Towards a More General Theory of Capital

This paper starts from the fact that a decision to invest in a new industrial project is a decision to invest in a flow of inputs over time in such a way as to produce a flow of outputs over time. The essential information is the quantity and value of each type of input invested, and the quantity and value of each type of output produced, at each date in the project. With this information it is possible to abstract and define the technique of production~jas the shapes of the flows of inputs and outputs over time. Further, it is possible to organise the information about alternative projects by defining a production function as the relationship between total output produced from a project, total inputs invested in a project, and the shapes of the input and output flows. (Output depends upon inputs and the technique of production.) The next step is to quantify the idea of the shapes of the input and output flows. The simplification which the Austrian theorists adopted was to assert that only the mean dates when input was invested, and output was produced, mattered, i.e. they measured the shapes by their mean dates. Actually they took the simplification a stage further and, defining the period of production as the difference between the mean date of output and the mean date of input, they asserted that it was only variations in output arising from variations in the period of production that were important. This approach leads to the more general device of treating the shapes as statistical frequency distributions, with time as variate and frequency at any date as the ratio of input invested (or output produced) at that date to total input invested (or total output produced) over the life of the process. Frequency distributions can be defined by the familiar measures of the characteristics of such shapes: the mean date measures the central tendency; the variance measures the dispersion about the mean, etc. In general, the set of such measures, known as cumulants, is needed to define a frequency distribution.2 With this device it is possible to present the Austrian theory in a more general form which avoids the difficulties encountered in the use of the mean dates alone (or the

Capital (architecture) · Econometrics · Economics · Function (biology) · Input/output · Mathematical economics · Microeconomics · Operations research · Production (economics) · Production function · Production theory · Statistics · Value (mathematics) · Capital Investment and Risk Analysis · Computer Science · Mathematics