationalization of capital and the worldwide equalization of the rate of profits. An analysis of the factors affecting this rate is an important task in contemporary accumulation and growth theory.

SEE ALSO Cambridge Capital Controversy; Equity Markets; Hedging; Liquidity Premium; Marx, Karl; Physical Capital; Psychological Capital; Social Capital

BIBLIOGRAPHY

Böhm-Bawerk, Eugen von. 1884. Kapital und Kapitalzins. Vol. 1: Geschichte und Kritik der Kapitalzins-Theorien. Innsbruck, Austria: Wagner. English translation: 1890. Capital and Interest: A Critical History of Economical Theory. Trans. William Smart. London: Macmillan.

Garegnani, Pierangelo. 1970. Heterogeneous Capital, the Production Function, and the Theory of Distribution. Review of Economic Studies 37: 291–325.

Garegnani, Pierangelo. 1976. On a Change in the Notion of Equilibrium in Recent Work on Value and Distribution. In Essays in Modern Capital Theory, eds. Murray Brown, Kazuo Sato, and Paul Zarembka, 25–45. Amsterdam: North-Holland.

Kurz, Heinz D., ed. 2000. Critical Essays on Piero Sraffa’s Legacy in Economics. Cambridge, U.K.: Cambridge University Press.

Kurz, Heinz D., and Neri Salvadori. 1995. Theory of Production: A Long-Period Analysis. Cambridge, U.K., and New York: Cambridge University Press.

Marx, Karl. 1905–1910. Theorien über den Mehrwert. Ed. by Karl Kautsky. Stuttgart, Germany: J. H. W. Dietz. English translation: 1954. Theories of Surplus Value. 3 vols. Moscow: Progress Publishers.

Sraffa, Piero. 1960. Production of Commodities by Means of Commodities: Prelude to a Critique of Economic Theory. Cambridge, U.K.: Cambridge University Press.

Heinz D. Kurz

Capital

Capital is the money or wealth needed to produce goods and services. In the most basic terms, it is money. All businesses must have capital in order to purchase assets and maintain their operations. Business capital comes in two main forms: debt and equity. Debt refers to loans and other types of credit that must be repaid in the future, usually with interest. Equity, on the other hand, generally does not involve a direct obligation to repay the funds. Instead, equity investors receive an ownership position in the company which usually takes the form of stock, and thus the term "stock equity."

The capital formation process describes the various means through which capital is transferred from people who save money to businesses that require funds. Such transfers may take place directly, meaning that a business sells its stocks or bonds directly to savers who provide the business with capital in exchange. Transfers of capital may also take place indirectly through an investment banking house or through a financial intermediary, such as a bank, mutual fund, or insurance company. In the case of an indirect transfer using an investment bank, the business sells securities to the bank, which in turn sells them to clients who wish to invest their funds. In other words, the capital simply flows through the investment bank. In the case of an indirect transfer using a financial intermediary, however, a new form of capital is actually created. The intermediary bank or mutual fund receives capital from savers and issues its own securities in exchange. Then the intermediary uses the capital to purchase stocks or bonds from businesses.

THE COST OF CAPITAL

"Capital is a necessary factor of production and, like any other factor, it has a cost," according to Eugene F. Brigham in his book Fundamentals of Financial Management. In the case of debt capital, the cost is the interest rate that the firm must pay in order to borrow funds. For equity capital, the cost is the returns that must be paid to investors in the form of dividends and capital gains. Since the amount of capital available is often limited, it is allocated among various businesses on the basis of price. "Firms with the most profitable investment opportunities are willing and able to pay the most for capital, so they tend to attract it away from inefficient firms or from those whose products are not in demand," Brigham explained. But "the federal government has agencies which help individuals or groups, as stipulated by Congress, to obtain credit on favorable terms. Among those eligible for this kind of assistance are small businesses, certain minorities, and firms willing to build plants in areas with high unemployment."

