Objectively Determined Valuations

a term used to designate partial derivatives of an objective function, taken in relation to constraints in problems of linear or convex programming. The term was introduced by Soviet scientist L. V. Kantorovich in 1959 and is mostly used in solving economic problems by mathematical programming. It is analogous to the terms “optimal valuations,” “dual valuations,” “shadow prices,” and “resolving multipliers.”

In economic problems objectively determined valuations show the economic consequences when an additional unit of a particular production component is introduced into the economic process. The dimensionality of the objectively determined valuations corresponds to the dimensionality of the criterion of optimality (monetary, physical, or standardized physical units of measure). Objectively determined valuations follow from the conditions of the statement and solution of an economic problem. They are determined by the aggregate of concrete economic factors that are taken into account in the mathematical formalization of production and economic activity. Thus they are an effective means of analyzing current economic activity, making it possible to identify and quantitatively evaluate “bottlenecks.” Objectively determined valuations make it possible, assuming a certain stability, to indicate ways of improving the indexes of the work of an economic unit.

Depending on how the problem is formulated, objectively determined valuations may reflect the production and economic conditions of particular sections (or workshops), enterprises, sectors, regions, and the national economy as a whole. In the last case the valuations obtained can theoretically be interpreted as the prices of the optimal economic plan or as social (rent) valuations of resources (natural resources, capital assets and labor). They describe growth in the criterion of optimality of the socialist system (growth in prosperity and the level of satisfaction of social needs) resulting from incremental growth in the production of particular types of output (or an increase in a resource). They also describe the acceptable maximum of expenditure to produce an additional unit of this output. Objectively determined valuations keep this characteristic only for small economic changes, and their values ordinarily change with the development and modification of plans for the expansion of production. The organic link between objectively determined valuations and a plan may clearly be seen in mathematical economic problems of any level, both in static and dynamic models, where they make it possible to compare expenditures and effects at different time periods.

Objectively determined valuations have also been treated in depth in the works of A. L. Lur’e and in the conception of differential expenditures in the national economy worked out by V. V. Novozhilov. The problem of objectively determined valuations is currently being further developed and is the subject of discussion by Soviet and foreign economists.