Knowledge that Transforms

The sequential nature of activities like research, development, or exploration requires optimal funding criteria to take account of the fact that subsequent funding decisions will be made throughout the future. Thus, there is a continual possibility of reviewing a project's status, based on the latest information. After setting up a model to capture this feature, optimal funding criteria are investigated. In an important special case, an explicit formula is derived. As well as throwing light upon the nature of development activities, the analysis is also relevant to the general theory of information gathering processes.

[Understanding of the relationship between producer choice of product qualities and consumer preferences has been enhanced by the development of models specialized to a particular quality attribute--durability. Durability choice is invariant with respect to market structure under certain conditions but capital market imperfections and income taxes can upset this strong independence result. Income taxes are shown to mimic the effect of a capital market distortion on a monopolist selling a durable. Moreover, contrary to previous results the tax can increase as well as lower durability. A tax on "true income" is neutral in its effect and hence tax reform provides an alternative to regulatory control of product life.]

Akira Yamazaki, Diversified Consumption Characteristics and Conditionally Dispersed Endowment Distribution: Regularizing Effect and Existence of Equilibria, Econometrica, Vol. 49, No. 3 (May, 1981), pp. 639-654

[If independent observations x are drawn from the distribution located at @m, f (x; @m)=c"3 exp[-g(x -@m)], and if g is symmetric and strictly convex, then the maximum likelihood estimate of μ lies between the smallest and largest folded sample observations. If the distribution has fatter tails than a normal distribution, then the maximum likelihood estimate lies between the smallest and largest means of trimmed subsamples. If the distribution is assumed to be symmetric and unimodal, the centers of tight clusters of observations can be maximum likelihood estimates. If observations are not independent, then there is no bound: given any example any number is a maximum likelihood estimate for some sampling distribution. Stationary is not sufficient to bound the estimate between the minimum and maximum observations.]

This paper presents a model of general equilibrium stability in which agents understand that they are not at equilibrium. Rather, agents expect prices to change and contemplate the possibility that they may not be able to complete their own transactions. They optimize their actions taking account of such price changes and transaction constraints. It is shown that a necessary condition for instability is the continuing perception of new, previously unforeseen opportunities (real or imagined). Without this, old opportunities will be arbitraged away and the system will converge to equilibrium. The equilibrium approached will depend on the history of the system and may not be Walrasian if transaction constraints are present.

We consider economies with preferences drawn from a very general class of strongly convex preferences, closely related to the class of convex (but intransitive and incomplete) preferences for which Mas-Colell proved the existence of competitive equilibria [13]. We prove a strong core limit theorem for sequences of such economies with a mild assumption on endowments (the largest endowment is small compared to the total endowment) and a uniform convexity condition. The results extend corresponding results in Hildenbrand's book [8]. The proof, which is based on our earlier result for economies with more general preferences [2], is elementary.