Steady state analysis and endogenous fluctuations in a finance constrained model

The overlapping generations model, like the one studied by Reichlin (1986) or Cazzavillan (2001), can be interpreted as an optimal growth economy where consumption is totally constrained by capital income. In this paper, we analyze steady states and dynamic properties of an extended version of such framework by considering that only a share of consumption expenditures is constrained by capital income. We notably establish that the steady state is not necessarily unique. Moreover, in contrast to the intuition, consumer welfare can increase at a steady state following a raise of the share of consumption constrained by capital income, i.e. the market imperfection. Concerning dynamics, we show that endogenous fluctuations (indeterminacy and cycles) can emerge depending on two parameters : the elasticity of intertemporal substitution in consumption and the elasticity of capital-labor substitution. Such fluctuations appear when these two parameters take values in accordance with empirical studies and without introducing increasing returns or imperfect competition.