Microeconomics questions

2. A monopolist faces a single consumer with utility function u = 9 q2 T, where 6 is private information of the consumer, q is the level of consumption and T is the amount of money that the consumer pays the monopolist. The monopolist's cost of producing q equals ch for some constant c > 0. The consumer's reservation utility equals 0. The (Pareto) CDF of 6 is F(6) = 1 6'\" for all (9 E [1, 00), where oz > 1. (a Derive the monopolist's optimal bundle (q, T) assuming that it knows 9. ) (b) Write down the monopolist's nonlinear pricing problem. (c) Derive the optimal nonlinear pricing schedule and compare it with (a). ) (d What can you say about distortions at the top? (Here, \"top\" means 9 > oo.)