User:Paul Schächterle/Notebook/LDR

Law of diminishing returns (Raw draft)

The law of diminishing returns (LDR) is a concept in economic theory. It states that the output per input (productivity) declines if the input of a production factor is increased over a certain limit. Under the name law of diminishing returns actually exist two different concepts: one classical and one neoclassical. These concepts bear similarities but are based on different reasons.

The classical concept

In classical economics the LDR states the following: If you have at least two different production factors, the highest productivity is gained if an optimal proportion between these factors is kept. Any divergence from that proportion will result in lower productivity.

If one production factor is fixed, the proportion between the production factors will change with rising production i.e. rising input of the variable factor. According to the classical LDR this leads to a production function that has four phases with the following characteristics:

1. Rising marginal productivity, rising average productivity.
2. Diminishing marginal productivity, rising average productivity.
3. Diminishing average productivity.
4. Negative marginal productivity, i.e. an increase of the variable factor will result in a decrease of the overall product.

(Graph)

History

Historically the concept was developed independently by J. Turgot and J. v. Thünen. It was mainly related to agricultural production and the use of fertilizer in relation to a fixed amount of soil.

(Ref. to Turgot and Thünen?)

Turgot, Observations sur le mémoire de M. de Saint-Péravy en faveur de l’impôt indirect, 1768

« Les dépenses de la culture consistent à donner aux terres les préparations les plus propres à les rendre fécondes. Or il s’en faut de beaucoup que le succès de ces préparations, dont dépend la production, soit proportionné à la dépense. […] La production suppose des avances ; mais des avances égales dans des terres d’inégale fécondité donnent des productions très différentes, et c’en est assez pour faire sentir que les productions ne peuvent être proportionnelles aux avances ; elles ne le sont même pas, placées dans le même terrain, et l’on ne peut jamais supposer que des avances doubles donnent un produit double. La terre a certainement une fécondité bornée, et en la supposant labourée, fumée, marnée, fossoyée, arrosée, sarclée autant qu’elle peut l’être, il est évident que toute dépense ultérieure serait nuisible. Dans ce cas, les avances seraient augmentées sans que le produit le fût. […] En accordant à l’auteur du Mémoire que, dans l’état de la bonne culture ordinaire, les avances rapportent 250 p. 100, il est plus que probable qu’en augmentant par degré les avances, depuis ce point où elles rapportent 250 p. 100 jusqu’à celui où elles ne rapporteraient rien, chaque augmentation serait de moins en moins fructueuse. […] La semence, jetée sur une terre naturellement fertile, mais sans aucune préparation, serait une avance presque entièrement perdue. Si on y joint un seul labour, le produit sera plus fort ; un second, un troisième labour pourront peut-être, non pas doubler et tripler, mais quadrupler et décupler le produit qui augmentera ainsi dans une proportion beaucoup plus grande que les avances n’accroissent, et cela, jusqu’à un certain point où le produit sera le plus grand possible, comparé aux avances. Passé ce point, si on augmente encore les avances, les produits augmenteront encore, mais moins, et toujours de moins en moins jusqu’à ce que, la fécondité de la nature étant épuisée et l’art n’y pouvant rien ajouter, un surcroît d’avances n’ajouterait absolument rien au produit. »

Critique

A production factor is only fixed if it is indivisible or if it is limited. Therefore it is generally possible to produce with an optimal proportion of factors and to use any available excess portion of one factor in a different area. Thus the classical LDR is closer related to business studies than to economics or political economy.

(Ref?)

The neoclassical concept

In neoclassical economics the LDR signifies that an increasing input of any production factor will result in diminishing marginal productivity. This leads to a production function with the following characteristics:

• Zero input of a production factor results in zero output i.e. the graph starts at the origin.
• Marginal productivity is highest at the first unit of output.
• Marginal productivity decreases continuously.

(Graph)

History

The origins of the neoclassical production function i.e. the neoclassical LDR date back to the time of classical economics. Then the concept was used to describe the effect of an increase in wheat production where good soils were limited. To increase the production of wheat inferior soils would have to be used, which would deliver less wheat for the same amount of labour.

(Ref. to Ricardo, Malthus?)

Neoclassical economists extended the idea to the claim that any economically rational producer would use any production factor first for the most productive task, then for the next productive task, etc., and/or would use the best unit first, then the second, etc. (Ref. to whom?) Thus the idea is applied to all production factors. (Necessary assumption: there must exist different applications with different productivities for the units of one factor). <F/H, S. 55, Fn. 4>

3-D Representation

In modern neoclassical theory two factors of production are assumed: capital and labour. With two factors of production the production function can be represented by a 3-dimensional graph.

(Graph)

Image: Cobb-Douglas production function with 2 factors and production elasticity complying to the neoclassical LDR, i.e. decreasing returns to scale.

Y = A × C^α × L^β; α, β < 1

Possibly link to: [1]

Implications

The neoclassical LDR is one cornerstone of the General Equilibrium Theory.

Critique

Necessary assumptions:

• either diminishing quality of the factor (classical argument/wheat production)
• or different fields of application with different productivity (see above).

(Ref ?)

Contrary to economies of scale. (Ref ?)

Contrary to survey among producers (Ref: Eiteman/Guthrie 1952)