A competitive firm has the following short-run cost function: c(y) = y 3 −8y 2 +30y+5.

(a) Please write out: fixed cost function, average cost function, variable cost function, average variable cost and marginal cost function.

(b) In the graph, plot marginal cost curves in black, average variable cost in blue, and average cost in red. As well, please broaden the supply curve.

(c) Figure out the output level when marginal cost equals average variable costs. And what is the corresponding market price?

(d) If the firm will supply zero output, what could the price be?

(e) At what price would the firm supply exactly 6 units of output? Illustrate its profit and costs in the diagram