Production Technology: Two Variable Inputs
Production Surface (or Total Product Hill):
Isoquants:
A curve that demonstrates all of the combinations of labour and capital that can produce a given level of output.
MRTS (Marginal rate of Technical Substitution)
MRTSL,K = −ΔK/ΔL
From Q = f (L,K) , we can get the following equation by totally differentiating the production function.
ΔQ = MPL . ΔL + MPK . ΔK = 0.
Finally, we can get:
MRTSL,K = −ΔK/ΔL= MPL/MPK and d2K/dL2 > 0 implies the Law of Diminishing MRTS.
Elasticity of Substitution:
σ = (percentage change in capital - labour ratio)/(percentage change in MRTSL,K)= [(Δ(K/L)/(K/L))]/[ΔMRTS/MRTS]K/L at A = slope of ray OA = 4
MRTS at A = 4K/L at B = slope of ray OB = 1
MRTS at B = 1As the firm moves from A to B, the elasticity of substitution equals 1.
Example: Q = LK = 100 (left diagram)
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