The Austrian approach: Bohm-Bawerk and Wicksell

The mistake of a measurement of capital as an amount of value in the specification of production methods is avoided in the “Austrian” approach of Bohm-Bawerk and Wicksell, a development of the analyses of Thunen and Jevons; but the total demand and supply of capital are still measured in value; and the negative interest elasticity of the demand for capital is obtained through the very restrictive assumptions justifying the average period of production.

Jevons supplies intuitions, more than a developed supply-and-demand theory, to sub­sequent authors. He argues that capital is a subsistence fund, an advancement of wages that permits a delay between work and enjoyment of the results, allowing for the produc­tion of useful capital goods first; the longer the average time for which the same total amount of labour is advanced, the greater the product (but less and less so), with the rate of interest reflecting the marginal increase. His conception of vertically integrated production processes as starting with unassisted labour will be called “Austrian” because it was adopted by Austrian authors, but in fact it is already in Smith. For the case of a given input of labour yielding some time later an output q of a consumption good that increases at a decreasing rate with the length of the intervening (or average) delay T, Jevons argues that the rate of interest must equal q'(T)lq. However, these intuitions are not developed into a complete theory; neither the supply side nor the demand side of the market that should determine the rate of interest are well specified.

Bohm-Bawerk (1891), like Jevons, assumes an “Austrian” structure of production, and adopts the conception of capital as a subsistence fund as well as the idea that labour productivity increases, but less and less, with a lengthening of the average delay between labour and final product, a lengthening that, for a given real wage and a given labour force, requires an increase of the subsistence fund.

His verbal exposition is formalized by Wicksell (1893), who makes it clear that the average period of production allows the determination of the normal price of commodi­ties and of a decreasing demand curve for capital if (1) capital goods are only circulating capital, (2) land is free (or always has exactly the same average period as labour), and (3) simple instead of compound interest is assumed (in Bohm-Bawerk this assumption is implicit in his numerical examples). A synthetic presentation of his model is in Garegnani (1990: 27). Wicksell shows that with simple interest at rate r the price (in terms of a rep­resentative basket of consumption goods) of a good produced by one unit of total direct and indirect labour advanced for an average period T is w + rwT, where w is the real wage, and the value of the capital employed in the vertically integrated sector producing that good as net product is wT. If r increases, the goods produced by processes with a greater T become relatively dearer; technical and consumer substitution then imply that as the rate of interest increases and the real wage decreases, the economy-wide weighted average of the T^,s of the several vertically integrated industries producing final goods, call it T*, decreases, and thus one obtains an even greater decrease of wT*. Letting A represent the total and fully employed labour supply, the value of the stationary net product if produced with the desired average periods is wA + rwAT*, hence wAT* is the demand for capital, a decreasing function of r, which if combined with a given supply of capital will allow a supply-and-demand determination of the rate of interest. Wicksell formalizes this last step by writing K = wAT*, where the value of capital K is a given number, with respect to which he writes that, in the process of achieving equilibrium, though “the forms of capital change, its total value remains unchanged, since, in place of the consumed capital goods, new ones of equivalent value enter successively” (1893: 103).

However, can one treat the subsistence fund as unchanged when income distribution changes? Following Garegnani (1960: 164-75), let us consider a stationary economy producing a single consumption good as net product, initially in equilibrium with full employment of labour and a value of capital equal to wAT*. Now w increases to w', with - let us assume - no change in quantities produced nor production methods. The result is a revaluation of the capital goods in existence as prices adapt to the new normal prices; the value of capital rises to w'AT*. There has been an increase of the subsistence fund owing only to the change in income distribution, without any net savings in any acceptable sense: the economy as a whole continues to consume as much as before. Every period the flow of wage advances has risen to w’A but this does not require the com­munity as a whole to have performed net savings; it is only another face of the income redistribution from interest to wages. Thus when income distribution is what must be determined, there is no right to treat the value of capital as given: any change in income distribution will alter it, showing that the value of capital reflects income distribution rather than being one of its determinants. This is a general conclusion, also valid with compound interest and with wages paid in arrears: the normal value of capital changes with changes in income distribution, even if physically nothing changes. To this basic problem can be added the short-period deviations of the values of existing capital goods from their normal values any time there is technical change or changes of demand.

Wicksell does not seem to be conscious of this problem in 1893, but he soon grows dissatisfied with the other limitations of the theory, and the attempt to surmount them makes him eventually realize the problem with the value endowment of capital too. In the Lectures (1934; first Swedish edition, 1900) he admits compound interest, drops the period of production, and adopts a representation of the production conditions of con­sumption goods via differentiable production functions with dated quantities of labour and of land as inputs, as if firms were vertically integrated (again Garegnani 1990: 29-31 offers a synthetic presentation of the model). Wicksell’s preference for this representa­tion (that requires “Austrian” production processes) derives from his continued belief that the key to the explanation of the rate of interest lies in the increase in production obtained by increasing the delay between use of “original” factors and final output; but now he admits problems. On the demand side, he notes that the rate of interest is gener­ally not equal to the marginal product of capital, because of the revaluation of capital goods due to the change in income distribution associated with the employment of one more unit of capital; this revaluation, afterwards named “price Wicksell effect”, makes him unsure whether a lower rate of interest will always cause a greater demand for value capital; at one point (Wicksell 1934: 183) he writes that the issue should be further studied (reverse capital deepening - see below - will show he was right to have doubts). For the same reason he admits problems on the supply side: after treating capital as a quantity of value in earlier chapters, when he must “close” the complete model of general equilibrium with the equality between supply and demand for capital, Wicksell cannot hide doubts on the legitimacy of taking the value of the capital endowment as given; he writes “it would clearly be meaningless - if not altogether inconceivable - to maintain that the amount of capital is already fixed before equilibrium between production and consumption has been achieved”, because any change of relative prices during the ten­dency toward equilibrium would change the value of capital goods, with a consequent “indeterminateness” of the endowment of capital (1934: 202); still, although hesitatingly (he does not write down the equation), he finally takes the total value of capital as given (1934: 204). He has grown dissatisfied with a value endowment of capital but is unable to find an alternative.