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, 17 = 1, 2. The principal hires one agent for each project; we identify the agent associated with project 1' as Agent 1'. Each Agent 1' separately chooses effort ei to produce an idea for his own project 1'. Each Agent 1"s effort cost is %e,2. At the same time, the Principal P chooses effort levels E1 and E2 to devote to each project. Her total effort cost is 031 + E2)2. The probability that Agent i produces an idea for Project i equals his effort 2;. The probability that P produces an idea for Project 1' equals Ei. For Project 1: if the Principal's idea is implemented, then the Principal and Agent 1 both receive 1. lngent 1's idea is implemented, then the principal receives 0