1. Consider the problem of a monopolist producing water at a constant marginal cost of$10per kiloliter. The preferences of every household are separable in water and money, and households valuexkiloliters of water according to the functionu(x) = 100 log(x+ 1). Hence, their utility when purchasingxkiloliters at a total pricepsimply amounts tou(x)-p.

(a)First suppose that the monopolist can offer contracts which specify the water supply to a household and the total price charged for this supply. Find the profit-maximizing contract offered to households.

(b)Next suppose that the monopolist can only specify a price per kiloliter at which water is sold and that households then choose how many kiloliters to purchase. Find the profit- maximizing price set by the monopolist and the water supply to households at such a price.

(c)Compare the utility of households and the profits of the monopolist in parts (a) and (b). Comment on eficiency and fairness of outcomes in both settings.