In a perfectly competitive market within a constant-cost industry, the long-run supply curve is perfectly elastic. This means it's a straight horizontal line. This occurs because, in such markets, numerous firms are producing and selling identical products. As a result, no single firm can influence the market price by independently altering its output level.

When firms produce at their lowest average total cost (ATC), they reach a state of efficiency, producing goods at the cheapest rate possible. This scenario encourages firms to supply any quantity of the product at a fixed price, the price that just covers their production costs, without making extra profits.

The constant-cost industry part means that even as more firms enter or exit the market, the costs of resources per unit produced doesn't change. Because of this stability, the supply curve remains flat. Firms are willing to offer more goods at the same price because it still covers their costs, ensuring that consumers always have access to the products they need at consistent prices and the market operates smoothly without dramatic price changes.

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