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 1' as Agent 1'. Each Agent 1' separately chooses effort 3,- to produce an idea for his own project 1'. Each Agent is ebrt co st is e? At the same time, the Principal P chooses effort levels E1 and E2 to devote to each project. Her total ebrt cost is 031 + Elf. (Note that this means that there is a strong crowdingout effect for the principal: if he exerts more effort in one task, it becomes mo re costly for him to exert effort in the other task.) The probability that Agent i produces an idea for Projecti equals his effort 9,. 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 and Agent 1 receives 1f2. 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 D