Outputs of scale

The outputs of scale are an indicator of the Variation of the Production of a Entreprise compared to the variation of its Factors of production.

The economies of scale are the same indicator, but evaluated in monetary unit (with the Prix of the production and the factors of production) and not physical units (kg of metal, m ² of fabric, many parts, etc). The change of unit is without incidence on the analysis, and the two expressions are frequently used one for the other.

Types of outputs

The economic analysis is interested in the output because it determines the optimum quantity treated by an industry, and thus the size of the firms on a market. The technical requirements are of course the determining main thing of the outputs, and technological advance makes move the things.

• the outputs are increasing when the production varies in a way more important than the variation of the factors of production used. The production of an additional unit is accompanied then by a fall of the unit costs, and the same quantity of factors makes it possible to produce more. One speaks in this case there about economy of scale .

• the outputs are constant when the production varies in the same proportion as that of the factors of production used. The cost remains him also constant.
• the outputs are decreasing when the production varies in a way less important than the variation of the factors of production used. This means that the marginal cost is increasing (the more one produces and the more expensive it is to produce an additional unit) or that one needs more factors to produce a unit. When the outputs become negative, one speaks about wasting of scale or deseconomy of scale .

Formal definition

A Fonction of production $F\; (K,\; L)\; \backslash ,$ has constant outputs of scale if $F\; (aK,\; Al)\; =aF\; (K,\; L)\; \backslash ,$, increasing outputs of scale if $F\; (aK,\; Al)\; >aF\; (K,\; L),\; \backslash ,$ and outputs decreasing if

For example, a function of production of the type Cobb-Douglas has constant returns: the function is form $F\; (K,\; L)\; =AK^\; \{\backslash \; alpha\}\; L^\; \{1\; \backslash \; alpha\}\; \backslash ,$, where $A\; >\; 0\; \backslash ,$ and . Consequently, $F\; (aK,\; Al)\; =A\; (aK)\; ^\; \{\backslash \; alpha\}\; (Al)\; ^\; \{1\; \backslash \; alpha\}\; =Aa^\; \{\backslash \; alpha\}\; a^\; \{1\; \backslash \; alpha\}\; K^\; \{\backslash \; alpha\}\; L^\; \{1\; \backslash \; alpha\}\; =aAK^\; \{\backslash \; alpha\}\; L^\; \{1\; \backslash \; alpha\}\; =aF\; (K,\; L)\; \backslash ,$.

Economies of scale

In practice, the outputs are generally increasing for minor amounts, to become constant, then decreasing for very great quantities. There exists a optimal size then for the company, which makes it possible to maximize the outputs.

Almost all the activities require initial investments (research, training, tools, storage capacity, notoriety, etc), which should be made independently of the produced quantity. It is necessary to amortize these investment on the produced quantities, and as long as they will not be saturated, a unit more will be less expensive than the first: for this reason the outputs are initially increasing.

When one approaches the saturation of production capacities, the things become more complicated. Difficulties which did not exist yet starts to arise: difficult clocking, waste of time which becomes unbearable, waste which starts to become awkward and which it is now necessary to extract and treat, intermediate storage which becomes necessary whereas he was not it at the beginning, factors of production which become less available and which it is necessary to replace by others (more expensive or less productive, since one useful firstly the best factors), problem of internal circulation, transport, etc

These problems increase the quantity (and the quality) of the factors of production, and starts to weigh on the growth of the output with the quantities. According to the cases, they will do nothing but reduce the rise of the output (which will continue of which to increase, but less quickly), or they will end up carrying it and lowering the output more and more (general case, in practice, since there is physically always a limit with the quantity of matter which can be worked in a place and a period of time given).

Visible price differences exist between the small series (engine of rocket, prototype) and the great series such as the current consumer goods. The price of material can be appreciably equal, but the labor which holds a very important place in the productions with small series can be replaced by a robotization for the large ones. However nothing prevents in the principle a factory robotized to work 24:00 per day and 365j per annum.

The mass production makes it possible to introduce a thorough automation and a statistical quality control of manner. N the other hand, if it becomes possible to manufacture a car every 8 seconds, they should be sold with the same rate/rhythm what will raise difficulties of another nature.

The economies of scale are one of the three basic principles of the urban economy with the Externalité S and the costs of transport

See too

• Law of the decreasing outputs
• Effect of network
• Taylorism
• savings in scale

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