# Theory of production

Production function – A general description of the interaction between the factors of production and the product produced. Total record:

Q = f (K, L, n)
Q – the volume of production, the maximum possible
K – the used capital resource
L – the labor process used
n – other factors such as: land, raw materials, return on scale, management resources, etc. unidentifiable factors.

Features of the production function:

It is a technical description of the cost-production relationship
The goal is maximum production volume
Reflects only efficient production methods (X-inefficiency)
Different combinations of the two (or more) resources are possible
In a very long period, changes in all factors are possible, incl. and in technology
The production function is usually seen as a product function, but companies produce a wide range of goods
Labor intensive and labor saving production
Capital intensive and capital saving production. Reference: Product Life Cycle, definition of product life cycle, Reference
Time periods

Very short period – this is a period in which all factors are fixed
Short – a fixed factor
Long – a period of time in which all factors can be changed.
Very long – the fundamental principles in technical and technological terms are changing.
Product features:

Total product – from a given factor (TP) is the total volume of production that the company produces over a period of time. It characterizes its overall performance
Average product of a given factor – Apt = TP / F This is the product that creates a unit of factor used expresses the average duration of the company over a period of time is measured by the ratio of total product and units of factor used
Marginal product of the MPf factor – the additional product that is created using each subsequent unit of factor added to production. It illustrates the additional or marginal performance of the factor. It is measured by the ratio between the growth of the total product and the growth of the factor that gave rise to it – MPf = lTP / lF
The graphic illustration of the total product expresses the effect of the law of diminishing returns, it is manifested from where the graph from the concave joint protrudes to the axis Oy. In the graphic illustrations of the middle and marginal product, the law begins to operate from where they begin to decrease. When the function of the total product reaches a maximum, the marginal product is 0, the marginal product may be negative if the next unit of factor used in production leads to a reduction in its total volume.

Long-term production:

Izoquant lines – graphic illustrations of the same volume of production obtained from the use of 2 production factors – capital and labor. One isoquant line creates the same common product in the simultaneous use of labor and capital.
The isoquant lines are negatively inclined because in order to maintain the same volume of production, if the producer increases one factor, he necessarily decreases the other. The slope is called the marginal rate of technical substitution (MRTS) and shows the substitutability in production between labor and capital MRTS = MPl / MPk

The isoquant lines in their totality form a map of the isoquants, it is the menu for selection before the entrepreneur, who in a long period has to choose with how much capital and labor to produce a corresponding volume of production. Isoquant lines do not intersect as long as the basic technological principles are preserved and the same volume of production cannot be produced with a constant number of units from one factor and changing units from the other. The farther from the origin of a coordinate system an isoquant line is, the greater the volume of total product expressed

Isoscent restriction:

The same costs that the entrepreneur makes when hiring and using the 2 factors
The type and slope of the isosceles line, as well as the distance from the beginning of the coordinate system, reflect the action of 2 factors:
Income directed to investment
The prices of the production factors used
Slope – S = Pl / Pk It is measured by the ratio of the prices of the 2 production factors. The slope is negative.
Manufacturer’s equilibrium conditions – the manufacturer is in equilibrium when it manages to touch the farthest possible isoquant curve with its isosceles constraint line. Thus, it produces the maximum volume of production according to the possibilities it has – the amount of investment and prices of production factors. At the point of contact, the slopes of the 2 lines coincide, which gives grounds to express the equilibrium as MPl / MPk = Pl = Pk or MPl / Pl = MPk / Pk

Maximum production volume
Within the budget
According to the prevailing prices
Economies of scale:

Economies of scale – the company derives economies of scale when the rate of increase in production and costs (labor and capital resources used) is lower than the rate at which production volumes increase.