Suppose, there are three types of consumers with taste preferences 1 2 3. The i-th consumer's payoff

from qi

is iV (qi). Proportions of type-1, type-2, and type-3 are 1, 2, and3 respectively. Ti

is amount

paid by i-type of consumer.

Answer the following questions:

(a) Which of the three types of consumers will pretend and which will not? (5)

(b) Write down the optimization problem of monopolist if it can not distinguish among types [which condi-

tions are relevant for which type of consumers.]