<p>At the microeconomics course I have to prove monotonic transformation of the function </p>

<p>U(x,y) = A(x^a)(y^b)</p>

<p>into </p>

<p>U(x,y) = (x^0.5)(y^0.5)</p>

<p>Since the MRS are ay/bx and x/y resp. I can obviously only prove that the transformaton isn't monotonic. </p>

<p>But the ordinal equivalence seems to be impossible to prove without having certain x &amp; y values at which I would compute the utility levels for each function. Is it possible to derive a general proof that I don't know?</p>

CC BY-SA 4.0
2019-12-27T08:54:14.377Z
What's the question again? You said, "I have to prove monotonic transformation of the function ... into ..." but I don't think that's a complete sentence.
Art
CC BY-SA 4.0
2019-12-27T11:28:35.500Z
Yes, that's all. I assume the type of transformation is the unspecified one that transforms the first function into the second one.
Svit
<microeconomics><utility>
How to prove monotonic transformation of the function and equivalence?
Svit
# How to prove monotonic transformation of the function and equivalence?

(Asked by: username_0 on 2019-12-26)

At the microeconomics course I have to prove monotonic transformation of the function

U(x,y) = A(x^a)(y^b)

into

U(x,y) = (x^0.5)(y^0.5)

Since the MRS are ay/bx and x/y resp. I can obviously only prove that the transformaton isn't monotonic.

But the ordinal equivalence seems to be impossible to prove without having certain x & y values at which I would compute the utility levels for each function. Is it possible to derive a general proof that I don't know?

**Tags:** microeconomics, utility

> **Comments:**
> **username_1**: What's the question again? You said, "I have to prove monotonic transformation of the function ... into ..." but I don't think that's a complete sentence.  
> **username_0**: Yes, that's all. I assume the type of transformation is the unspecified one that transforms the first function into the second one.  

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## 0 answers

