Question

Consider a Cobb-Douglas Utility Function: u(x1 , x2 ) = x c 1x d 2 ; Find out the MRS and show that a monotonic transformation couldn’t change the marginal rate of substitution.

Answer 1

$MRS(x1,x2) = \frac{MUx1} {MUx2} = \frac{u'(x1) } {u'(x2)} = \frac{c×x1^{c-1}×x2^{d}} {d×x1^c×x2^{d-1}} = \frac{c×x2} {d×x1}.$

A monotonic transformation of a utility function will either multiply the whole function by some value or will add or subtract some constant.