Question #72186

Consider a production function given as Q(X_(1 ,) X_2)=x_1^0.4 x_2^0.6
Calculate the marginal rate of technical substitution of x_(1 )for x_2

Expert's answer

Q(X1, X2) = x1^0.4*x2^0.6,

MP1 = Q'(x1) = 0.4x2^0.6/x1^0.6,

MP2 = Q'(x2) = 0.6x1^0.4/x2^0.4,

The marginal rate of technical substitution of x1 for x2 is:

MRTS (x1, x2) = MP1/MP2 = 0.4x2^0.6/x1^0.6*x2^0.4/0.6x1^0.4 = 2x2/3x1.

MP1 = Q'(x1) = 0.4x2^0.6/x1^0.6,

MP2 = Q'(x2) = 0.6x1^0.4/x2^0.4,

The marginal rate of technical substitution of x1 for x2 is:

MRTS (x1, x2) = MP1/MP2 = 0.4x2^0.6/x1^0.6*x2^0.4/0.6x1^0.4 = 2x2/3x1.

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