Question

7. State (and explain) whether these are monotonic transformations or not for the utility function u = (x,y).

f(u) = 3.14u

f(u) = 5000-23u

f(u) = 1/u2

Answer 1

A monotonic transformation is a transformation that does not change the order of the numbers assigned to objects.

a) f(U) is a valid monotonic transformation, because for any utility U, all the values will be increased by 50, and their order of preference woukd still remain the same.

b) u-1000 is a valid monotonic transformation.

c) -u is a non valid monotonic trnasformation, because if amongst two numbers x and y, x>y, then -x<-y. This chamges the order of preference.

d) u2 is a valid monotonic trnasformation.

e) 1/u2 is a non valid monotonic trnaformation, because if x>y, then x2>y2. But 1/x2 will be less than 1/y2. Thus the order is not preserved.

f) -1/u is a valid monotonic transformation.