The demand for milk and the total costs of a dairy are specified by the following equations: P(Q) = 100 - Q TC(q) = 30q
(a) Suppose there is a monopoly in the industry. Derive an equation for marginal revenue of the monopolist. Graph the demand and marginal revenue curves.
(b) Derive the marginal cost (MC) and average cost (AC) of milk production. Graph MC and AC on the same graph as (a).
(c) Show the monopoly's profit-maximizing price (Pm) and quantity (Qm) on the graph. How much are its profits? Show these on the graph. Will these profits persist in the long run? Explain your answer.
(d) What is the efficient level of milk production? Show on the graph the total surplus associated with efficient production. Show the consumer surplus that would result under monopoly. Indicate the region which is the difference between these two consumer surpluses. Explain what happens to this "missing surplus" under monopoly.