Answer to Question #231625 in Microeconomics for Anisha Radhika Kum

Question

Consider the production function Q = 2(KL) ^0.5

a)     What is the marginal product of labour and capital

b)     What is the marginal rate of technical substitution of labor for capital

 

c)     What is the elasticity of substitution at a point K = 1, L = 1 if we increase K by one unit?

 

Answer 1

a) Q = 2(KL)^0.5

Q=2K^0.5L^0.5

Marginal product of labor = Differentiate the above production function with respect to L

dQ/dL=0.5×2K^0.5L^-0.5

dQ/dL=0.5×2K^0.5L^-0.5

dQ/dL=K^0.5L^-0.5

dQ/dL=K^0.5/L^0.5

Marginal product of capital = Differentiate the above production function with respect to K

dQ/dK=0.5×2K^-0.5L^0.5

dQ/dL=K^-0.5L^0.5

dQ/dL=L^0.5/K^0.5

b) marginal rate of technical substitution of labor for capital =change in capital/chang in labor

=$\frac{∆K}{∆L}$

=K^0.5L^-0.5 /K^-0.5L^0.5

=K/L

c)  Elasticity of substitution σ is given by

σ=dln(k/l)/dlnMRTS

σ=dln(k/l)/dlnMRTS =1

MRTS=K/L

​σ = 1

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