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\begin{equation} \left(\frac{u^_{j}}{- \alpha^}\right) = \left(\frac{\betaVec^{}}{- \alpha^{}}\right)' \xVec_{j} + \left(\frac{\alpha^{}}{- \alpha^{}}\right) p_{j} + \left(\frac{\varepsilon^{}_{j}}{- \alpha^{}}\right), \quad\quad \left(\frac{\varepsilon^{}_{j}}{- \alpha^{}}\right) \sim \textrm{Gumbel} \left(0, \frac{\sigma^2}{(- \alpha^{*})^2}\frac{\pi^2}{6} \right) \label{eq:utilityWtpScaled} \end{equation}
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