Function of production

In Microéconomie, a function of production expresses the relation between entering of a Entreprise and its Production. It indicates, in the form of equation or of graph, which the firm can produce starting from various quantities and combinations of entering. In particular, it indicates the possible maximum production per unit of time starting from any combination of Factors of production, being given the equipment of factors and the state of technology available. One can build functions of production different for each technology from production.

One can also define a function of production like the specification of the minimum of entering necessary to manufacture a given quantity of production, being given technology available.

The relation expressed by the function of production is not-monetarist, i.e. the function binds a production in volume to entering in volume, without taking account of the prices and the costs.

The concept of function of production was invented by the British economist Philip Wicksteed in 1894.

Technological constraints of the combinations of factors of production

There exist three principal constraints in microeconomy.

1st constraint: it is considered that the factors of production (Work, Capital and raw materials) are perfectly divisible
2nd constraint: it is considered that the factors of production are perfectly substitutable.
3rd Constraint: it is considered that the means of production are measurable and homogeneous.

A function of production is valid only for one date given in a given state of technique. In other words, technological advance modifies the functions of production. The economists call “Clay clay” the functions of production where the factors of production are used in proportion fixed or complementary. In the same way, “Putty Putty” indicate the always substitutable functions of production with factor.

Form mathematical

In a general way, a function of production is expressed in the form:

Q = F (X_1, X_2,…, X_n) \,

where Q is the produced quantity and

X_1, X_2,…, X_n

are the factors of production.

A function of additive production takes the form: $Q = C + a_1.X_1 + a_2.X_2 +… + a_n. X_n \,$ where $C, a_1, a_2,…, a_n$ are constants determined by technology.

A Fonction Cobb-Douglas takes the form: $Q = c.X_1^ {a_1}. X_2^ {a_2} ..... X_n^ {a_n} \,$ .

A function of Leontieff takes the form: $Q = min (X_1* {a_1}, X_2* {a_2} ..... X_n* {a_n}) \,$ . The factors of production are complementary.

Often, one uses only two factors of production: the work, noted L, and the Capital , noted K. Thus, a function theDouglas one takes the form: $Q = c.K^ {\ alpha}. L^ {\ beta} \,$ .

The Rendements of scale constitute an essential property of a function of production.

Short period and Long period

The short period is one sufficiently short period so that certain factors of production cannot be modified (and, increased in particular). It is generally considered that the factor Capital (K) is fixed and the factor Travail (L) is variable in short period. Contrary, the long period defines a situation in which all the factors are variable.

Law of the decreasing outputs

When one increases a variable factor by maintaining the other factors fixed beyond a threshold, the physical marginal product becomes decreasing. This law does not exclude the existence from a first phase where the outputs would be increasing. Also, this law functions only if ONE factor is variable. Indeed, when the variable factor increases, there is less and less fixed factor available per variable unit of factor, and the use of the fixed factor becomes increasingly intensive. Let us take the example of a field with fixed size (K) and farmers of variable number (L) and growing. If one unceasingly increases the number of farmer without increasing the size of the field, it will arrive one moment when the farmers “will walk themselves above” and will not be used any more for nothing (their output will fall), if is not to be destroyed their workspace.

the intensity of use of the factor fixes (IUFT) = quantity of variable factors/quantity of fixed factors

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