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.
"MRS(x1,x2) = \\frac{MUx1} {MUx2} = \\frac{u'(x1) } {u'(x2)} = \\frac{c\u00d7x1^{c-1}\u00d7x2^{d}} {d\u00d7x1^c\u00d7x2^{d-1}} = \\frac{c\u00d7x2} {d\u00d7x1}."
A monotonic transformation of a utility function will either multiply the whole function by some value or will add or subtract some constant.
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