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\subsection{Preferences}  Since productivity has a stochastic trend some variables will not be stationary.Indeed, stationary. Indeed,  in equilibrium all variables, excepting leisure, leisure --and therefore labor--,  will grow at constant expected rate, defining a Balanced Growth Path. In what follows, variables with tilde (i.e. $\tilde{C}, \tilde{Y}$, etc.)  are non-stationary. A social planner tries to maximize