Microeconomic Theory of Individual Agents

Abstract

The notion of duality is used differently and is often misleading.¹ Usually, the attention is drawn to certain symmetry properties of statements or optimization problems. For example, we can formulate in accordance with mathematical logic the subsequent duality principle for the statements A and B which are either “true” or “false”: if the word “and” is exchanged everywhere with the word “or” in the two semantically equivalent statements H₁ and H₂ which are only composed of the functional words “and”, “or”, and “not”, then the resulting dual statements H₁^* and H₂^* are semantically equivalent, too.² When the text stresses this dual view of different statements, then such a substitution principle is intended bearing the symmetry properties in mind.³