(Cournot's Mineral Water Monopoly) Consider a monopolist who own an exclusive source of spring water, which produces water at 0 cost. The demand curve of the springwater is

q = 1pif p > p*

q =1pif 0 p p*

Your answer is conditioned on p*

1. Suppose thatp*= 0.4. Suppose that the monopolist chooses quantityqto maximize the profit. Write down the profit maximization problem. Calculate the profit maximizing quantityqmand the market pricepmif the monopolist sets the quantity asqm.
2. Calculate the realized social surplus (which is the sum of the pro- ducer surplus and the consumer surplus). Calculate and draw the social surplus as a function ofp*between 0 and 1.
3. "A monopoly market is inefficient." Is this statement true, false or uncertain? Justify your answer. (Your point is based mostly on your justification.)