A competitive firm has the following short-run cost function: C(y) = y3 − 8y2 + 30y + 5. (a) Find the firm’s marginal cost function. (b) Find the firm’s average variable cost function. (c) Sketch graphs of the marginal cost and average variable cost functions as functions of output, y. At what point does the average variable cost curve intersect the marginal cost curve? In what intervals does the average variable cost curve decrease and increase? (d) Sketch the graph of the firm’s short-run supply function. (e) What is the shut-down price.

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