PLEASE DO PART A, B AND C ONLY

In this question, we'll consider a version of the authority model where the principal can, at a cost, choose the degree of alignment between himself and the agent. There is one Principal and one Agent who work on a project. The Principal produces an idea with fixed probability p. The Agent's effort effort e, at cost21e2, leads to an idea with probability e. The Agent has decision-making authority. If the Principal's idea is implemented, then the Principal receives V=1 and the Agent receives v=2/3+a. If the Agent's idea is implemented, then the Principal receives V=2/3 and the Agent receives v=1. So we may think of a as capturing how well-aligned the Agent is with the Principal's preferred project. At the start of the game, the Principal can choose the agent's degree of alignment a, at a cost a2/2. The principal is restricted to 2/30. Explain in words why, unlike in (c), the principal prefers to make the agent more rather than less aligned with the principal. (Hint: In this question, we'll consider a version of the authority model where the principal can, at a cost, choose the degree of alignment between himself and the agent. There is one Principal and one Agent who work on a project. The Principal produces an idea with fixed probability p. The Agent's effort effort e, at cost21e2, leads to an idea with probability e. The Agent has decision-making authority. If the Principal's idea is implemented, then the Principal receives V=1 and the Agent receives v=2/3+a. If the Agent's idea is implemented, then the Principal receives V=2/3 and the Agent receives v=1. So we may think of a as capturing how well-aligned the Agent is with the Principal's preferred project. At the start of the game, the Principal can choose the agent's degree of alignment a, at a cost a2/2. The principal is restricted to 2/30. Explain in words why, unlike in (c), the principal prefers to make the agent more rather than less aligned with the principal. (Hint