"…Moreover, Rothbard refuted every alternative theory as nonsense, nonoperational, or false. It is nonsense, for instance, to define a monopolist as someone who has control over his price (a “price-searcher”). Every businessman has perfect control over his price (and no control at all over the quantity bought at that price by consumers). Hence, under this definition, no one exists who is not a monopolist. Likewise, is it nonsense to define a monopolist as “the only seller of any given good,” for in an objective sense, every seller of every product is always the only seller of his own unique product (brand). Thus, everyone is a monopolist with a one-hundred-percent market share of one’s own product. Yet, this circumstance does not affect in the slightest that each entrepreneur must compete at all times with every other entrepreneur for consumer spending, regardless how unique or different one’s goods may be.
On the other hand, in a subjective sense, no seller of anything can ever be established definitely as a monopolist. According to this interpretation, the term “given good” means “a good as defined by consumers.” Thus, the determination of whether or not the seller of something is its only seller, or of how large his market-share is, depends on the consumers’ definition of what this good is; that is, on their classification of particular physical objects into various groups of homogeneousgoods. Not only can such classifications continually change, but different consumers can classify the same physical objects differently. Hence, in this sense the term monopolist becomes practically useless and non-operational, and all attempts to measure a product’s market share must be considered futile…”
— Hans-Hermann Hoppe, Economics, Science and Liberty