Power Utility Function Inverse

Question

If power utility is $p = \frac{x^{1- \gamma} -1}{1 - \gamma}$ then is the inverse of the power utility function just $\frac{1 - \gamma}{p^{1- \gamma} -1}$?

The inverse of the function $f(x)$ usually means the function $g$ such that $g(f(x))=f(g(x))=x$... — 5xum, Oct 24 '18 at 09:32
I don't know what "power utility" is, and I don't know what it is you are trying to calculate, but you do not have the inverse function of the first function, no. But you might have what you need. I can't know that. — 5xum, Oct 24 '18 at 09:37
It would be better if you give the definition of power utility. — Kemono Chen, Oct 24 '18 at 09:39
It's also called the isoelastic utility function does that help? — user6259845, Oct 24 '18 at 09:42
Do you want to compute the inverse function of $$p=\frac{x^{1-\gamma}-1}{1-\gamma}$$? — Dr. Sonnhard Graubner, Oct 24 '18 at 09:45

score 0 · Answer 1 · answered Oct 24 '18 at 10:00

Given that $p= \frac{x^{1-\gamma}- 1}{1-\gamma}$ we find the inverse by solving for x- Multiply both sides by $1-\gamma$: $p(1-\gamma)= x^{1-\gamma}-1$. Add 1 to both sides: $p(1-\gamma)+ 1= x^{1-\gamma}$.

Finally, take the $1-\gamma$ root of both sides: $(p(1-\gamma)+ 1)^{\frac{1}{1-\gamma}}= x$.

Power Utility Function Inverse

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