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A competitive firm facing a constant market price maximizes profit by producing where marginal cost equals price (P = MC). In the short run, the firm will shut down if price falls below minimum average variable cost. The firm's supply curve is its marginal cost curve above the shutdown point, showing how quantity supplied responds to price. Long-run supply requires price to cover average cost.
A competitive firm is a price-taker: it sells into a market where the price is set by the intersection of all buyers and sellers, and its own output is too small to shift that price. From your study of perfect competition, you know this means the firm's demand curve is perfectly horizontal at the market price P — every unit it sells fetches P, neither more nor less. From your study of profit maximization, you know the general rule is MR = MC. For a price-taking firm, MR = P always (because selling one more unit adds exactly P to revenue). So the profit-maximizing rule simplifies to P = MC: keep expanding output as long as the price received exceeds the cost of producing one more unit, and stop when they're equal.
The supply curve of a competitive firm is derived directly from this logic. If the price rises from $10 to $12, the firm now finds it profitable to push output further up its rising marginal cost curve until MC again equals the new price. If price falls, the firm walks back down. The supply curve is therefore the MC curve itself — specifically, the portion of the MC curve above a critical threshold called the shutdown point. The shutdown point is the minimum of the average variable cost (AVC) curve. Here is why: even a loss-making firm should keep operating in the short run as long as it covers its variable costs, because fixed costs are sunk regardless. If P ≥ min AVC, operating loses less money than shutting down. If P < min AVC, every unit sold deepens the loss beyond the unavoidable fixed costs — better to produce nothing. So the short-run supply curve traces MC above min AVC and is zero below it.
The long-run adds another threshold. In the long run, fixed costs are no longer sunk — the firm can exit and avoid them entirely. The long-run shutdown condition is therefore tighter: the firm exits if price falls below average total cost (ATC), not just AVC. The long-run supply curve traces MC above min ATC. At the minimum of ATC, marginal cost and average total cost intersect — this is the break-even point, where economic profit is exactly zero. A competitive industry's long-run equilibrium lands here: free entry drives economic profit to zero, and each firm operates at efficient scale. The P = MC = min ATC condition characterizes this efficient competitive equilibrium and is the benchmark against which other market structures are compared. Monopoly, for instance, produces where MR = MC but P > MC — a wedge between the price charged and the cost of the last unit produced, representing deadweight loss.