Final answer:
A monopolist typically operates where demand is elastic, shutting down only when price is below AVC to minimize losses. The inelasticity of demand widens the gap between price and marginal revenue, and while monopolies can earn economic profits, it is not guaranteed in the long run.
Step-by-step explanation:
The question asks about the characteristics of a monopoly and related economic concepts. One of the statements posits that a monopolist produces on the inelastic portion of its demand curve; however, a profit-maximizing monopolist actually prefers to operate where the demand is elastic, where lowering the price leads to a proportionally larger increase in quantity demanded, thereby increasing total revenue.
Another statement claims that in the short run, a monopoly will shut down if price (P) falls below average variable cost (AVC). This is true because the firm would not be able to cover its variable costs, and shutting down would minimize losses, leaving only fixed costs unpaid.
The assertion that the more inelastic the demand, the closer marginal revenue is to price, is incorrect. Actually, the more inelastic the demand, the greater the difference between price and marginal revenue, because a firm with inelastic demand can increase the price without significantly decreasing quantity sold, which separates marginal revenue from the price.
Finally, the claim that a monopolist always earns an economic profit is not necessarily true. While monopolies may have the potential to earn economic profits due to market control, in the long term, economic profits can be eroded by various factors, including new entrants if the market is contestable, regulatory intervention, or changes in demand.