Suppose that the cost function of a firm is C(q) = 10 + 3q + 0.1q 2 and that it operates under perfect competition.
(a) If p = 4, find the optimal quantity, the costs, the revenue and the profits.
(b) Find the price at which the firm makes zero profits, that is, the price at which the average total cost is at a minimum.
(c) Find the price at which the firm shut-downs, that is the price at which the average variable cost is at a minimum.
(d) Suppose now that price is p. Graph all cost curves in a diagram, and in this diagram, show the supply curve of the firm given price p. Find the analytical expression for the supply function.