hand write asap Problem 4.An agent can work for a principal. The agent's effort, a affects current profits, q1 = a +Eg, and futureprofits, 92 = a + Eqp, where ég, 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 q2. However, hiscompensation can depend on the stock price P = 2a + Ep, where ep - N(0,07). The agent's utility functionis exponential and equal towhere t is the agent's income, while his reservation utility is I.' The principal chooses the agent's compen-sation contract t = w+ fq1 +sP to maximize her expected profit, while accounting for the agent's IR andIC constraints.1. Derive the optimal compensation contract t = w + fq1 +sP.2. Discuss how it depends on of and on its relation with of. Offer some intuition?

We have to derive the optimal compensation contract

profits, q2 = a+ €g, where eg, are random shocks, and they are i.i.d with normal distribution N(0,0). %3D The agent retires at the end of the first period, and his compensation cannot be based on q2. However, his compensation can depend on the stock price P = 2a + Ep, where ep - N(0,0). The agent's utility function is exponential and equal to where i is the agent's income, while his reservation utility is i.' The principal chooses the agent's compen- sation contract t = w+fq +sP to maximize her expected profit, while accounting for the agent's IR and IC constraints. 1. Derive the optimal compensation contract t = w+ fq1 +sP. 2. Discuss how it depends on o and on its relation with o. Offer some intuition?