Factor substitution

In economics, the term factor substitution describes the exchange of production factors according to the economic principle . The aim is either to maximize the output for given production factors or to minimize the input factors for a given output volume. As part of the production process to support production functions , the decision as to whether and to what extent a production factor is replaced by another (substituted).

Historical classification

After Johann Heinrich von Thünen's pioneering work in the field of production and distribution theory in the middle of the 19th century, Knut Wicksell succeeded in developing the concept of production functions. In 1893, Wicksell first implemented the theories developed by Thünen in a consistent mathematical formulation. It is usually assumed that the factors of production are substitutable.

Production process

In the production process, companies transform inputs into outputs ( products ). The inputs or production factors are usually divided into the categories labor , land (raw materials) and capital , each of which can comprise more narrowly defined sub-categories. The input of a bakery includes, for example, the work of the employees, the raw materials such as flour and sugar as well as the capital invested in ovens and other equipment. These input factors are required for the production of outputs, such as bread, cakes and pastries in this example.

Production function

The relationship between the inputs for the production process and the resulting outputs is described by the production function. A production function indicates the maximum amount of production that a company can produce with any specified combination of inputs. If different combinations of production factors achieve the same output quantity, they can be summarized graphically in a curve called isoquant . The isoquant shows the flexibility of companies when it comes to production decisions, since a certain output can be achieved even with different combinations of inputs. For a given production function, the choice of the combination of factors is influenced by the costs of the possible production factors. A changed combination of the production factors may allow cost reduction and profit maximization. ${\displaystyle q}$

It should be noted that the production function is aimed at a specific technology . What is meant is a certain level of knowledge about the various methods that can be used to convert the factor input quantities into quantities of goods. As technology advances and the production function changes, a company can achieve greater output for a given amount of input.

Ultimately, the production function describes what is technically feasible when the company works efficiently - that is, when the company uses every input combination as effectively as possible. It is reasonable to assume that profit-oriented entrepreneurs do not waste resources and therefore always make production technically efficient.

Factor substitution

According to the production function, the quantities of goods can be produced in different ways. For the sake of simplicity, it is assumed that only two production factors exist. Both input and output should be freely divisible. In the model it is assumed that the output remains the same and that certain amounts of one factor can be dispensed with if the input amount of the other factor is increased. The output increases or remains at least the same as long as the use of one factor is increased while the other is constant. (Therefore the isoquantas have a negative slope.) If fewer and fewer units of one production factor are available, then one unit of this factor must be replaced or substituted by the more units of the other factor. (Thus, in most production technologies, the isoquants are convex.)

To better illustrate the model, it is assumed that the inputs are labor and capital . The production function indicates the highest output volume as follows. ${\displaystyle L}$ ${\displaystyle K}$ ${\displaystyle q}$

${\displaystyle q=F(K,L)\!\,}$

For the production function in the equation, this can mean using more capital and less labor or vice versa. For example, wine can be made in a labor-intensive manner with a large number of workers or in a capital-intensive manner with the help of machines and with only a few workers. In this example the factor labor is substituted by the factor capital.

Marginal rate of factor substitution

Since a marginal rate of substitution is also determined in household theory , it is referred to in production theory as the marginal rate of technical substitution (GRTS) or factor substitution. The GRTS corresponds to the slope of the isoquant and indicates how many units of one factor can be replaced by a unit of the other factor while the output remains constant. The basic idea here is that a producer can use several production factors (usually two for simplicity) in the production of his goods. In most cases, however, the factor input ratio is not clearly specified, so that one production factor can be substituted for another. In the following example, the GRTS describes how many additional units of labor are needed to achieve the same output with one less unit of capital . It should be the amount used additionally work, the less amount used capital. ${\displaystyle L}$ ${\displaystyle K}$ ${\displaystyle \Delta L}$ ${\displaystyle \Delta K}$

${\displaystyle GRTS_{LK}={\frac {\Delta L}{\Delta K}}}$

Since the increase (+) in one factor is opposed to a decrease (-) in the other, the marginal rate of factor substitution assumes a negative value. The GRTS drops if one factor ( ) is constantly used less than this, as this must always be compensated for by using the other factor ( ) more. As a result, the "power of substitution" of the substituting factor ( ) decreases . ${\displaystyle \Delta K}$ ${\displaystyle \Delta L}$ ${\displaystyle \Delta L}$

The marginal rate of factor substitution plays a role above all when using different production functions.

