Abstract The article applies mathematical control theory to the analysis of a simple model of an accounting and budgeting problem. The objective is not only to make the model operational for practical applications but also to use the framework and results of mathematical control theory in order to get new insights into accounting and budgeting problems. The article shall be primarily concerned with the process of the operations of the firm looked at from an accounting standpoint. In accounting, a firm is represented by a set of quantities that indicate the stocks of assets of various types that are under the control of the firm and the firm's activities are indicated by the changes in these quantities. Using mathematical notation one can say that the firm at time t has a vector x(t) whose components indicate the physical amounts of each asset the firm has at time t. The results of the activities of the firm between t1 and t2 are measured by the vector difference x(t2)-x(t1). It is found that firm's activities at time t are indicated by &xdot;(t), which in turn affects x(t).

Michael J. Hamburger, Gerald L. Thompson, Roman L. Weil, Jr., Computation of Expansion Rates for the Generalized von Neumann Model of an Expanding Economy, Econometrica, Vol. 35, No. 3/4 (Jul. - Oct., 1967), pp. 542-547

Suresh P. Sethi, Gerald L. Thompson, Applications of Mathematical Control Theory to Finance: Modeling Simple Dynamic Cash Balance Problems, The Journal of Financial and Quantitative Analysis, Vol. 5, No. 4/5 (Dec., 1970), pp. 381-394

Abstract In this paper we have devised methods for allocating overhead, charges on the basis of mathematical programming models of the firm's production and sales possibilities. The basic scheme was to charge products on the basis of their utilization of the scarce resources of the firm. The prices for use of these resources were obtained from the dual variables associated with the constraints of profit-maximizing programming models. Special attention was given to traceable and avoidable overhead and overhead subsidies that arise because of sales and production interdependencies or managerial constraints. Our objective, in all of these procedures, has been to devise a method for allocating overhead that does not distort the relative profitability of products so that managers would make identical product related decisions both before and after the overhead allocation. As such, the method captures a principal benefit of direct costing analysis while significantly extending this benefit to recognize scarce resource utilization and interaction with other products in reporting profitability. At the same time, the method avoids a difficulty of direct costing systems in that it is a full costing system with all overhead being allocated to products. Also the availability of the original programming model (before any overhead allocations) facilitates marginal analysis for short term product related decisions and expansion of scarce resources.