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.
An expository note on individual risk without aggregate uncertainty
Abstract In economies where agents bear some risk, the analysis would often be facilitated by the assumption that the risks are i.i.d. and disappear in the aggregate. A formal appeal to the law of large numbers requires the consideration of a sequence of finite economies. In an economy with a continuum of agents there are countable families of sets for which it is impossible for a law of large numbers to be valid. With countably many agents and a finitely additive measure, independence is compatible with the law of large numbers.
Comparative studies of α-Lactalbumin and lysozyme: Echidna lysozyme
Summaryα-Lactalbumin is a modifier protein for galactosyl transferase in the biosynthesis of lactose and lysozyme catalyses the cleavage of β(1–4) glycosidic linkages. It is now generally believed that α-lactalbumin and lysozyme have diverged from a common ancestor. Comparative studies of these proteins from several species are reported here.The presence of lactose and lactose synthetase activity is shown in mature milk samples from a variety of placental mammals (eutheria) and a pouch bearing mammal (marsupialia). The isolation of the α-lactalbumins involved and their properties are compared.The position is different in the milk samples of monotremes. The α-lactalbumin, lactose and lactose synthetase activity levels in the two platypus samples studied are very low. The levels of lactose and lactose synthetase activity in some echidna(Tachyglossus aculeatus) samples are low, but appreciable in others. No α-lactalbumin is present. The lysozyme activity is appreciable, some samples containing a different lysozyme from that present in others. One of these (designated echidna lysozyme I) is capable of lactose synthetase modifier activity in the presence of bovine “A protein”.The properties of this lysozyme are compared with those of lysozymes and α-lactalbumins from a variety of species and their significance is discussed.