Bubbles and chaotic dynamics in economies with externalities
The present thesis deals with some consequences of the existence of external effects a la Homer, i.e. positive spillovers from the capital stock onto the efficiency of labour, and is mainly considering problems of discrete dynamics in the absence of any intrinsic (i.e. exogenous) shock. In the first chapter, using a one-sector three- period OLG model with borrowing constraints, it is shown that the standard result stating that, in the presence of externalities, any simple tax/subsidy policy undertaken to get rid of a bubble on an intrinsically useless asset creates an IOU which has exactly the same negative effects as the bubble itself, fails if there are agents who must borrow at some moment of their life. The other three chapters are mainly studying the problem of endogenous fluctuations in competitive equilibrium models. The second chapter looks at the possibility of Hopf bifurcations in the dynamical system characterizing a two-sector OLG economy meeting all neo-classical assumptions from the point of view of the private sector, and its ILA analogue : it demonstrates the existence of economies with stable closed orbits, derives some conditions on the parameters and compares the results to the continuous time modelization, concluding to a non robustness with regard to the time structure assumption. The third chapter is considering endogenous fluctuations in self-sustaining growth : using the same framework as previously, but under another assumption on the externalities, we establish that even if production inputs substitute perfectly and savings increase monotonically with the interest rate, cycles or even chaotic trajectories of the growth rate are possible. We show that this requires a strong externality in the consumption good sector in the absence of bubbles or sunspots, but not necessarily in their presence. Furthermore, we prove the existence of economies where, in the absence of any intrinsic uncertainty, the only possible equilibria involve bubbles or sunspots. The last and very short fourth chapter is a critical note on a recently published paper ; its main purpose is to show why current mathematical knowledge does not allow to sustain the claim of chaos in the proposed ILA framework.