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Let us consider a function $F$ twice differentiable, concave and let $x_1,\cdots,x_n\geq 0$, $\sum x_i=1$, $c>0$. When can the argmax for $\prod_{i=1}^n F(x_i)$ and argmax for $\prod_{i=1}^n (F(x_i)+c)$ be equal?

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What is $c$? A arbitraty number? And what you mean with argmax? The maximum? –  Umberto Jan 10 at 7:52
    
$c>0$, argmax is the argument for which we will obtain the maximum value –  fryderyk Jan 10 at 8:54
    
Sorry. Can you define argmax a bit better? $\prod_{i=1}^n F(x_i)$ is not a function of variable. Is a number (given $n$). So which argument are you talking about? –  Umberto Jan 10 at 11:05

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