2. Consider a principal-agent problem with a risk-neutral principal and a risk-averse agent. let the agent have CARA utility with parameter r > 0. Profits are x = / + E, where u is the agent's effort and E is distributed N(0, o2). The agent's effort cost is c( M) = KH2 "2 , and its outside option payoff is normalized to 0. (a) Identify the full-information (i.e., zero variance) first-best contract: effort, wage, and principal profit. (b) Now let the variance be positive and finite. Consider the wage schedule w(x) = a + Bx. Solve for the constrained-optimal effort wage schedule and principal profit. Note that to find the principal's profit, you need to solve for both a and B. (c) Now suppose that the principal observes additional information y. Specifically, let y be such that Ely] = 0, Vly] = 3, and Coule, y] = poyo. For wage schedule w(x) = a + Bix + Bzy, solve for the optimal B1 and B2, optimal effort and principal profit. Is the first-best ever achievable