Non-linear endogenous fluctuations with free entry and variable markups

The paper explores the effects of markup variability, associated with free entry of Cournotian firms, on the occurrence of local indeterminacy, local Hopf bifurcations and multiplicity of steady states. It uses an overlapping generations model with capital, in which differentiated intermediate goods are produced with constant marginal cost plus a positive fixed cost. If the markup factor were constant (the case of no free entry or the case of zero fixed costs leading to the perfectly competitive outcome), no local endogenous fluctuations or multiplicity of steady states can emerge, unless factors of production are complementary. On the contrary, with any positive (variable) market power, indeterminacy and multiplicity of steady states is possible for any value of the elasticity of technological substitution, and local Hopf bifurcations may also emerge, provided (variable) market power is high enough.