This paper examines some implications of the observation that the same Lagrange multiplier test is sometimes appropriate for quite different alternative hypotheses. A characterization of the class of such alternatives is developed which suggests a simple approach to testing for misspecification, and the consequences for finite sample power properties are examined by Monte Carlo experiments.

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.]