le chatelier's principle is used as a very simple way to predict the effect of a change in conditions on a chemical equilibrium. . however, several studies have reported the violation of this principle, still there is no reported simple mathematical equation to express the exact condition of violation in the gas phase reactions. in this article, we derived a simple equation for the violati...

This paper considers an overlapping generations model of endogenous fertility, savings and intergenerational transfers. While subgame perfect equilibrium notion is more relevent to analyze individual incentives in this set-up, due to computational complexity and lack of an appropriate equilibrium selection theory, most previous studies employed the open-loop Nash equilibrium. This paper introdu...