Thursday, August 6, 2015

Marginal rate of technical substitution

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Marginal rate of technical substitution (MRTS) or just RTS is the amount by which the quantity of one input has to be reduced (∆x2) when one extra unit of another input is used (∆x1) so that output remains constant.
RTS is measured by the slope of the tangent to a point on an isoquant.
RTS = -dx2/dx1
let q = f(x1, x2)
∴ dq = f1dx1 + f2dx2
Since, dq = 0 for movements along an isoquant
f1dx1 + f2dx2  = 0
=> f1dx1 = -f2dx2
=> f1/f2 = -dx2/dx1 = RTS
So, RTS at a point equals to the ratio of the MP of of x1 to the MP of x2 at that point.
∴ RTS = MP1/MP2
[Because, f1= MP1]
1. Wikipedia

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