A world renowned monopoly sells flacons of their most exquisite perfume. The monopoly has two types of consumers in equal proportions: high type and low type, denoted by H and L. Each consumer would like at most two flacons. Their valuations of the good are as follows. The H type would be willing to pay 35+ 10X to get one flacon, and 75+ 10X to get two. The L type would be willing to pay 30+ 10X to get one unit, and 40+ 10X to get two. You should substitute X for the last number of your student ID number. Getting no flacon is worth zero. Let T(q) denote the price charged when consuming q units, where T(0) = 0. The monopolist chooses T(q) to maximize her profit. We assume that the cost of production is zero.
(a) Assume that the monopolist can distinguish the consumers and use first degree price discrim- ination. How much would each type of consumer buy and at what price? From now on, assume now that each consumer's type (H or L) is private information.
(b) Explain the reasons why the monopolist cannot keep the price schedule found in part (a)
