In economics many ideas of improvement through qualitative change have been advanced, but none has been translated into a successful formal model. There are two such excellent examples: Bohm-Bawerk's theory of roundabout production, and Adam Smith's theory of labour division.
Bohm-Bawerk, in his "Kapital und Kapitalzins" from 1900, discusses how step by step the production process becomes more and more roundabout, but pays off in terms of an increased productivity which more than compensates for the time spent on capital formation:
"A farmer needs and wants water for drinking. The spring bubbles at some distance from his house. In order to satisfy his need for water he can choose different ways. Either, he goes each time to the spring and drinks from his hollowed hand...
Or... the farmer makes a jug from a block of wood and carries in it his daily use at once from the spring to his living place... but in order to achieve this it would have been necessary to make a not insignificant detour: the man might have to carve on this jug a whole day, he should, in order to be able to carve it..., fell a free ... even before that produce an axe, and so on ...Finally ... in stead of one tree he could fell many, hollow them all in the centre, build a pipe from them, and bring an abundant stream of water to his house. Obviously roundaboutness is now even more considerable. As a compensation it leads to a much enhanced achievement."
Likewise Adam Smith in his "Wealth of Nations" from 1776 speaks almost lyrically of the productivity increases resulting from specialization of labour. His famous example is that of specialized pin-making, where both organisation and training, combined with specialization in accordance with natural talent, result in improved productivity:
"One man draws out the wire, another straightens it, a third cuts it, a fourth points it, a fifth grinds it at the top for receiving the head; to make the head requires two or three distinct operations; to put it on, is a peculiar business, to whiten the pins is another; it is even a trade by itself to put them into paper; and the important business of making a pin is, in this manner, divided into about eighteen distinct operations...
Each person, therefore, ... might be considered as making four thousand eight hundred pins a day. But if they had all wrought separately and independently and without any of them having been educated to this peculiar business, they certainly could not each of them have made twenty, perhaps not one pin in a day."
It is interesting to consider how economists would nowadays model the benefits of roundaboutness or specialization. Roundaboutness would be introduced as an increase of some homogeneous input of capital in the production function, a proxy for the quantity of jugs and pipes, whereas division of labour would just be represented by a multiplicative productivity constant, multiplied either into the quantity of some again homogeneous labour input, or else just into output.
This practice must be regarded as very crude, doing no justice at all to the original ideas. It is obvious that not much of the phenomena discussed by Bohm-Bawerk and Smith are caught this way.
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