Despite these federal government programs, the cost of capital for small businesses tends to be higher than it is for large, established businesses. Given the higher risk involved, both debt and equity providers charge a higher price for their funds. "A number of researchers have observed that portfolios of small-firm stocks have earned consistently higher average returns than those of large-firm stocks; this is called the 'small-firm effect,' " Brigham wrote. "In reality, it is bad news for the small firm; what the small-firm effect means is that the capital market demands higher returns on stocks of small firms than on otherwise similar stocks of large firms. Therefore, the cost of equity capital is higher for small firms." The cost of capital for a company is "a weighted average of the returns that investors expect from the various debt and equity securities issued by the firm," according to Richard A. Brealey and Stewart C. Myers in their book Principles of Corporate Finance.

CAPITAL STRUCTURE

Since capital is expensive for small businesses, it is particularly important for small business owners to determine a target capital structure for their firms. The capital structure concerns the proportion of capital that is obtained through debt and that obtained through equity. There are tradeoffs involved: using debt capital increases the risk associated with the firm's earnings, which tends to decrease the firm's stock prices. At the same time, however, debt can lead to a higher expected rate of return, which tends to increase a firm's stock price. As Brigham explained, "The optimal capital structure is the one that strikes a balance between risk and return and thereby maximizes the price of the stock and simultaneously minimizes the cost of capital."

Capital structure decisions depend upon several factors. One is the firm's business risk—the risk pertaining to the line of business in which the company is involved. Firms in risky industries, such as high technology, have lower optimal debt levels than other firms. Another factor in determining capital structure involves a firm's tax position. Since the interest paid on debt is tax deductible, using debt tends to be more advantageous for companies that are subject to a high tax rate and are not able to shelter much of their income from taxation.

A third important factor is a firm's financial flexibility, or its ability to raise capital under less than ideal conditions. Companies that are able to maintain a strong balance sheet will generally be able to obtain funds under more reasonable terms than other companies during an economic downturn. Brigham recommended that all firms maintain a reserve borrowing capacity to protect themselves for the future. In general, companies that tend to have stable sales levels, assets that make good collateral for loans, and a high growth rate can use debt more heavily than other companies. On the other hand, companies that have conservative management, high profitability, or poor credit ratings may wish to rely on equity capital instead.

SOURCES OF CAPITAL

Debt Capital

Small businesses can obtain debt capital from a number of different sources. These sources can be broken down into two general categories, private and public sources. Private sources of debt financing include friends and relatives, banks, credit unions, consumer finance companies, commercial finance companies, trade credit, insurance companies, factor companies, and leasing companies. Public sources of debt financing include a number of loan programs provided by the state and federal governments to support small businesses.

Types of debt financing available to small businesses included private placement of bonds, convertible debentures, industrial development bonds, leveraged buyouts, and, by far the most common type of debt financing, a regular loan. Loans can be classified as long-term (with a maturity longer than one year), short-term (with a maturity shorter than two years), or a credit line (for more immediate borrowing needs). They can be endorsed by co-signers, guaranteed by the government, or secured by collateral—such as real estate, accounts receivable, inventory, savings, life insurance, stocks and bonds, or the item purchased with the loan.

When evaluating a small business for a loan, lenders like to see a two-year operating history, a stable management group, a desirable niche in the industry, a growth in market share, a strong cash flow, and an ability to obtain short-term financing from other sources as a supplement to the loan. Most lenders will require a small business owner to prepare a loan proposal or complete a loan application. The lender will then evaluate the request by considering a variety of factors. For example, the lender will examine the small business's credit rating and look for evidence of its ability to repay the loan, in the form of past earnings or income projections. The lender will also inquire into the amount of equity in the business, as well as whether management has sufficient experience and competence to run the business effectively. Finally, the lender will try to ascertain whether the small business can provide a reasonable amount of collateral to secure the loan.

