In this question, we'll consider a version of the authority model that captures the idea that 'over- stretching1 by the Principal may increase the incentives of the Agent(s). To keep things simple, we'll focus only on the case of P-authority. There is one principal P who is in charge of n 2 1 of projects. The principal hires one agent for each project; we call the agent associated with project i as 14,-. Each Agent 1' separately chooses effort 6, to produce an idea. for his own project a". Each Agent is effort cost is $23. At the same time, the Principal P chooses effort levels E1, E2, En to devote to each project. His total effort cost is %(E1 + E2 + + En)? The probability that A, produces an idea for Project '6 equals his effort 8.3;. The probability that P produces an idea for Project 2i equals 13,-. As before, if P's idea is implemented for Project 1', then P receives 1 and A,- receives 0