This paper shows that control through decentralization can be affected in general if additional information in the form of preemptive goals is delegated to individual units as well as prices. It is shown that the procedure is a robust one and results in small errors in profit. The technique of preemptive goals providing further control advantages in an economy where structural change is taking place over time as reflected by changing technological coefficient matrices of individual units is indicated.

The article discusses the use of mathematical models across a variety of disciplines and practices. Mathematical models, naturally, are represented by means of mathematical relations. The mathematical models which will be of interest in this article generally proceed via the special kinds of mathematical relations called "functions," which are used to represent some or all of the relations. Double-entry accounting has been used as a basis for planning and control at both economy-wide and individual-enterprise levels. This is to say that double-entry accounting provides a tool of great utility which can be employed in a variety of ways and contexts. Beyond the convenience of moving back and forth between accounting and interindustry analyses, the mathematics associated with this modeling has permitted a variety of other uses and extensions. The examples in this article should make it clear, however, that this is not the end. Still more may be available from further research in model equivalences and related explorations. Indeed the "models" definition we introduced in the first section of the preceding paper is designed to underscore the potential value of such continuing explorations.