Why is the marginal cost curve, above the average variable cost curve, a supply curve?

The supply curve describes the quantity a firm is willing to supply at any given price level. In a competitive market, firms are price takers. To maximize profit, they will produce until price is equal to marginal cost. Therefore, for a given price, if we ask how much the firm will produce, we can get the answer by tracing the marginal cost curve until the quantity is such that the marginal cost is equal to price. For this reason, the marginal cost curve is equal to the supply curve.

However, only the portion of the marginal cost curve that is above the average variable cost curve is relevant. This is because if the price is below the average cost curve, then the firm is better off shutting down than producing. Hence, the quantity supplied will be zero in this case. Thus, this portion of the marginal cost curve is irrelevant for the firm's supply decision.