Marginal Rate Substitution
The marginal rate of technical substitution (MRTS) in the theory of further production is matched by the marginal rate of substitution (MRS) in the indifference curve of consumer's demand. Marginal rate of technical substitution indicates the rate at which factors can be submitted at the margin without altering the level of output. More precisely marginal rate of technical substitution of factor X for factor Y is defined as the amount 0 factor Y which can be replaced by one the level of output remaining unchanged. The correct of marginal rate of related substitution can be easily understood from table 2
Factor combination Labour Capital
Output Units MRTS of Capital of labour
A 1 15 50 -
B 2 12 50 3:1
C 3 10 50 2:1
D 4 9 50 1:1
All the factors combinations namely A, B, C, D in table 2 produce the same quantity of output i.e. 50 units. They are all iso-products combinations can be replaced by 1 unit of labour. Hence, the marginal rate of (MRTS) at this stage is 3:1 a comparison of factor combination B and C REVEALS. LIKEWISE THE (MRTS) between factor combinations C and D is 1:1
In fig. at point B the MRTS is AS/SB at point C it is BT/TC and at D, CR/RD
The marginal rate of technical substitution at a point on the isoquent can be known from the slope of the isoquent at that point. Consider a small amount of factors Y (say ΔY) is replaced by one any loss of factor X (say ΔX) without any loss of output. The slope A is therefore equal to Δ Capital. Thus, marginal rate of substitution =slope = ΔY/ ΔX Δ Labour or Δcapital/ ΔLabour
Slope of the point and hence the marginal rate of technical substitution (MRTS) can also be known by the slope of the tangent drawn on the isoquent at that period in fig.9 the tangent given is equal product curve IQ. The slope of the tangent AB is equal to OA. Therefore the marginal Rate of substitution at point C on the equal product curve IQ therefore the marginal rate technical substitution at point D is equal to OE/OF.
An important point to be remembered about the marginal rate of technical substitution is that it is equal to the ratio of the marginal physical products of two factors. Since by definition output remains constant on the equal product curve the loss output from a small increment in factor X.
The loss in output is arrives at by multiplying the marginal physical product of capital by the number of subtracted units of capital. The gain in output can be easily being multiplying the marginal rate of technical substitution with the additional units of labour.
Thus,
Slope, MRTS = ΔC (change in capital)/ ΔL (change in labour)
Loss in output = Marginal Physical Product of Capital or MPPC × ΔC
Gain in output = Marginal Physical Product of labour or MPPL × ΔL
Since Loss of Output = Gain of output
MPPc × ΔC = MPP ΔL
Or, ΔC/ ΔL = MPPl/ MPPc
MRTSlc = MPPl/ MPPC
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