\begin{equation}\label{Ionx}
\begin{split}
x_I=\dfrac{\partial x}{\partial I}=\dfrac{t'(I)\pi^{*}_{x^*x^*}}{D}>0 \\
x^{*}_{I}=\dfrac{\partial x^*}{\partial I}=-\dfrac{t'(I)\pi^{*}_{x^*x}}{D}<0
\end{split}
\end{equation}
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