Notes on Continuous Dynamic Models: the Benhabib-Farmer Condition for Indeterminacy

In these notes, starting from the discrete case, we provide some useful insights on the way in which are derived the necessary (and sometime) sufficient conditions for the solution of a maximum problem developed in continuous time. Moreover, we exploit such conditions to solve the Benhabib-Farmer (1994) model deriving the condition for an indeterminate equilibrium path. Finally, referring to the equilibrium condition of the labour market, we explain the mechanism that in the one-sector optimal growth model leads prophecies to be self-fulfilling.