(Second-degree price discrimination) There are N1 consumers of type 1 and N2 consumers of type 2. Each type 1 consumer has the demand curve D1 : p1 = 10 q1 and each type 2 consumer has the demand curve D2: p2 = 14 q2. The monopolist cannot engage in first-degree price discrimination because he does not know which consumers are of type 2. However, the monopolist knows N1 and N2. The monopolist bears no cost of production, that is, c (Q)=0, for all Q. For the different cases below, find the monopolist's optimal non-linear pricing schedule, that is his best couple of quantity-total payment packages.

1. N1 = N2 = 1

2. N1 = 2, N2 = 1

3. N1 = 1, N2 = 2

4. N1 = 1; N2 = 3