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How large does a company have to get before its a monopoly?
The size of the firm has no implication on its monopoly status. The only condition for a firm to become a monopoly is that there are no other firms in the market. So, for example, if a firm controls a patent on some product, no other firm can enter the market. Therefore, regardless of how large the firm becomes (even if it just has 1 employee and sales of $10 per year), it will be a monopoly as long as the patent is in place since no other firms will be able to enter the market.