Alan Greenspan once said monopolies cannot exist in a free market...?

Greenspan did not say that monopolies cannot exist in the free market only that coercive monopolies cannot exist. A coercive monopoly is one which maintains its monopoly through force usually via the government. In a free market monopolies can exist but only by providing a good or service so well that competition is unable to arise, or compete, a good example of this is alcoa, which produced aluminum so efficiently and cheaply that no one else could successfully challenge them. They were eventually brought down however by the government. In a free market the odds of doing so well as to negate competition is very hard however, because as a general rule someone else can innovate a better product and gear their business accordingly, where as the monopoly would have to retool their entire operation which would be extremely costly. Also in a free market, abusing ones monopoly would be all but impossible for once profit margins increase competition will return. And any subsequent price war would only serve to benefit the consumer, and per unit would hurt the larger company more. As a side note, i would like to point out that we do not live in a free market economy, we live in a "mixed market" economy, which is a fancy way of saying socialism, where the government readily intervenes in the economy, and simply leaves the operational control of a business in private hands while the state itself remains supreme over all. Able to control the economy through a variety of means, such as: taxation, quotas, interest rates, subsidies, tariffs, duties, anti-trust laws, and patent confiion, etc.