Final answer:
A firm in a duopoly with differentiated products does not lose all its customers when the rival lowers its price because each firm's product is distinct, and customers have brand or product preferences. The firms face a downward-sloping demand curve that is more elastic than a monopoly but less so than a perfectly competitive market.
Step-by-step explanation:
The question pertains to a duopoly with differentiated products. Among the given options, the correct statement is A: A firm does not lose all its customers when its rival lowers the price of its product. In a duopoly with differentiated products, each firm has a downward-sloping demand curve, which resembles a monopolistically competitive market. This implies that firms have some degree of market power, and consumers may prefer one firm's product over the other for various reasons such as brand loyalty, product features, or quality.
Firms in such a market can adjust their prices without losing all of their customers because the products are not perfect substitutes. If one firm lowers its price, it may attract some customers from the rival firm, but not all, as some customers may continue to purchase from the original firm due to their preference for that particular brand or product variant.
Therefore, the demand curve for firms in a duopoly with differentiated products is neither perfectly inelastic nor perfectly elastic, but rather more elastic than that of a monopoly and less elastic than that of a perfectly competitive market.