Suppose there are two consumers (type-H & type-L) in a market with utility functions
vi(q, T ) = \theta iu(q) − T
where i = L, H, q is the quantity consumed, T is the consumer’s total expenditure on the good,
and \theta L < \theta H . Assume
u(q) = 4q − q2, for 0 <= q <= 1
The monopolist has no fixed cost and constant marginal cost c. Derive the optimal two-part
tariff when the monopolist finds it optimal to serve:
1. both types of consumers;
2. only one type of consumers.