Sunspot in Economic Models with Externalities

In this paper, we consider a general class of endogenous growth two-sector models with externalities (see Mulligan and Sala-i- Martin, 1993, Venturi 2014): the model deals with the maximization of a standard utility function. Following Benhabib, Nishimura, and Shigoka, 2006, we construct cycles (Hopf cycles) and sunspots equilibria in a general class two-sector model. We are able to show that optimal control model with externalities possess stochastic characteristics which arise from indeterminate equilibrium closed to steady state and cycles (Hopf cycles) (see Chiappori and Guesnerie, 1991, Benhabib, Nishimura, and Shigoka, 2006. Slobodyan 2009). As applications of this general class of models, we consider the models due to Lucas, Romer, and Bella (a disposal natural resource model). In our formulation, the stochastic approach suggest a way out from the cycle trap (the poverty environments trap, see Slobodyan 2009).