Show that the utility functions V(X,Y) = XaY1-a and U(X,Y) = a ln(X) + (1-a)ln(Y) represent the same ordering of bundles
What will be an ideal response?
ln(V(X,Y)) = ln(XaY1-a) = ln(Xa) + ln(Y1-a) = U(X,Y)
Because ln(x) is a monotonic increasing function, the preference ordering is preserved.
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