In this problem, we will consider a principal-agent model with an altruistic(1) agent who cares about the principal's payoff.

The principal's utility function is, as usual: Up = y w where y = e. The agent has payoff function Ua = w + Up 21 e2, where 0 < < 1/2. So, the agent is altruistic: he prefers outcomes where the principal gets a higher payoff, independently of how well he does himself. The parameter is fixed and represents the player's altruism towards the principal.

Assume that the principal cannot charge the agent a participation fee or any other fixed payment. That is, the principal offers the agent an incentive scheme of the form w = y.

The timing is:

Step 1. Principal chooses . Step 2. Agent chooses e. Step 3. Principal pays agent w = y.

We'll go through the problem step-by-step.

For step 3, given the principal's offer (w = y), write down the agent's maximization problem, and calculate his payoff-maximizing effort choice e as a function of . How does the agent's effort choice change with his altruism for a given level of ?

For step 1, write down the principal's maximization problem, and calculate his payoff- maximizing choice of incentive scheme (). Does the principal offer stronger or weaker incentives () to an agent who is more altruistic (higher )?

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 becomes more altruistic? Why does the principal choose to weaken incentives as the agent becomes more altruistic?

(1)For our purposes: altruism is a preference to benefit someone other than oneself, for the sake of that person.