Question 2 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 =e; . At the same time, the Principal P chooses effort levels E, and E, to devote to each project. Her total effort cost is =(E; + Ez + E, E2). (Note that this means that there is a crowding-out effect for the principal: if he exerts more effort in one task, it becomes more costly for him to exert effort in the other task.) 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 1's idea is implemented, then the Principal receives 1/2 and Agent 1 receives 1/2. For Project 2: if the Principal's idea is implemented, then the Principal and Agent 2 both receive 1. If Agent 2's idea is implemented, then the Principal receives 0