Why is the portion of the marginal cost curve above the minimum average variable cost the short-run supply curve in perfect competition?

The shutdown rule for a firm in perfect competition in the short run is that the firm should continue to operate if the revenue is equal or greater than the average variable cost. In the long run, the firm has no fixed costs because there is time to change all production factors. If a firm cannot cover all its cost in the long term, it should exit the market.

Because the variable cost is the point where a firm can operate in the short run and the long run, all costs are variable, the firm's supply schedule is the portion of the marginal cost curve above the average variable cost.