Features of the Production and Use of Capital

Features of capital and its production are as follows:

  • Capital – unlike bread, clothes, and entertainment – is not consumed by people; it is used to produce products other than itself.
  • Capital often takes a long time to be produced and installed, though such a statement is merely descriptive of some capital. It is not a precise defining, explanatory element of all capital.
  • Prescinding for the moment from critically important human capital developed by training and work and study, a unit of material capital is often a unit of material and controls, but it is to be understood in macroeconomic dynamics as a double summation of a.) rates of application of factors of production over b.) a series of units of enterprise in a series of activities from origination through all transformations to the completed unit.
  • This is formulated generally as

qi = ΣΣqijk

The left-hand side is an individual product qi; the right-hand side is a double-summation of activities (k), such as labor, management, land, use of capital through a series of units of enterprise (j). The units of measure on each of the sides of the equals sign are not common. But we will find a common unit of measure when we apply prices and can speak in terms of dollars or pesos.

  • Since the subscript k represents rates of application of factors of production by compensated human beings, k represents, also, a rate of compensation, i.e. a rate of money outlays, i.e. a functional flow of money.
  • Since the economic process is always the current, dynamic productive process, and since we are at all times dealing with the process as a process of interdependent rates and accelerations, it is necessary to understand the whole capital production process as a set of rates of application of factors, terminating in the sale of integral units of a composite capital good or service, capital products are finally emergent (are sold) at a rate of emergence (sale).
  • Capital is used; it deteriorates, it depreciates, its parts wear out, it breaks down (and may even become obsolete);

Again, in correspondence with each advance of practical intelligence, there is a technological obsolescence of capital equipment. The old shops still have their shelves and counters; the old machines may suffer no material or mechanical defect. But the new models produce better goods more efficiently; and trade now walks on different streets. [CWL 3, 208/233]

it must be maintained, repaired, sometimes upgraded, and sometimes written off and sent to the scrap heap.

  • Financially, a new unit of capital requires a.) the initial progress payments constituting investment, followed by b.) ongoing annual payments for repair and maintenance, and c.) subsequent ongoing payrolls to people sufficient to maintain satisfactory demand for the fruits of the new unit of capital. Henry Ford must pay his workers enough to purchase the cars they are producing.
  • An additional unit of capital produced at time t-a serves to increase or accelerate production flows per period in the next lower stage at the later times t, t+1, … This is formulated generally as the lagged technical accelerator, with which the reader should be familiar.  kn[f’n(t-a)-Bn] = f”n-1(t) – An-1 [1]
  • Because a unit of capital is completed and installed to be used over an indefinite series of intervals. It is defined with respect to the current time as a set of component velocitous factors in a correspondence of current-determinate-point-to-indeterminate-future-series[2] with factors in the elements of the standard of living. The correspondence is point-to-line, or point-to-surface, or point-to-volume, etc
  • In other words, the unit of capital’s nature, understood in the form of a point-to-line geometric correspondence is a correspondence of its component functional velocities to the functional velocities of components emergent by sale into the standard of living. This correspondence is point-to-point.
  • This is in contrast to the current-determinate-point-to-current-determinate-point correspondence of the factors of basic production to basic composites emergent by sale into the standard of living.
  • Again, this point-to-line correspondence in the form of a geometric projection with respect to time constitutes the unit of capital’s current abstract functional nature. We regard the unit as having a geometric correspondence of point to series over time. It is “one step removed” and distinct from basic production’s correspondence of point-to-point.
  • Current-determinate-point-to-current-determinate-point and current-determinate-point-to-indeterminate-future-series implicitly define one another in a pure dichotomy. The terms are purely relational.
  • Because of an indeterminacy with respect to duration and efficiency, the future usage and productivity of new equipment can only be estimated by the risk-assuming entrepreneur. With respect to financial self-justification, the unit of capital is a unit of long-term financial uncertainty or risk.
  • There are limits or normative constraints to capital expansion. In, for example, a von Neumann model regarded as a matrix game,[3] the growth factor (generalized eigenvalue) obtained from the game-theoretic solution of the matrix of technical coefficients of available input components and the matrix of estimated technical coefficients of outputs shows us that there are normative limits for the quantity of new and/or more efficient capital to be installed. In a given state of cultural, institutional, and technical development, the technical coefficients of the materials and the human resources at any point in time yield a normative quantity of capital which should be installed.
  • But it is possible to overproduce capital items and, thus, exceed the normative limits of efficient and productive use. Conversely, it is possible to underproduce and fail to realize the full potential of existing resources.
  • The economic process has classical laws relating functions to one another and statistical laws stating the probabilities of events.
  • There is a current indeterminacy about the future events at the then-current point of installation of equipment. After capital has passed from being under production in the current process into use as an installed factor of production, it will be used in each subsequent interval at a determinate then-current rate of so many units of usage per interval of time. Still, that rate of future use can not be known at the current point of installation. It can only be estimated. One can not have it both ways and argue in a circle. One cannot second-guess and criticize current prudent choices on the basis of a later 20/20 hindsight. Current prospective indeterminacy is not cancelled by retrospective determinacy. And a future retrospective determinacy does not cancel an earlier current indeterminacy. Prospective indeterminacy is prospective indeterminacy.
  • The actual quantity of new capital produced and its ongoing rate of use is typically decided upon by the risk-taking entrepreneur who is committed to paying back the money he borrowed (from himself or others) to purchase the capital. In addition to being legally committed, in all likelihood he is emotionally hopeful, optimistic, and determined. His optimism supplies the motive power of the process. But there is risk; his investment may come a cropper.



[1] CWL 15, p. 37

[2] or current-point-to-indeterminate-future-surface, or higher correspondence

[3] See Peter Burley section