. . . In the legal field, lawyers are granted the power to vet their own membership by the state. That’s a monopoly. Same thing goes for the practice of medicine.
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I guess I see your reasoning, but would that make the practice of driving a monopoly, too? Since the state requires that drivers pass tests administered by other drivers . . . It’s all a matter of how you define something, I suppose. IMHO, a monopoly eliminates competition and allows the monopolizing entity to decide the price of the monopolized goods or services. There is a large variation in the fees of the professional services that you mention here, so I would disagree with the breadth of your definition.