Final answer:
The average revenue curve under perfect competition is horizontal, not downward-sloping, because a firm in perfect competition faces a perfectly elastic demand at the market price. Total revenue for such a firm increases at a constant rate, with the slope of that increase equal to the good's price.
Step-by-step explanation:
The statement that the average revenue curve under perfect competition is a downward-sloping curve is false. In a perfectly competitive market, a firm perceives the demand curve that it faces to be perfectly elastic, meaning it is a horizontal line rather than downward-sloping. This reflects the fact that the firm can sell any quantity of output at the market price but has no power to influence that price. Any single firm's production is too small a fraction of the total market to affect the market price.
For a perfectly competitive firm, total revenue increases at a constant rate as output increases, because the price remains constant regardless of quantity sold. The slope of the total revenue curve is equal to the price of the good. Consequently, the maximum profit for the firm occurs at the quantity where the gap between total revenue and total cost is largest, where marginal revenue equals marginal cost, and not because the average revenue curve is downward-sloping.