I've been trying to solve this question for a couple of days and I'm having no success.
The only part I remotely have an idea about is part (i), where I think I would integrate the IR constraint between 1 and 0 with respect to D. After which, differentiate it with respect to w and solve? With this method, however, I lose all the D terms so cannot find w in terms of D, P and beta as asked.
The question is a principal-agent problem with the agent being able to observe the state of the world and then decide upon an effort level. The first part of the question asks to find the level of effort that the manager will put forward. The second part asks for the constant payment that the principal offers the agent.