In the short run the supply curve for a firm is the short-run marginal cost curve (above the point of minimum average variable cost). Why is the supply curve in the long run not in the long-run marginal cost curve (above the point of minimum average net cost)?
In the short run, a variation in the market price induces the profit-maximizing firm to change its optimal level of output. This optimal output takes place when price is equal to marginal cost, so long as marginal cost exceeds average variable cost. Thus, the supply curve of the firm is its marginal cost curve, above average variable cost. (While the price falls below average variable cost, the firm will shut down.)
In the long run, the firm adjusts its inputs so that its long-run marginal cost is equivalent to the market price. At this level of output, it is operating on short-run marginal cost curve where short-run marginal cost is equivalent to price. As the long-run price changes, gradually the firm changes its mix of inputs to minimize cost. Hence, the long-run supply response is this adjustment from one set of short-run marginal cost curves to another. Note down also that in the long run there will be entry & the firm will earn zero profit, so that any level of output where MC>AC is not possible.