Equity Capital

Equity capital can be secured from a wide variety of sources. Some possible sources of equity financing include the entrepreneur's friends and family, private investors (from the family physician to groups of local business owners to wealthy entrepreneurs known as "angels"), employees, customers and suppliers, former employees, venture capital firms, investment banking firms, insurance companies, large corporations, and government-backed Small Business Investment Corporations (SBICs).

There are two primary methods that small businesses use to obtain equity financing: the private placement of stock with investors or venture capital firms; and public stock offerings. Private placement is simpler and more common for young companies or startup firms. Although the private placement of stock still involves compliance with several federal and state securities laws, it does not require formal registration with the Securities and Exchange Commission. The main requirements for private placement of stock are that the company cannot advertise the offering and must make the transaction directly with the purchaser.

In contrast, public stock offerings entail a lengthy and expensive registration process. In fact, the costs associated with a public stock offering can account for more than 20 percent of the amount of capital raised. As a result, public stock offerings are generally a better option for mature companies than for startup firms. Nonetheless, public stock offerings may offer advantages in terms of maintaining control of a small business by spreading ownership over a diverse group of investors rather than concentrating it in the hands of a venture capital firm.

BIBLIOGRAPHY

Bierman, Harold. The Capital Structure Decision. Springer, 2002.

Brealey, Richard A., and Stewart C. Myers. Principles of Corporate Finance. 6th ed. McGraw Hill, 2002.

Brigham, Eugene F., and Joel F. Houston. Fundamentals of Financial Management. 5th ed. South-Western College Publishing, 2003.

Caselli, S. and S. Gatti. Venture Capital. Springer, 2003.

Culp, Christopher L. The Art of Risk Management. John Wiley & Sons, 2002.

Downes, John, and Jordan Elliot Goodman. Finance & Investment Handbook. Barron's Educational Series, 2003.

"Strategies for Effective Capital Structure Management: Executive Summary." Healthcare Financial Management. August 2005.

                                  Hillstrom, Northern Lights

                                   updated by Magee, ECDI

capital. Chapiter, head, or topmost member of a colonnette, column, pilaster, pier, etc., defined by distinct architectural treatment, and often ornamented. Types of capital include:Aeolic: primitive type of Ionic (see aeolic);basket: Byzantine bell-type (a), ornamented with carving resembling wicker-work or basket-weave;bell: inverted bell-like form, found in Ancient Egyptian architecture (e) and First Pointed Gothic (b) and providing the essential shape of the basket-capital and core of the Corinthian capital;block: see cushion;bud: Ancient Egyptian type (f ) in the form of a lotus-bud;Composite: see composite order;Corinthian: see corinthian order;crocket: Gothic capital (c) with stylized rolled leaves resembling small volutes;cube: see cushion;cushion, also block or cube capital: Byzantine and Romanesque (d) form, essentially a cube with its lower corners shaved off and rounded in order to accommodate the transition from square abacus to circular shaft, its four faces are reduced to semicircular lunettes;Doric: see doric order;Hathor-headed: Ancient Egyptian (e) type carved on each face with an image of the goddess Hathor and having a large block-like abacus, also carved with a variety of images;Ionic: see ionic order;lotus: Ancient Egyptian type in the form of a lotus-bud (f ) or decorated with lotus-flowers; moulded: any capital shaped with horizontal mouldings, e.g. in the Perp. style of Gothic (i); palm: Ancient Egyptian type (g) like the top of a palm-tree (palmiform), surrounded by closely arranged vertical palm-fronds and leaves, the column-shaft frequently having vertical bands or large convex reed-like forms. A variant is the Greek Corinthian capital from the Tower of the Winds, Athens (c.50 bc), with one row of acanthus-leaves and an upper row of palm-leaves under a square abacus (h);protomai: with the upper part of figures, mostly animals, projecting from the angles, usually in Romanesque work;scallop: Romanesque type (j), like the cushion, with the curved lower part further shaped with conical forms resembling trumpets (k);stiff-leaf: late-C12 and early C13 Gothic or Transitional type with stylized leaves, usually with large projections (l );Tuscan: see tuscan order; volute: usually associated with the Ionic Order, variants can also be found in Egyptian (m) and medieval work; water-leaf: late-C12 Transitional or early Gothic type with a big, wide, unribbed leaf growing outwards above the convex moulding on top of the shaft, turning upwards and inwards at the corners to the abacus(n).

