1. Consider a principal hiring an agent. The principal can observe the profits that emerge from the agent's effort, but cannot directly observe the amount of effort that the agent exerts. For simplicity, assume that the agent can only exert two levels of effort, high or low (H or [), yielding only two levels of outcomes, 300 or 0, with the following conditional probabilities: x =0 x = 300 CH 0.5 0.5 eL 0.75 0.25 The principal's profit function is a(x, w) = x - w, where x indicates the outcome (300 or 0) and w is the salary that he pays to the agent. The agent's utility function is u(we) = w - c(e) , where the cost of effort c(e) becomes c(ew) = 1 when he exerts a high level of effort but zero otherwise, c(er) = 0. Assume that the agent's reservation utility is u = 5. a. Consider that the principal is the only firm in the industry competing for the agent. Set up the principal's problem and find the equilibrium salary and effort. b. In the setting of part (a), assume that the government forces the principal to pay a fixed salary, that is a salary that is not affected by the firm's profit realization. Find the salary w that the principal offers in this context, and the effort that such a fixed salary induces. Then compare the agent's utility and the firm's profits in both scenarios. c. Consider now that the principal competes for the agent against several other firms (perfect competition), thus forcing the principal to make zero expected profits. Set up the principal's problem and find the equilibrium salary and effort. d. In the setting of part (c), assume that the government forces the principal to pay a fixed salary. Find the salary w that the principal offers in this context, and the effort that such a fixed salary induces. Then compare the agent's utility and the firm's profits in both scenarios