Return to scale

The concept of economies of scale (also level marginal product , Eng. Returns to scale ) is a component of the theory of production . Unlike the economies of scale economies of scale enter the rate to, an at least two of the factors of production -based production increases with a proportional increase in all factors of production.

Disambiguation

The terms return to scale and the economies of scale are defined in production theory of business administration and in microeconomics as the dependence of the amount of production on the amount of production factors used.

The returns to scale indicate the rate of increase at which output increases with a proportional increase in input. They show how the production volume reacts if all factors are increasingly used with the same usage ratio. Returns to scale are a characteristic of the production function .

Economies of scale, on the other hand, are the effects that result from increasing or decreasing returns to scale.

In the context of economies of scale, there are other terms that are very similar but must be distinguished from one another. The concept of the composite effect ( composite advantages ) should be mentioned here in particular .

Types of returns to scale

Constant returns to scale

Constant returns to scale

Of constant returns to scale (constant returns to scale) is when in a proportional change in input factors by a factor a and the output by a factor of a rise. The following applies: ${\displaystyle (x_{1},x_{2})}$

${\displaystyle f(a\cdot x_{1},a\cdot x_{2},\dots ,a\cdot x_{n})=a\cdot f(x_{1},x_{2},\dots ,x_{n})}$

With constant returns to scale, the production function is homogeneous of degree 1.

The first figure shows constant returns to scale. It can be seen that for an output of ten units, an input of 2 machine hours ( ) and five working hours ( ) is necessary. If you now double the input from two to four machine hours and from five to ten working hours, you get an output of 20 units, assuming constant returns to scale. The second graphic shows the linear course and the dependency of the output with the change in factor a of constant returns to scale. Example: ${\displaystyle x_{2}}$ ${\displaystyle x_{1}}$

With constant returns to scale, it is assumed that an optimized production process is used in a company. As a result, one can expect a second company with the same production process to generate the same output. This theory becomes understandable using the example of a service company in the city of A.

In order to offer services, the company needs capital (workplace) and labor (clerk) to generate a certain output (service). In order to double the output, it would be conceivable that this company would offer the same service with the same ratio of capital and labor in city B. The size of the company does not play a role here, as the company needs a clerk and a job to offer a service. If ten services are to be offered, the company needs ten clerks and ten jobs. With constant economies of scale, the size of the company does not influence the productivity of the input factors.

However, the assumption of constant returns to scale is not always fulfilled. This is the case if, if the input factors were doubled, they could be used more efficiently. I.e. if the input factors are doubled and used more efficiently, the outputs would more than double. This could be triggered by specialization and / or division of labor (e.g. through better utilization of machines). In this case one speaks of increasing economies of scale.

Increasing economies of scale

Increasing returns to scale exist when the output increases by more than a- fold. Then:

${\displaystyle f(a\cdot x_{1},a\cdot x_{2},\dots \dots ,a\cdot x_{n})>a\cdot f(x_{1},x_{2},\dots \dots ,x_{n})}$

Increasing economies of scale

The second figure shows the increasing returns to scale. The starting point is again an output of 10 units with an input of 2 machine hours (x1) and 5 working hours (x2). If you want to generate an output of 20 units, you need less than double the input. In the present case, an input of 3 machine hours (x1) and 8 working hours (x2) is required for an output of 20 units. If the output is increased to 30 units, the theory of increasing economies of scale becomes clear. Only approx. 3.5 machine hours (x1) and approx. 9 working hours are required for this. If one compares the production process with that of constant economies of scale, it becomes apparent that with increasing economies of scale for an output of 30 units, almost less than half of the input is required. The distance between the isoquants decreases steadily as the output volume increases. The reason for this is the disproportionate growth in output with a proportional use of factors  a .

The second graphic shows this trend. There are various reasons for increasing economies of scale:

• Advantages from the division of labor, in which complex processes are broken down into simple, easily repetitive activities. The resulting learning curve effects a. contribute to increasing economies of scale.
• Savings by using larger means of production, such as B. larger ovens and tanks.

It should be noted here that it is not the furnace that produces the scale yield, but the larger amount that can be accommodated in a larger furnace.

• Rationalization through the use of automated production equipment (robots)
• Use of standardized parts and centralized reserve management.
• Improved lot size coordination for successive production stages.

Decreasing returns to scale

Decreasing returns to scale exist when the yield only grows disproportionately. Then:

${\displaystyle f(a\cdot x_{1},a\cdot x_{2},\dotsc ,a\cdot x_{n})<a\cdot f(x_{1},x_{2},\dotsc ,x_{n})}$

Decreasing returns to scale

The third figure shows the decreasing returns to scale. These behave in a mirror-inverted manner to those of the increasing economies of scale, which were already explained in advance. There are essentially two reasons for declining returns to scale. On the one hand, there are administrative problems in the case of too large production quantities and, consequently, too large production facilities. Second, geographic factors. For example, the location of an additional production facility may be worse than that of the existing production facility.

The declining returns to scale can be illustrated by the example of some companies that operate on a large scale. In such companies, the difficulty lies in managing and organizing employees. If management does not perform these tasks, the employees are not deployed efficiently enough. Another not insignificant problem of large companies is due to internal communication. As a result, work steps are carried out twice or not at all. The input used does not lead to the desired yield.

See also

• Scale elasticity

literature

• John Eatwell: Returns to Scale . In: Steven N. Durlauf and Lawrence E. Blume (Eds.): The New Palgrave Dictionary of Economics, Second Edition . 2008, doi : 10.1057 / 9780230226203.1432 .
• George J. Stigler : The Economies of Scale. The Journal of Law & Economics 1 (1958): pp. 54-71. www.jstor.org/stable/724882.

Individual evidence

1. ↑ Robert S. Pindyck, David L. Rubinfeld: Microeconomics . 5th edition. Pearson Studium, Munich 2003, p. 289.
2. ^ ^{A b c} Hanusch, Kuhn, Canter: Volkswirtschaftslehre . Vol. 1: Basic Micro and Macroeconomics . 6th edition. Springer Verlag, Berlin 2002, p. 173
3. ↑ Varian: Microeconomics . 3. Edition. Oldenbourg, ISBN 3-486-22483-2 , pp. 15-16