5. A perfectly competitive firm has cost function C(q) = 100 + 10q - q2 + q3. a. Draw in a diagram its marginal and average variable cost curves and its supply curve. At which output is marginal cost equal average variable cost? b. Explain why marginal cost equal average cost where average cost is minimised. c. Using the relation between profit and producer surplus, find an expression for the producer surplus, find the producer surplus when p = 10. (Although you could use integration to answer this question, DO NOT do so; think of an alternative way.) Illustrate in your diagram