Information and the Existence of Stationary Markovian Equilibrium
We describe conditions for the existence of a stationary Markovian equilibrium when total production or total endowment is a random variable. Apart from regularity assumptions, there are two crucial conditions: (i) low information—agents are ignorant of both total endowment and their own endowments when they make decisions in a given period, and (ii) proportional endowments—the endowment of each agent is in proportion, possibly random, to the total endowment. When these conditions hold, there is a stationary equilibrium. When they do not hold, such an equilibrium need not exist.
A strategic market game with secured lending
We study stationary Markov equilibria for strategic, competitive games, in a market-economy model with one non-durable commodity, fiat money, borrowing/lending through a central bank or a money market, and a continuum of agents. These use fiat money in order to offset random fluctuations in their endowments of the commodity, are not allowed to borrow more than they can pay back (secured lending), and maximize expected discounted utility from consumption of the commodity. Their aggregate optimal actions determine dynamically prices and/or interest rates for borrowing and lending, in each period of play. In equilibrium, random fluctuations in endowment- and wealth-levels offset each other, and prices and interest rates remain constant. As in our related recent work, KSS (1994), we study in detail the individual agents' dynamic optimization problems, and the invariance measures for the associated, optimally controlled Markov chains. By appropriate aggregation, these individual problems lead to the construction of stationary Markov competitive equilibrium for the economy as a whole. Several examples are studied in detail, fairly general existence theorems are established, and open questions are indicated for further research.
Erratum to: Characterization and gene cloning of a maltotriose-forming exo-amylase from Kitasatospora sp. MK-1785
A maltotriose-forming amylase (G3Amy) from Kitasatospora sp. MK-1785 was successfully isolated from a soil sample by inhibiting typical extracellular α-amylases using a proteinaceous α-amylase inhibitor. G3Amy was purified from the MK-1785 culture supernatant and characterized. G3Amy produced maltotriose as the principal product from starch and was categorized as an exo-α-amylase. G3Amy could also transfer maltotriose to phenolic and alcoholic compounds. Therefore, G3Amy can be useful for not only maltotriose manufacture but also maltooligosaccharide-glycoside synthesis. Further, the G3Amy gene was cloned and expressed in Escherichia coli cells. Analysis of its deduced amino acid sequence revealed that G3Amy consisted of an N-terminal GH13 catalytic domain and two C-terminal repeat starch-binding domains belonging to CBM20. It is suggested that natural G3Amy was subjected to proteolysis at N-terminal region of the anterior CBM20 in the C-terminal region. As with natural G3Amy, recombinant G3Amy could produce and transfer maltotriose from starch.