# What is the elasticity of the substitution

## Substitution elasticity

the ratio o of the relative change in the input ratio of two production factors to the accompanying relative change in the technical substitution rate; this substitution rate indicates the ratio in which the factors under consideration must be exchanged for one another if - with the remaining factor quantities remaining constant - the production level is to remain unchanged. The elasticity of substitution can be taken as a measure of how easily one production factor can be replaced by another. The value o = 0 means that it is impossible to change the factor input ratio, i.e. that the factors are not substitutes. If the elasticity of substitution approaches infinity, then changes in the factor input ratio do not lead to changes in the substitution rate, and the factors are perfect substitutes. The concept of elasticity of substitution initially relates exclusively to the properties of the production function. In a competitive economy, minimizing costs for companies means that the technical substitution rate matches the factor price ratio. According to the marginal productivity theory of distribution, the elasticity of substitution thus becomes decisive for the relationships between factor prices and functional income distribution. The proportions of the factors in total income develop like their relative prices when the elasticity of substitution is less than one, i.e. the factors are bad substitutes. If the elasticity of substitution is one, the proportions of the factors are constant. If the factor input ratio reacts elastically to changes in the relative factor prices or if the factors are good substitutes, then the proportion of the factor that has become relatively cheaper in the functional distribution increases. Literature: Allen, R. G. D., Mathematik für Volks- und Betriebswirte, Berlin 1956, p. 353 ff. Bartmann, H., Distribution Theory, Munich 1981, p. 123 ff.

The elasticity of substitution characterizes the strength of the substitution between substitutional production factors.

Measure of the mutual substitutability of two production factors in a company, branch or economy. The most common, the HICKS elasticity of substitution, is equal to the relative change in the quantitative ratio of two production factors, based on the relative change in their marginal substitution rate, measured along an isoquant. With A (work) and K (capital) applies

The elasticity of substitution is inversely proportional to the isoquantum curvature:

A high value of b means good substitutability and low curvature (extreme case b = 00: linear isoquantum curve), a low value of b means poor substitutability and strong curvature (extreme case b = 0: limitationality). In general, b can take on a different value at every point of the isoquantum field. In the case of the CES production function, however, it is the same everywhere; in the case of homothesis of the production function, it is the same in all points on an original ray through the isoquantum field. In the minimum cost combination, the marginal rate of substitution in the expression for b is equal to the ratio of the factor prices, so b indicates how much changes in the factor price ratio influence their cost-minimizing input quantity ratio. Implication for the - distribution of income: If b is smaller (greater) than one, the ratio of wage and capital costs, i.e. the factor income, changes in favor of the relatively more expensive (cheaper) production factor. For b equals one, the distribution relation is independent of the factor price (COBB-DOUGLAS production function). Literature: Hesse, H., Linde, R. (1976a). Gahlen, B. (1973). Krelle, W. (1969)

The elasticity of substitution characterizes the strength of the substitution between substitutional production factors.

Measure of the mutual substitutability of two production factors in a company, branch or economy. The most common, the HICKS elasticity of substitution, is equal to the relative change in the quantitative ratio of two production factors, based on the relative change in their marginal substitution rate, measured along an isoquant. With A (work) and K (capital) applies

The elasticity of substitution is inversely proportional to the isoquantum curvature:

A high value of b means good substitutability and low curvature (extreme case b = 00: linear isoquantum curve), a low value of b means poor substitutability and strong curvature (extreme case b = 0: limitationality). In general, b can take on a different value at every point of the isoquantum field. In the case of the CES production function, however, it is the same everywhere; in the case of homothesis of the production function, it is the same in all points on an original ray through the isoquantum field. In the minimum cost combination, the marginal rate of substitution in the expression for b is equal to the ratio of the factor prices, so b indicates how much changes in the factor price ratio influence their cost-minimizing input quantity ratio. Implication for the - distribution of income: If b is smaller (greater) than one, the ratio of wage and capital costs, i.e. the factor income, changes in favor of the relatively more expensive (cheaper) production factor. For b equals one, the distribution relation is independent of the factor price (COBB-DOUGLAS production function). Literature: Hesse, H., Linde, R. (1976a). Gahlen, B. (1973). Krelle, W. (1969)

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