1. Monopolist selling to two types of consumers Consider a monopolist selling sweets to two types of consumers (assume sweets are innitely divisible, so that the monopolist can sell any nonnegative quantity). The demand of consumers of type 1 is given by p1(q1) = 9 Son. The demand of consumers of type 2 is given by 302012) = 8 5q2. All quantities are expressed in kilograms and prices in pounds sterling. The monopolist can produce sweets at no cost. There are equal numbers of both types of consumers. (a) 5 marks Suppose the monopolist can distinguish between the two types of con- sumers and is also able to offer them xed-quantity packages, so that they cannot continuously choose any amount they want. What packages will the monopolist offer to each type (state quantities and fees)? What prot will the monopolist earn per consumer? 5 marks Suppose the monopolist can still distinguish between the two types of consumers, but now, because of regulation, it must supply any amount of sweets that the consumers choose (i.e., it cannot restrict consumers' choice to a menu of xed packages). Thus, the monopolist will charge each type of consumer a different constant price per kilo of sweets. Furthermore, the monopolist is not allowed to charge consumers any xed fees. What price will the monopolist set for each type? What quantities will be consumed, and what will be the monopolist's prot per consumer? Now suppose that the monopolist cannot distinguish anymore between the two consumers, but is allowed to offer xed packages. How can the monopolist achieve the highest prot (state quantities and fees for each package)? What is the monopolist's prot per consumer? For this part, suppose the monopolist still cannot distinguish the con- sumers, and is still allowed to offer xed packages. Instead of there being equal numbers of both types, there are now 75 consumers of type 1 and 100 consumers of type 2. What are the optimal quantities now? You do not need to compute the fees or the prots. (Hint: Revisit the derivation of the optimal packages in the lecture slides and try to adapt that to the case of unequal numbers of consumers.)