The Paretian Tradition During the Interwar Period by Pomini Mario;

Author:Pomini, Mario;
Language: eng
Format: epub
ISBN: 1707434
Publisher: Taylor & Francis Group

General dynamic equilibrium of production and the energy viewpoint of the productive process

Throughout his research, Amoroso remained a nineteenth-century economist who tried to base the scientific claims of the economic investigation on analogies with natural sciences.3 This epistemological project found its most complete expression in the interpretation, in energy terms, of the productive process contained in the text dated 1942. According to Amoroso, the similitude between mechanic and economic phenomena is complete: even in the sphere of production it is possible, keeping into account the interpretative differences which nonetheless exist, to find the principle of energy conservation at work, one of the basic principles of classical physics, in the form of the minimum means principle; with the only difference that while in nature it derives from the experimental evidence but we do not know the origin, in economics it is the intentional outcome of a rational behaviour. We can follow Amoroso’s line of reflection introducing the part on dynamic equilibrium concerning the enterprise’s behaviour and thus production.

The mathematical nature of the problem concerning the producer is totally analogous to that of the consumer, once the production is made dependent not only on the quantity of the factors used but also on their rate of variation (Lezione XIV. La dinamica dell ’impianto industriale). In this case the total revenue (T) and the total production cost (Θ) are represented by the following expressions

T = pz(x,ẋ)e−it Θ = qxe−it [5]

where p represents the price of the product, q that of the productive factor; x in turn, indicates the flow of productive investments and z the quantity of product supplied in a specific temporal interval. It is important to notice how the dynamic element of the model is constituted by the fact that the total revenues do not depend only on the intensity of the investment but also on its variation (ẋ), exactly as in the case of the dynamic choice of the consumer. The entrepreneur’s aim is to maximize the accumulation of profits within the interval t0 ≤ t ≤ t1,

[6]

In this regard, Amoroso observes,

With this hypothesis we can admit that the producer inspires his action to the principle of maximun return , which thus appears formally analogous to the principle of minimum action. With this fundamental difference: the principle of minimum action represents a law of nature, while the principle of maximum return, expression of the general economic principle of minimum means, represents a principle of conduct.

(Amoroso 1942: 150)

The application of Eulero’s equation leads to the following relation (called by Amoroso, Langrange’s production equation),

[7]

This equation constitutes a reformulation from a dynamic viewpoint of the condition of optimum static determined by the equality of the marginal revenue, which now depends also on the variation rate of the factor, with the marginal cost. Besides the stationary case, there is a new term, to which Amoroso offers the following interpretation:

[…] if the regime is not stationary, the maximum return is conditioned by the forming of a gap between value and marginal cost of production. This

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