In this question, we'll consider a version of the authority model where the principal works with two agents, each on a separate project. There is one principal who is in charge of two projects, i = 1, 2. The principal hires one agent for each project; we identify the agent associated with project i as Agent i. Each Agent i separately chooses effort e; to produce an idea for his own project i. Each Agent i's effort cost is -er. At the same time, the Principal P chooses effort levels E, and Ez to devote to each project. Her total effort cost is = (E, + Ez ). The probability that Agent i produces an idea for Project i equals his effort e;. The probability that P produces an idea for Project i equals E;- For Project 1: if the Principal's idea is implemented, then the Principal and Agent 1 both receive 1. If Agent I's idea is implemented, then the principal receives 0