Question

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 method of transforming one set of numbers into another set of numbers in a way so that the order of the numbers remains the same and does not change.

1. f(u)= 3.14u : Yes, it is an example of Monotonic Transformation. If you multiply any number with u, the order will not change.

Take the following understanding:

When f(u)=u

	F(u)= u
Person A	1
Person B	2
Person C	3

And when f(u)= 3.14u,

	F(u)
Person A	3.14
Person B	6.28
Person C	9.42

In this case, the order remains the same (A>B>C), which is exactly the definition of Monotonic transformation.

Now, with the help of above understanding procedure, you can figure out the following parts too.

2. f(u)= 5000-23u : Not, it is not an example of Monotonic Transformation
3. f(u)= 1/u2 : No, it is not an example of Monotonic Transformation