ECON5323 Organisational Economics Problem Set 1
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ECON5323 Organisational Economics
Problem Set 1
Problem 1
In this problem, we will consider a principal-agent model with an altruistic1 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 + λUp − 
e2 , where 0 < λ < 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 λ 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 = βy .
The timing is:
Step 1. Principal chooses β .
Step 2. Agent chooses e.
Step 3. Principal pays agent w = βy .
We’ll go through the problem step-by-step.
1. For step 3, given the principal’s offer (w = βy), write down the agent’s maximization problem, and calculate his payoff-maximizing effort choice e* as a function of β . How does the agent’s effort choice change with his altruism λ for a given level of β?
2. For step 1, write down the principal’s maximization problem, and calculate his payoff- maximizing choice of incentive scheme (β). Does the principal offer stronger or weaker incentives (β* ) to an agent who is more altruistic (higher λ)?
3. Show that the effort level of the agent does not change with his altruism.
4. 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?
Problem 2
In this problem, we will consider a multitasking problem where the principal can only incentivize the agent on one task, but where there is a “crowding-in” effect: the agent’s effort in one task reduces the agent’s marginal cost of effort in the other task.
There are two tasks (task 1 and task 2). The principal benefits from the agent’s effort in both tasks: Up = y1 + y2 − w where y1 = e1 and y2 = e2 . The agent has payoff function Ua = w − 
(e1(2) + e2(2) − e1 e2 ).
(Note that the agent may choose negative effort levels, potentially resulting in negative output.)
The principal cannot reward the agent for total output; instead, he can only reward the agent for his performance in the first task. That is, the principal can offer the agent an
incentive scheme of the form w = α + βx, where x = e1 .
The timing is as usual:
Step 1. Principal offers agent an incentive scheme w = α + βx.
Step 2. Agent may accept or reject the offer. If he rejects, he receives an outside option of
zero.
Step 3. If agent accepts, then he chooses e1 and e2 .
Step 4. Principal pays agent w = α + βx.
We’ll go through the problem step-by-step.
1. For step 3, given the principal’s offer (w = α + βx), write down the agent’s maximization problem, and calculate his payoff-maximizing effort choices e1 and e2 as a function of α and β .
2. For step 1, write down the principal’s maximization problem, and calculate his payoff- maximizing choice of incentive scheme (α and β).
3. What effort levels does this incentive scheme induce in the agent?
4. Calculate the efficient effort levels (i.e. the effort levels e1 , e2 that maximize total payoffs Up + Ua).
5. Explain, in words, why your answers to (3) and (4) differ (if they indeed differ).
2022-11-12