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 ei to produce an idea for his own project i. Each Agent i 's effort cost is 21ei2. At the same time, the Principal P chooses effort levels E1 and E2 to devote to each project. Her total effort cost is 21(E1+E2)2. (Note that this means that there is a strong 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 ei. The probability that P produces an idea for Project i equals Ei. 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 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