Problem 4. An agent can work for a principal. The agent's effort, a affects current profits, 91 = a +9, and future profits, 92 = a + q3, where eg are random shocks, and they are i.i.d with normal distribution N(0,0%). The agent retires at the end of the first period, and his compensation cannot be based on 92. However, his compensation can depend on the stock price P = 2a +p, where ep ~ N(0,0%). The agent's utility function is exponential and equal to where t is the agent's income, while his reservation utility is . The principal chooses the agent's compen- sation contract t = w+f91 +sP to maximize her expected profit, while accounting for the agent's IR and IC constraints. 1. Derive the optimal compensation contract i = w +91 +SP. 2. Discuss how it depends on op and on its relation with o. Offer some intuition