1. Introduction The development of the principle of complementarity in the 20-s of the twentieth century by the outstanding Danish physical scientist, Nobel laureate Niels Bohr (1885-1962), to explain quantum mechanics phenomena was a convincing demonstration of exceptional cognitive abilities of dialectical research method. Experimental physical scientists investigating quantum objects faced apparently conflicting results: these objects manifested themselves both as corpuscles and as waves. "The idea of a photon with all its fruitfulness,--Niels Bohr wrote in this regard,--issued completely unforeseen dilemma, since any corpuscular radiation pattern is clearly incompatible with interference phenomena, which represent an important feature of radiation processes and can be described only by means of the wave pattern" (Bohr, 1958, 34). By studying this kind of contradictions, N. Bohr concluded that these experimental data in fact not exclude but complement each other, characterizing objectively existing properties of quantum phenomena. According to the principle of complementarity, data obtained under different experimental conditions cannot be covered by a single pattern; these data shall be regarded rather as complementary in the sense that only the aggregate of various phenomena may provide more complete picture of object properties (Bohr 1949). Relying on the principle of complementarity, as a general philosophic regularity, N. Bohr stated a thesis that "opposites are complementary", i.e. that the unity of opposites is an indispensable additional characteristic of the phenomenon of nature and society which the researcher reaches as soon as he gets into their essence. "... In cognitive process, to reproduce object integrity, as explained by A. Pozner, one shall use mutually exclusive "additional classes of categories, each applicable under their specific conditions" (Pozner, 1962, 52). 2. Three--Tier Rule In terminology, this means that intrinsic nature of the phenomena studied, in principle cannot be expressed by a single category whatever significant and universal it is. At least three categories are required to solve this task. It is a kind of Three-Tier Rule. One category is required to describe the phenomenon per se (so to say, the basic phenomenon), not reducible to any of its inherent features, and the other two additional categories are needed to express its dualistic internally contradictory essence. Niels Bohr, facing the fact of the unity of opposites in the study of quantum phenomena, as L.I. Ponomarev explains, "... came to the conclusion that this is not an exception, but a general rule: any truly profound natural phenomena can not be unambiguously determined by the words of our language, and requires at least two mutually exclusive additional categories for its determination" (Ponomarev, 1984, 158). It is demonstrative that N. Bohr considered it necessary to apply the principle of complementarity to the analysis of not only physical, but also biological and social phenomena significantly differing from them. He wrote: "The integrity of living organisms and characteristics of humans having consciousness, as well as human cultures, are traits of integrity, which reflection requires a typical complementary way of description" (Pozner, 1962, 52). 3. Structural Similarity of Economic Phenomena and Phenomena of the Micro World Economic phenomena with all their huge difference from atomic phenomena are strikingly similar in their structural properties to microworld objects--atoms and their constituents--protons, neutrons and electrons etc., which form the matter of our Universe. First, attention is drawn to the fact that they both are inherently dual. As an American physical scientist and philosopher F. Capra says: "At the atomic level, matter has dual aspect: it appears as particles and as waves" (Capra, 2010, 190). As an English biophysicist and social scientist Dave Hooks explains in his work "Quantum Theory of Political Economy", that quantum theory has discovered many dialectical contradictions; the most famous of them is wave-particle duality. …