Question 1 (Nonlinear Pricing with Three Types) Consider the nonlinear pricing model with three types, 03 > 02 > 01. The utility of agent Oi is u(0i) = 0iq -t Denote the bundle assigned to agent Oi by (qi, ti). We now have six (IC) constraint and three (IR) constraints. For example, (IC,) says that 01 must not want to copy 02, i.e. 0191 - t1 2 0192 -t2 (IC?) The firm's profit is 3 [ milti - c(qi)] i= 1 where mi is the proportion of type : agents and c(q) is increasing and convex. (a) Show that (IR2) and (IR3) can be ignored. (b) Show that 93 2 92 2 91. (c) Using (IC2) and (IC?) show that we can ignore (IC?). Using (IC2) and (IC?) show that we can ignore (ICi). (d) Show that (IR1) will bind. (e) Show that (IC2) will bind. (f) Show that (IC?) will bind. g) Assume that 93 2 92 2 q1. Show that (IC?) and (IC?) can be ignored