امنیت اجتماعی به عنوان تعادل مارکوف درمدل نسلهای تداخل کننده : یک یادداشت

I refine and extend the Markov perfect equilibrium of the social security policy game in Forni (2005) for the special case of logarithmic utility. Under the restriction that the policy function be continuous, instead of differentiable, the equilibrium is globally well defined and its dynamics always stable.

Summarizing, I have shown that assuming that the policy function has to be continuous, but not necessarily differ- entiable, results in an equilibrium that is valid globally for the economy studied in Forni (2005). Multiple expectational equilibria exist for values of C ∈[ C , ̄ C ] . If there is an equilibrium with positive intergenerational transfers, the policy func- tion is initially zero, later rises up to a maximum corresponding to k = k ss u , then decreases up to ̄ k , being zero thereafter. Thus, an economy that starts with a low level of capital will evolve to a steady state with a (relatively) high PAYGO tax rate and low capital intensity. Since this steady state is semi-stable, a perturbation can send the economy to another steady state with a lower PAYGO tax rate and higher capital intensity. The refinements made in this note, and the richer description of the dynamics, would also be useful to other politico-economic models that build on Forni (2005)