CAPITAL, also capital letter. A large LETTER such as A, B, as opposed to a small letter, a, b, so named because it can appear at the ‘head’ of a text, chapter, page, paragraph, sentence, or word. The written and printed form of English has two interlocking systems of letters: large letters, known variously as capitals, upper-case letters, majuscules, and small letters, or lower-case letters, minuscules. Not all written languages have such a system; Arabic and Hebrew have only one set of letters. Lower-case letters are revisions of the forms of Latin capitals, developed in the minuscule script of the Carolingian period in France (8–9c).

Capitalization

The consistent use of capitals in Western European languages, to begin the first word of a sentence and for the first letter of a proper name (for example, John, Mr Smith, New York), began in the late Middle Ages, and was not fully systematized in English until the end of the 16c. During the 17c and 18c, common nouns and other words were often capitalized, much like (though less consistently than) the capitalizing of common nouns in present-day German. This practice is now largely restricted to abstract nouns like Liberty, Equality, Fraternity; even then the use is often ironic, truth being usually less absolute and grand than Truth. The practice of capitalizing content words in the titles of books, book chapters, articles, etc., is well established, but is not followed in all systems of reference, so that although Gone with the Wind is the dominant usage, Gone with the wind is also found. Despite the expectation that there are or should be rules for capitalization, above all for proper nouns, conventions remain unstable: should/Should the first word in a clause that follows a colon be capitalized? In BrE, the practice is generally not to capitalize in such cases, whereas AmE tends to favour a capital. Is it the Earl of Essex or the earl of Essex? There is no absolute rule, but there is a consensus in printing styles for Earl when designating an actual title.

Additional uses

(1) To identify a word more closely with a particular ethnic or other source: the Arabic language (contrast arabic numbers); the Roman alphabet (contrast roman numerals, roman type). (2) To identify a word more closely with a particular institution or highlight a particular term, usage, etc.: the State as opposed to the state; the Church as opposed to the church; Last Will and Testament as opposed to last will and testament. (3) To give prominence to such special temporal usages as days of the week, months of the year, and epochs (Monday, September, the Middle Ages), and such institutional usages as certain religious terms (God, the Mass) and trade names (Coca-Cola, Kleenex). (4) In a series of block capitals or block letters, to ensure that a handwritten word or name is clear. Serial capitals used to represent stressed speech are a largely 19c development: ‘“MISS JEMIMA!” exclaimed Miss Pinkerton, in the largest capitals’ ( W. M. Thackeray, Vanity Fair, 1847–8, ch. 1); Tweedledum, in Lewis Carroll's Through the Looking-Glass (1871, ch. 4), crying in a great fury, ‘It's new … my nice NEW RATTLE!’, where small capitals grow to full capitals, because his voice ‘rose to a perfect scream’. (5) Initial capitals are widely used to highlight or dramatize certain words: ‘The first rule of politics is Never Believe Anything Until It's Been Officially Denied’ ( Jonathan Lynn & Antony Jay, Yes Prime Minister, 1986). (6) ‘Internal’ capitals have become fashionable in recent years, especially in computing and commerce, to indicate that in a compound or blend the second element is as significant as the first, as in CorrecText, DeskMate, VisiCalc, WordPerfect. Related word- and letter-play may also occur, as in VisiOn, CoRTeXT. Such a convention allows an unlimited range of visual neologism. See ALPHABET, PUNCTUATION.