Why is the MC curve the same as supply curve in perfect competition?Watch
The reason is because of the P=MR condition of perfectly competitive markets (since they're price takers, firms get P per additional good sold no matter what they do). We know that firms that are profit maximising produce at MC=MR, therefore if P=MR, such firms will only produce when P=MC. Hence, we have established the relationship between the price of the good and the quantity supplied. Remember of course that firms will not produce below AVC.
In the the perfect competition firms will continue to operate as long as price is above minimum average variable cost (which is exit point) so the marginal cost curve above the point crossing AVC can automatically be referred to the firm’s supply curve.