Monotonic Transformations

[@felipecabral2047]

Thank you very much! It was very helpful for my microeconomics and math exams.

[@rishinarla]

Incredibly helpful thank you

[@riseofai8492]

The Video has bad audio. It needs fixing.

[@vwaliaaa]

Thank you !!

[@jcll1978]

what is the difference btn Monotonic Transformations and Affine Transformations?

[@000datazero]

Audio needs to be cleaned up.

[@Anon-rd8ul]

thank you

[@SirArvy]

I 've read in google that we can determine if a function is a monotonic transformation if it's derivative does not change sign. If the derivative of u=1/v^2 is 2/v^3 then why it is not a monotonic transformation?? That is according to the book of varian. Someone please help me!. 😭😭😭

[@learnyoodles519]

A function is monotonic if the derivative is positive (it isn't about sign change, just about positive/negative). In your example, u=1/v^2 is the same as u=v^(-2) which makes it easier to see that the derivative is actually -2/v^3. This derivative is actually negative, which means this is not a monotonic transformation.

[@SirArvy]

One more thing. In -1/v^2 , how is it similar to v^(2)? Is it right that since the power is -2 and the numerator is -1, i end up in v^(2)???

[@learnyoodles519]

@@SirArvy You end up with 1/v^3, which is positive. So -1/v^2 is a monotonic transformation.

[@SirArvy]

@@learnyoodles519 1/v^3? Or 2/v^3???

[@tarabradshaw5730]

What about U=x^2*y to 2ln(x)+ln(y)? If it is a monotonic transformation would it be 2(u) or 2ln(u)?

[@adamroberts6472]

I'm not sure I understand your question. If U=y*x^2, then ln(u) is a monotonic transformation to 2ln(x)+ln(y). The transformations 2(u) or 2ln(u) are completely different transformations, although they both would be legal monotonic transformations of the original U function.

[@VinaySingh-tv2nr]

It will be just ln(u)

[@bangjiedeng6272]

i like how you say it means yes, it is a monotonic transformation. sounds like yes all shitty profs, this is how simple it is.