# Elasticity of technical substitution. B.4 Marginal rate of technical substitution 2019-01-23

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## Elasticity of substitution

For example, if capital becomes cheaper, the producer will substitute capital for labour. In other words, the production technology has a constant percentage change in factor e. Assume that no other goods matter. How does demand for Coke change when the price for Pepsi changes? If the numerical value of σ is unity, then we have a Cobb-Douglas production function. The concept of elasticity of substitution also occupies an important place in the theory of distribution. Hence, one and only one combination of inputs can produce specified output. Elasticity of factor substitution can take any value from zero to infinity, always being positive.

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## B.4 Marginal rate of technical substitution

It measures the strength of substitution effect. Intuitively we are looking at how a consumer's relative choices over consumption items change as their relative prices change. On the other hand, if wages price of labour fall, the producer will use relatively more labour than capital. If the composition of the factors of production is not profitable, there will be shift of resources from one use to the other so as to increase the profitability by increasing or decreasing outlay in one resource or the other. For example, the rate of substitution between and may be expressed as: The denominator in the above expression is known as the.

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## Constant elasticity of substitution

Therefore, a fall in the price of one factor will induce the producer to replace the costly factor completely by the cheaper one. Specifically, it arises in a particular type of aggregator function which combines two or more types of consumption goods, or two or more types of production inputs into an aggregate quantity. Hence, increase in one factor will be accompanied by a constant decrease in the other factor. If, on the other hand, it declines rapidly, elasticity of substitution will be low. The substitutability or one luctor for another depends on the elasticity or substitution. The elasticity of substitution between factors is simply the ratio of proportionate change in the slopes of two rays from the origin to two points on an isoquant to the proportionate change in the slopes of isoquants at these points Fig.

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## B.4 Marginal rate of technical substitution

If the difficulty in substitution increases faster, i. The elasticity of substitution between factor inputs is not infinite. The above expressions may be illustrated graphically using equal product curves and. Mathematical Derivation : This proposition can be established mathematically in the following way. More specifically from the partial elasticity of labour productivity it can be inferred that if σ more than 1, then there will be higher substitution possibilities and if σ is less than one, then there will be lower substitution possibilities. The problem of auto­correlation can be reduced by adopting the first difference method. Hence, the elasticity of factor substitution is equal to infinity.

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## What is the Concept of Elasticity of Factor Substitution?

Elasticity of substitution is the of the ratio of two inputs to a production or utility function with respect to the ratio of their marginal products or utilities. There are always 2 sides to the market; here we are talking about the receiver, since the elasticity of preference is that of the receiver. We always substitute relatively cheaper factor for the dearer one. The relative share of labour in output, i. The greater the convexity of ixoquant the less will be , and vice versa. Which of these effects dominates depends on the magnitude of the elasticity of substitution. The magnitude of the elasticity of substitution can be assessed by looking at the curvature of isoquants.

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## American Economic Association

The above equation will be estimated underlying the assumption of constant returns to scale. Capital and labour are not good substitutes here. It affects the distributive shares of the factors of production. The manner and the rate at which the two factors will be substituted for each other will depend upon the marginal rate of technical substitution between the factors and change in their relative prices. This aggregator function exhibits constant.

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## American Economic Association

Therefore there is a need to follow other production function. We may conclude then that in a two-factor production function, if the relative price of one of the factors L increases, owing to an increase in the relative supply of the other factor K , then the relative share of the factor L would increase, decrease, or remain unchanged if the elasticity of substitution a of the factor L for the other factor K is less than, greater than, or equal to unity. Therefore, the coefficient of elasticity of substitution σ may be taken to be the We may simplify the value of σ as given by 8. How does demand for Pepsi change when the price for Coke changes? If they arc perfect substitutes, thai is, if either factor can he used equally well to produce the product, the marginal rate of sub. The relative share of labour is. The elasticity of substitution also governs how the relative expenditure on goods or factor inputs changes as relative prices change.

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## Elasticity of substitution, technical progress and returns to scale in branches of Soviet industry: A new CES production function approach

That is, we arc concerned with what may he called elasticity of technical suhst union. Thus, it is clear that the elasticity of factor substitution increases from zero to infinity, as one move downwards along a substitution curve Fig. From the above function, the marginal productivity of labour will be obtained as follows: The marginal productivity theory of wages will generally be accepted on the grounds that it gives an adequate explanation for wage determination. In this case, capital and labour are good substitutes. Here we discuss to what extent a factor of production, sa labour, can be substituted for another factor. In other words, it shows the relation between inputs, and the trade-offs amongst them, without changing the level of total output. Here, change in the relative price of a factor cannot lead to any substitution and therefore, elasticity of factor substitution is zero and the isoquants will be right angled in such case.

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## B.4 Marginal rate of technical substitution

We cap it off by explaining the elasticity of substitution measure. In such a case, the elasticity of substitution between the two factors is infinite. The greater the convexity of isoquants, the smaller would be the elasticity of substitution. Where it is one as exhibited in the , there exist constant returns to scale, i. We can refer to the shape of lsoquants or equal product curves to determine the magnitude of elasticity of substitution he tween factors.

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