Question 3 (8 points) We'll consider a version of the authority model with multiple principals (and a single agent). There are two projects (Project 1 and Project 2) and two principals (one for each project). For each of the two projects 1' 6 {1, 2}, its Principal 1' chooses effort E,- at cost E372 where 0 g E,- S 1, and produces an idea specically for Project 3' with probability E}. There is one agent who works on both projects at the same time. The agent chooses eifort e at cost .92 f 2 and produces an idea with probability a where 0 s e S 1. The agent's idea is general and, if produced, can be used in both projects at the same time, if chosen for both projects. (So the agent only makes one effort choice, not two.) Each principal has authority over their own project. Each Principal i receives project value of a; if their own idea is implemented for their project, V,- = 1/2 if the agent's idea is implemented for their project, forz' = 1, 2 0 if no idea is implemented for their project. where (11 and a2 represent the principals' valuations of their own ideas, and 1/2