What are the similarities and differences between perfect competition and a monopoly?

Monopoly and perfect competition are at two completely different ends of the spectrum. A monopoly only has one firm because of strong barriers to entry that prevent all new firms from entering the market. In perfect competition, on the other hand, there are no barriers to entry, so there are "many" firms. Due to the lack of competition faced by a monopoly, these firms may earn profits in the long run. In perfect competition, however, if positive profits are being earned, new firms will enter the market, causing the profits of existing firms to be reduced. This will continue as long as positive profits are being earned, meaning that all firms in perfect competition earn zero profits in the long run.

The main similarity between the two markets is that both maximize their profits by producing at the output level where the marginal revenue equals the marginal cost. With perfect competition, however, the price is determined by the market, so the price is equal to marginal revenue. Monopolies, on the other hand, are price setters, so the price is greater than the marginal revenue.