Different factors of production are used in the process of production so as to get maximum profit. 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.
A change in the price of one factor keeping all other prices constant will require a readjustment of factor proportion. This is due to the fact that change in the price of one factor destroys the equilibrium condition of the equality of price ratios between the two factors and the marginal rate of technical substitution.
The concept of elasticity of factor substitution was developed by J.R. Hicks in his book ‘The Theory of Wages’ in 1932 to estimate the relative responsiveness of the capital labour ratio to given proportional changes in the marginal rate of technical substitution of capital for labour.
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It measures the relative extent to which one factor will be replaced by the other, whenever there is change in their relative prices. For example, if capital becomes cheaper, the producer will substitute capital for labour.
On the other hand, if wages (price of labour) fall, the producer will use relatively more labour than capital. 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.
Elasticity of factor substitution is defined as the proportionate change in the factor- proportions to the proportionate change in the marginal rate of technical substitution, so that the output remains the same (one moves along an isoquant. It measures the strength of substitution effect. Therefore,
Intuitively, elasticity of factor substitution can also be thought of as a measure of the degree of ease with which one factor is substituted for the other. It can also be conceived as a measure of similarity of factors of production from a technological point of view.
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In equilibrium position, the marginal rate of technical substitution in the formula of ‘a’ will be replaced by the ratio of factor prices. Thus, in equilibrium
In practical life, replacement of marginal rate of technical substitution by factor price ratio is helpful, as information regarding latter is easily available. Moreover, changes in factor proportions in which factors are used are generally influenced by relative factor prices only.
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Thus, when exogenous input price ratio (PK/PL) change, we expect a simultaneous change in optimal input ratio (L/K) in the reverse direction. The reason is simple. We always substitute relatively cheaper factor for the dearer one. That is, the direction of change is clear, but the extent of input substitution will be measured by the above formula of elasticity of substitution.
Elasticity of factor substitution can take any value from zero to infinity, always being positive. If marginal rate of technical substitution declines slowly, elasticity of substitution between the two factors will be high. If, on the other hand, it declines rapidly, elasticity of substitution will be low. Elasticity of factor substitution is zero for Leontief function, one for Cobb Douglas function and constant for linear and CES function.
The shape of the isoquant is related to its elasticity of substitution. The magnitude of the elasticity of substitution can be assessed by looking at the curvature of isoquants. The greater the convexity of isoquants, the smaller would be the elasticity of substitution.
In the extreme case, when the two factors of production are perfect substitutes, production can be carried through both the factors or through any one of them. Here, both the factors are identical for all purposes. Hence, increase in one factor will be accompanied by a constant decrease in the other factor.
Thus, the marginal rate of technical substitution will be constant and uniform. Further, ∆MRTSK, I = 0 or L/K = 0. The isoquants between them will be straight lines. Therefore, a fall in the price of one factor will induce the producer to replace the costly factor completely by the cheaper one. In such a case, the elasticity of substitution between the two factors is infinite.
On the other extreme, suppose the two factors are perfect complements in the sense that both have to be combined in fixed proportions to produce a given output, i.e., ∆ (K/L) = 0. The marginal rate of technical substitution between such factors will be infinite or zero, as output will not increase by substitution of one factor by the other.
Hence, one and only one combination of inputs can produce specified 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. Here, MPK = 0 along vertical stretch and MPL = 0 along horizontal stretch of the isoquant.
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. 7.16).
Therefore, elasticity of substitution
Substitution curve can be plotted (Fig. 7.17) by taking K/L ratio on the X-axis and MRTS on Y-axis. Where the substitution curve AB is steep (above point ‘A’), the elasticity of factor substitution is low. Capital and labour are not good substitutes here.
On the other hand, the elasticity of factor substitution is high in the flat portion of substitution curve (below point ‘B’). In this case, capital and labour are good substitutes. The substitution curve becomes vertical at point ‘C’. Here, a given percentage changes in MRTS fails to bring in change in the capital labour ratio.
Hence, the elasticity of factor substitution becomes zero. On the other extreme, at point ‘D’, the substitution curve becomes horizontal. Here, even no change in MRTS brings an infinitely large change in the capital-labour ratio. Hence, the elasticity of factor substitution is equal to infinity.
Somewhere between points ‘A’ and ‘B’, a given percentage change in MRTS brings an equal change in capital-labour ratio making the elasticity of factor substitution equal to unity. Thus, it is clear that the elasticity of factor substitution increases from zero to infinity, as one move downwards along a substitution curve (Fig. 7.17).