Effects of special production functions

Figure 1: The isoquants for inputs that are perfect substitutes

Perfect substitutes

In order to be able to show the possible degree of substitution, the production function is divided into two extreme cases. In the first extreme (see Figure 1 ) the factors of production are perfect substitutes . In this case the GRTS is constant at all points of the isoquant. As a result, the same quantity of goods (for example ) can be produced almost exclusively with capital (in points ), almost exclusively with labor (in points ) or with a balanced combination of the two (in points ). For example, musical instruments can be produced almost exclusively with machine tools or with very few tools and highly skilled work. ${\displaystyle q_{3}}$ ${\displaystyle A}$ ${\displaystyle C}$ ${\displaystyle B}$

Fixed ratio of substitutes

At the other extreme, with a fixed employment ratio in the production function, there is no possibility of substituting the inputs with one another. That is, a specific combination of labor and capital is required for each level of production.

Figure 2: Production with a fixed employment ratio

Additional quantities of goods can only be obtained if labor and capital are added in a certain proportion. Consequently, the isoquantas have an L-shape, as do the indifference curves when two goods are perfectly complementary goods . An example of this is the construction of concrete footpaths with the help of jackhammers. One person is needed to operate a jackhammer - production is not increased by two people and a jackhammer, or by one person and two jackhammers.

In Figure 2 the products and technically efficient input combinations are shown. For example, a quantity of labor and a quantity of capital can be used to produce the quantity of goods as in point . If the capital remains fixed , the increase in labor does not change the quantity of goods. This also does not happen if the capital is increased with a fixed rate. Consequently, in the vertical and horizontal sections of the L-shaped isoquant, either the marginal product of capital or the marginal product of labor is zero. Higher quantities of goods are only achieved if both capital and labor are increased, as is the case when switching from the input combination to the input combination . ${\displaystyle A}$ ${\displaystyle B}$ ${\displaystyle q_{1}}$ ${\displaystyle A}$ ${\displaystyle L_{1}}$ ${\displaystyle K_{1}}$ ${\displaystyle K_{1}}$ ${\displaystyle L_{1}}$ ${\displaystyle A}$ ${\displaystyle B}$

literature

• Robert S Pindyck, Daniel L Rubinfeld: Microeconomics . 6th edition. Pearson Studies, Munich / Boston 2005, ISBN 978-3-8273-7164-5 .
• Eberhard Feess-Dörr: Microeconomics . 3. Edition. Metropolis-Verlag, Marburg 1995, ISBN 3-926570-23-7 .
• Anton Frantzke: Fundamentals of Economics . 2nd Edition. Schäffer-Poeschel, Stuttgart 2004, ISBN 978-3-7910-2066-2 .
• Harald Wiese: Microeconomics . Springer, Berlin 2005. ISBN 3-540-24203-1 .
• Renate Ohr: The Linder Hypothesis . In: Economics Studies . Munich, 14th year 1985, no.12 (Dec.). ISSN  0340-1650 .
• Marion Steven: Production Theory . Gabler, Wiesbaden 1998. ISBN 978-3-409-12930-5 .
• Paul Krugman, Maurice Obstfeld: International Economy . Pearson Studium, Munich 2004. ISBN 3-827-37081-7 .

Individual evidence

1. ↑ Fritz Söllner: The history of economic thinking . 2nd Edition. Springer, Berlin / Heidelberg 2001, pp. 69–70.
2. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 262.
3. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 262.
4. ↑ Dirk Diedrichs, Marco Ehmer, Nikolaus Rollwage: Microeconomics . 3. Edition. WRW-Verlag, Cologne 1999, p. 25.
5. ↑ Bernd Woeckener: Introduction to Microeconomics . Springer, Berlin / Heidelberg 2006, p. 214.
6. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 277.
7. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 263.
8. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 263.
9. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 263.
10. ↑ Winfried Reiss, Heide Reiss: Microeconomic Theory: historically based introduction . 5th edition, pp. 322-323.
11. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, pp. 262–263.
12. ↑ Eberhard Feess-Dörr: Microeconomics , 3rd edition. Metropolis-Verlag, Marburg 1995, p. 114.
13. ↑ Eberhard Feess-Dörr: Microeconomics . 3. Edition. Metropolis-Verlag, Marburg 1995, p. 488.
14. ↑ Dirk Diedrichs, Marco Ehmer, Nikolaus Rollwage: Microeconomics . 3. Edition. WRW-Verlag, Cologne 1999, p. 30.
15. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, p. 280.
16. ↑ Robert S. Pindyck, Daniel L. Rubinfeld: Microeconomics . 6th edition. Pearson Studium, Munich 2005, pp. 280–282.