The article is a natural continuation of previous author studies related to the study of Arrow-Debreu (AD) equilibrium with prices that are not countably cannot be implemented in sequential asset markets under standard portfolio constraints and general equilibrium, wariness and efficient bubbles. The authors reexamined some questions on the efficient consumption and assets accumulation in the light of a reformulation on the way infinite lived agents discount the future. An extremely useful and interesting model has been developed to analyze the existence of efficient stochastic bubbles. They have also been investigated the variation of the assets' price and its relationship with bubbles and their crashes, proving that the crashing of bubbles will increment the variation of the assets' price in the long-run. An appropriate (non-trivial) example is given, which is in line with the proposed model theory. The investigations are of interest to researchers of this topic.