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)

MRTS_L,K = −ΔK/ΔL

From Q = f (L,K) , we can get the following equation by totally differentiating the production function.

ΔQ = MP_L . ΔL + MP_K . ΔK = 0.

Finally, we can get:

MRTS_L,K = −ΔK/ΔL= MP_L/MP_K and d²K/dL² > 0 implies the Law of Diminishing MRTS.

Elasticity of Substitution:

σ = (percentage change in capital - labour ratio)/(percentage change in MRTS_L,K)= [(Δ(K/L)/(K/L))]/[ΔMRTS/MRTS]
K/L at A = slope of ray OA = 4

MRTS at A = 4
K/L at B = slope of ray OB = 1

MRTS at B = 1
As the firm moves from A to B, the elasticity of substitution equals 1.

Example: Q = LK = 100 (left diagram)

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