Slope of an Iso-quant:
Since along an iso-quant the level of output remains the same, if θL units of θL are substituted for K units of K, the increase in output due to θ L units θ L (namely, θ L.MP_{L}) should match the decrease in output due to a decrease of K units of K (namely θ K.MP_{K}). In other words,
when is a very small amount we can write . In the K - L input space, dK/dL represents the slope of the iso-quant at any point on it.
θ Slope of the iso-quant
The absolute value of dK/dL, denoted by |dK/dL| is known as the marginal rate of technical substitution of L for K. (MRTSLK). By definition, it measures the reduction in one input per unit increase in the other that is just sufficient to maintain a constant level of output. It is equal to the ratio of the marginal product of L to the marginal product of K.