This paper extends the Cass criterion for production efficiency to include uncertainty and uses it to show that a stock-market equilibrium in an overlapping-generations model with production uncertainty is efficient. It also develops a no-bubbles asset-pricing formula. Results are compared with...

The colony patterns of Bacillus circulans on agar medium were experimentally investigated to study about the growth mode transition. From the optical microscopic observation, the bacteria distribute inside the medium, that is, the colony grows three-dimensionally (3D) in the soft agar condition...