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