A numerical evaluation of the “dead loss” associated with a nonoptimal situation (in the Pareto sense) of an economic system is sought. Use is made of the intrinsic price systems associated with optimal situations of whose existence a noncalculus proof is given. A coefficient of resource utilization yielding measures of the efficiency of the economy is introduced. The treatment is based on vector-set properties in the commodity space.

Introduction

The activity of the economic system we study can be viewed as the transformation by n production units and the consumption by m consumption units of / commodities (the quantities of which may or may not be perfectly divisible). Each consumption unit, say the ith one, is assumed to have a preference ordering of its possible consumptions, and therefore an index of its satisfaction, si. Each production unit has a set of possibilities (depending, for example, on technological knowledge) defined independently of the limitation of physical resources and of conditions in the consumption sector. Finally, the total net consumption of all consumption units and all production units for each commodity must be at most equal to the available quantity of this commodity.