# Isoquant

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The **isoquant** (curve of the same product) is a set of possible combinations of the input of two factors of production, which allow to efficiently produce a given product size.

Izoquants with their appearance resemble curves of indifference. However, there is a fundamental difference between them, because the isoquants are marked by the amount of product that suits them, and not the levels of utility as in the case of indifference curves.

## Interpretation

The individual points on the isoquant reflect different methods of producing the same amount of product. Each point on the isoquant represents a different method of production - from the most capital - intensive to the most labor-intensive methods.

The location of several isocquants on the graph shows us a specific map. Each isokwanta shows different combinations of inputs used in the production process to produce a given product size.

## Types of Substitution

Isoquants depending on the shape of the curve can be distinguished on:

- Full substitution - one factor of production can be replaced by the other factor of production. Total freedom to replace one factor with another. In a substitution full, there may be a situation in which factors of production will be excellent substitutes for each other. This means that the replacement of factors with each other takes place in a certain proportion, e.g. 1. In this situation, the isoquant is a descending linear curve. There is also a situation in which production can be made at a fixed ratio. We define such an isocquant with a curve of perfect complementarity. It has the shape of a right-angle arm.
- An incomplete substitution - none of the factors of production can be completely replaced by the second factor of production. The curve does not touch the coordinate axes. The higher the degree of substitution, the stronger the curve will be emphasized towards the origin of the coordinate system.

In an incomplete substitution, each of the factors must be produced in a certain size, none of them can be completely replaced. Little freedom to replace one factor with the other because of the lack of the possibility to completely abandon the production of both factors of production.

## Features

Isoquants are characterized by three features:

- Because each of them refers to different sizes of production, they can not intersect each other.
- All isoquants have a negative slope. This is due to the fact that each enterprise, with limited resources of production factors and wishing to generate a given volume of production, will consider changing the technology to be more capital intensive only when it allows to reduce labor inputs and vice versa.
- The individual isoquants gradually "flatten" as they move to the right, which is the effect of engaging more and more additional capital to offset the successive reductions in the work needed to produce the same amount of product.

To sum up the isoquant it is the geometric place of such quantitative combinations of production factors that ensure the same level of production (product).

## Application

Isoquant is needed to calculate, among others:

- The optimum of production is the optimal combination of factors is the point of contact of the same cost line with the highest possible production isoquant. This is the point of balance of the company achieving maximum production.
- The product expansion path is a curve that connects points of contact between production isoquants and parallel unit cost lines. These points indicate optimal combinations of factors corresponding to different production levels

## References

- Clemhout, S. (1968).
*The class of homothetic isoquant production functions*. The review of Economic studies, 35(1), 91-104. - Van Marrewijk, C., & Van Marrewijk, C. (2002).
*International trade and the world economy*(Vol. 6). Oxford: Oxford University Press. - Liao, Z., Wan, Y., Thomas, S. N., & Yang, A. J. (2012).
*IsoQuant: a software tool for stable isotope labeling by amino acids in cell culture-based mass spectrometry quantitation*. Analytical chemistry, 84(10), 4535-4543.