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Explain in detail the law of variable proportions.

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Meaning : According to the law of variable proportions, when more and more units of a variable factor are mixed with the same amount of fixed factors, the total production increases at a rising rate, and then the rate decreases eventually. This means that marginal production increases first and then eventually decreases. The law of variable proportions is also known as the law of Factor of return. This is a short-term concept. In essence, when the production due a factor is sought to grow through a specific quantity of fixed factors in addition to the variable factors, then the law of variable proportions comes in operation. The ratio between the fixed factors and the variable factor varies, when variation is only in one factor, while retaining other factors as constant.

Definitions
(i) According to P.A. Samuelson, “An increase in some inputs relative to other fixed inputs will, in a given state of technology, cause output to increase; but after a point, the extra output resulting from the same additions of extra inputs will become less and less.”

(ii) According to G. Stigler, “As equal increments of one input are added; the inputs of other productive services being held constant, beyond a certain point the resulting increments of product will decrease, i.e., the marginal production will diminish.”

(iii) According to F. Benham, “As the proportion of one factor in a combination of factors is increased, after a point, first the marginal and then the average production of that factor will diminish,”

(iv) According to Mrs. Joan Robinson, “The law of diminishing returns, as is usually formulated, states that with a fixed amount of any one factor of production, success in increase in the amount of other factor will, after a point, result into a diminishing increment rate of output.”

It is obvious from the above definitions of the law of variable proportions (or the law of diminishing returns) that it refers to the behaviour of output as the quantity of one factor is increased, keeping the quantity of other factors fixed and further it states that if more units of a variable input are applied to a given quantity of fixed inputs, the total output may initially increase at an increasing rate, but beyond a certain level of output, the rate of increase in the total output diminishes. Precisely, the marginal increase in the total output eventually decreases when additional emits of variable factors are applied to a given quantity of fixed factors.

The law of variable proportion is based on the fact that not all factors of production can be replaced for each other. And it is a noted economic fact that the elasticity of replacement among the various factors is not infinite.

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