A firm's marginal cost curve above the average variable cost curve is equal to the firm's individual supply curve

An increase in marginal costs would cause the firm's marginal cost curve to shift to the left. This means that the firm's supply curve will shift to the left and be equal to the marginal cost curve everywhere above the average variable cost curve.

Firm Supply:A firm's supply decision is based on two of its cost curves: marginal cost and average variable cost. The marginal cost curve tells how much the firm is willing to supply at each price with one caveat. At any point below the average variable cost curve, a firm loses money by producing an extra unit so the firm will shutdown and produce zero output.