Consider the utility function u1(x1, x2, x3) = x21,x32 x3 .
Find a monotone transformation of u1(x1, x2, x3) such that the new utility function is of the form u2(x1, x2, x3) = (x1a, x2b, x3c)
Where a + b + c= 1.
Such monotonic transformation can be done so that the powers are added up to 1
We see that
After monotonic transformation of the new utility function is
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