Capital-labor substitution and competitive non-linear endogenous business cycles

We develop simple geometrical methods to study local indeterminacy, bifurcations, and stochastic (sunspot) equilibria near a steady state, in nonlinear two dimensional economic models. We present in particular a simple, constructive, geometrical characterization of the support of stochastic sunspot equilibria, not only arbitrarily near a steady state, but also along local bifurcations. These methods are applied to a simple aggregative model to study in particular the influence of capital-labor substitution and of the aggregate labor supply wage elasticity on the occurrence of competitive endogenous deterministic or stochastic fluctuations.