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I am looking for a utility function that will lead to the following demand

$$\alpha p^{\epsilon}$$.

I know it is most likely a CES utility since the elasticity of demand is constant and this is usually consequence of CES utility.

I also believe that the second good most likely was set as the numeare good or that the function must be a special case when the relative prices do not matter.

I am also little bit confused because of the positive relationship between price and demand I guess it must be a Giffen good.

I tried to solve several problems with different CES utilities but did not ever got this. I am not sure if there is any analytical way how to get from result like this to initial problem, I am just using trial and error, I would appreciate any help.

Herr K.
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1muflon1
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  • It is not a giffen good since (most likely) epsilon is a negative number in your case. – BB King Dec 17 '18 at 14:05
  • @BBKing if that’s the case there is no problem but then why would be the problem set up like this elsewhere in the notes if there is supposed to be negative exponent somewhere it’s just with - sign – 1muflon1 Dec 17 '18 at 18:30
  • Elasticity of demand is often simply a negative number. When it is defined as a positive number, then in these functions you would see a minus sign in front of epsilon. I agree that it is confusing. – BB King Dec 17 '18 at 18:39

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