b} c} d) In this problem. we will consider a principal-agent model with an altruisticIII agent who cares about the principal's payo'. The principals utility function is, as usual: 3': = x 1' where x = e. The agent has payoff function u = r + Air 22. where t} c it c ] f2. So, the agent is altruistic: he prefers outcomes where the principal gets a higher payoff. independently of how well he does himself. The parameter it is xed and represents the player's altruism towards the principal. Assume that the principal cannot charge the agent a participation fee or any other xed payment. That is. die principal offers the agent an incentive scheme of the form 1' = in; The timing is: Step 1, Principal chooses (2. Step 2. Agent chooses 6. Step 3. Principal pays agent 1* = bx. We'll go through the problem step-by-step. For step 3, given the prmcipal's offer (1* = bx}, write down the agent's maximization problem, and calculate his payoffmaximizing effort choice e' as a function of B. How does the agent's e'ort choice change with his altruism It for a given level of b? For step 1, write down the principal's maximization problem. and calculate his payoff-maximizing choice of incentive scheme (5). Does the principal offer stronger or weaker incentives (F) to an agent who is more altruistic (higher .1)? Show that the effort level of the agent does not change with his altruism. In words. why does the effort level remain constant even as incentives weaken when the agent be- comes more altruistic? Why does the principal choose to weaken incentives as me agent becomes more altruistic