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Joe I 05:19, 6 January 2006 (UTC)Reply

this and that

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Hello Coleca. For some people, wikipedia is a narcissistic venture. In anyone changes their text, for them it like smudging their very image, they react with derogatory language. In fact, such people actually have much to contribute - and they do - but their narcissism prevents other people from being constructive. C'est la vie. Politis 13:15, 31 January 2006 (UTC)Reply

Showing that the sum of conditional demand elasticity is zero

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Start with the definition of the cost function:

 

and use the envelope theorem to get

 

So, we can get the summation

 

 

 

The simpler solution is to notice that a scale change in prices does not change the optimal choice of x, so the conditional demand is homogeneous degree zero. Then by Euler's Theorem

 

so