Economic profit in the long run is possible for both a pure monopoly and a pure competitor, possible for a pure monopoly but not for a pure competitor, impossible for both a pure monopolist and a pure competitor, and only possible when barriers to entry are nonexistent.

 In economic theory, whether an entity can earn economic profit in the long run depends on the market structure and the presence of barriers to entry. Let's break down the possibilities:

1. Economic profit in the long run is possible for both a pure monopoly and a pure competitor: This scenario is not typically true. In a pure competition market (also known as perfect competition), there are many firms, no barriers to entry, and the products are homogenous, meaning in the long run, firms will only earn normal profit. Any economic profit is competed away as new firms enter the market, increasing the supply until the price drops to the level of average total cost.

2. Economic profit in the long run is possible for a pure monopoly but not for a pure competitor: This statement best reflects economic theory. A pure monopoly, having control over the entire market for a good or service with high barriers to entry, can maintain economic profits in the long run because new competitors cannot easily enter the market. The monopoly can set prices above marginal cost without worry that competitors will undercut them, unlike firms in perfect competition.

3. Economic profit in the long run is impossible for both a pure monopolist and a pure competitor: This is not accurate for a pure monopolist. While pure competitors cannot earn economic profits in the long run due to competition, a monopolist can continue to earn economic profit as it has no competition and faces barriers that protect its market.

4. Only possible when barriers to entry are nonexistent: This is incorrect. When barriers to entry are nonexistent or low, the market resembles a perfectly competitive one where firms cannot earn long-run economic profit. High barriers to entry actually help firms maintain economic profits by protecting them from new competition.