MRTS is equal to the ratio of the Marginal Product of the factors

 Proof:

We know that,

 

The slope of a curve is the slope of the tangent at any point of the curve. The slope of the tangent is defined by the total differential. In the case of the isoquant, the total differential is the total change in Output say   , resulting from small changes in factors labour, L and capita, K.  

Taking total differential of  

Now, along an isoquant the output, Q is constant, so that the total change in Q must be zero. This implies that the total differential must be equal to zero, i.e

 

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