A general extension theorem for binary relations

Article Abstract:

A general extension theorem for binary relations to linear, or strict linear, orders is proven and applied to various samples from welfare economics. The duality structure of binary relations is exploited so as to easily derive a general intension theorem. A special case is the proof that a complete, negatively transitive relation is the union of linear orders embedded within it. Another is that an irreflexive and negatively transitive relation is the union of strict weak orders embedded within it.

Mathematical logic, Linear systems, Binary system (Mathematics), Symbolic and mathematical logic

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Arrow's theorem in public good environments with convex technologies

Article Abstract:

The applicability of Arrow's theorem in public good environments is evaluated using fixed economic preferences and a feasible set of alternatives that provide public good. The theorem has restrictive properties and insufficient requisites when applied in spatial environment conditions which imposes a budget consideration. Procedures that use social choice functions provide optimal requirements that are absent in the theorem's original version that considers social welfare functions.

Externalities (Economics), Public goods, Convex sets

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The substitution theorem

Article Abstract:

A formulation of the substitution theorem in economics is presented via a model that has a finite number of commodities and labor units. As generally conceived, the substitution theorem states that an economy having many commodities but only one input, such as labor, would not be responsive to demand changes. This means that no substitution of inputs would occur under dynamic conditions.

Substitution (Economics)

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