Modernization of Bohm-Bawerkian Concepts
The best way to find out whether today the three causes are sufficient to generate a positive real rate of interest is to use very Bohm-Bawerkian analytical tools: the “modernized” period of production and an analogous “waiting period”.
Both are defined in terms of present values.We may look at the price pi of consumption good i in a competitive economy with a given nominal wage rate w and a given rate of interest r; thus pi = f(w; r). It then can be shown that 0f = Tifi (w; r) where Ti is the “modernized” Bohm-Bawerkian period or production as applied to consumption good i. Thus the percentage increase of the price of consumption good i, as the rate of interest rises one percentage point, equals the period of production of the labour inputs which directly and indirectly (via intermediate products) enter into the production of that good. This is a quite general result which does include models with fixed and circulating capital and as many capital goods and consumption goods as you like. It has a forerunner in Hicks’s Value and Capital, chapter XVII.
The result has consequences which very much vindicate Bohm-Bawerk’s idea of measuring capital intensity and roundaboutness by means of the average period of production. The first observation is that as the rate of interest rises techniques with a higher period of production induce a faster price rise than techniques with a lower period of production. Thus there is a tendency to switch to techniques with lower periods of production as the rate of interest rises. This can be called the substitution theorem of capital theory. The second observation is marginal productivity. Bohm-Bawerk claimed that at the equilibrium period of production the percentage increment in productivity resulting from a lengthening of the period of production by a (small) time unit will be equal to the equilibrium rate of interest.
Indeed, as the period of production rises by one unit the cost of the product directly and indirectly produced by one hour of labour rises by r in percentage terms. But since the period of production at the prevailing interest rate has been selected so as to minimize unit costs this must mean that the labour productivity in the production of good i must have risen by exactly the same percentage, which is r. Hence the private and social marginal productivity of roundaboutness is reflected in the rate of interest, as Bohm-Bawerk said. But we must remember that in comparison to Bohm-Bawerk the period of production is somewhat “modernized”.The third vindication of Bohm-Bawerk is the fact that the aggregate period of production serves as a good aggregate measure of roundaboutness and capital intensity. For this we observe that - beyond Bohm-Bawerk - we can define a parallel concept on the side of private households. It is the waiting period. Any given rate of interest p used to compute the present values induces a particular system of weights by which the weighted labour inputs along the time axis and the weighted consumption good outputs are used to find the period of production and the waiting period of consumers/savers. The waiting period is the average time distance between wage income and consumption good expenditures. For a steady-state economy growing at a constant rate of growth g it can then be shown that a general equilibrium of that economy exhibits an endogenously determined equilibrium real rate of interest r with the following property: there exists a notional rate of interest p which lies between g and r such that with present value weights induced by p the period of production T and the waiting period Z are equal. We may then speak of T as an aggregate measure of the demand for capital and speak of Z as an aggregate measure of the supply of capital. Thus, for a steady-state economy, these modernized Bohm-Bawerkian concepts serve as a useful aggregation device for millions of different capital goods.
On these three results, see von Weizsacker (1971: pt IV). They are also quite useful for actual policy issues such as, for example, public debt. We should by no means discard Bohm-Bawerk’s important contributions to economic theory.
Carl Christian von Weizsacker
See also:
Capital theory (III); John Bates Clark (I); German and Austrian schools (II); Income distribution (III); Karl Heinrich Marx (I); Carl Menger (I); Joseph Alois Schumpeter (I); Knut Wicksell (I); Friedrich von Wieser (I).