Final answer:
In a perfectly competitive market, each firm is willing to supply a positive amount of output at any price above their minimum average variable cost (AVC), which corresponds to the lowest point on the marginal cost (MC) curve. The firm will produce where price (P) equals marginal cost (MC) for profit maximization.
Step-by-step explanation:
Short-run supply decision for perfectly competitive firms is based on the principle that firms will produce a positive amount of output as long as the market price is above their marginal cost (MC). In the given cost function C = 25 + 9q + q², with the corresponding MC = 9 + 2q, the firm would be willing to supply a positive amount of output at any price above the point where MC first starts to rise from its minimum. This price corresponds to the minimum average variable cost (AVC). According to the economic theory of perfect competition, the marginal cost curve above the minimum point on the average variable cost curve becomes the firm's supply curve. A firm will maximize its profits by producing the quantity where the market price (P) equals marginal revenue (MR) and marginal cost (MC), ensuring that P = MR = MC. This occurs when the price is also greater than the minimum AVC, making the firm willing to supply output.
The marginal cost serves as the firm's supply curve in the short run, indicating the quantity the firm will supply at different prices. As price is accepted as given by the perfectly competitive firm, it will choose the output level where P = MC for profit maximization. If the market price goes up due to increased demand, firms will increase production until P = MR = MC at the new output level.