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Organisational Economics

Problem Set 1

Question 1

In this problem, we will consider a principal-agent model with an agent who dislikes the principal.

The principal’s utility function is, as usual: where . The agent has payoff function

all else equal, the agent prefers outcomes where the principal gets a lower payoff, independently of 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 .

The timing is:

Step 1. Principal chooses .

Step 3. Principal pays agent .

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

calculate his payoff-maximizing effort choice �� as a function of ��. How does the agent’s effort

choice change with his dislike �� of the principal for a given level of ��? ∗

choice of incentive scheme (��). Does the principal offer stronger or weaker incentives (�� ) to an

b) For step 1, write down the principal’s maximization problem, and calculate his payoff-maximizing

agent who dislikes the principal more (higher )?

c) Show that the effort level of the agent does not change with his dislike of the principal.

d) In words, why does the effort level remain constant even as incentives strengthen when the agent dislikes the principal more intensely? Why does the principal choose to strengthen incentives as the agent dislikes him more?

Question 2

In this question, we consider a version of the stealing model with a bonus-only incentive scheme, and where the agent exerts efforts both into producing output and into stealing some of the output.

A principal hires an agent to manage a project. The project revenue equals the agent’s productive effort . The agent can steal some of this revenue; if he exerts stealing effort , then he steals amount of revenue. So the net profit of the project is the revenue minus the amount stolen,

The agent’s effort cost is ² ² where the fixed parameter represents the ease of

The principal can measure the net profit of the project, but cannot monitor the project revenue and cannot detect if the agent is stealing (and thus cannot punish the agent for stealing). So, all the principal can do is to reward the agent based on net profit: he offers the agent a bonus-only incentive scheme of the form .

The principal’s payoff is thus the net profit minus the payment to the agent. The agent’s payoff is the amount stolen plus the payment from the principal, minus effort cost:

�� = �� + �� − ��.

The timing is as usual:

Step 2. Agent chooses �� and ��.

calculate his payoff-maximizing stealing choice �� as a function of ��.

��ch→oic0e of inc∗entive strength �� . (To check your calculation: you should find that ��

→ 1/2 when

Question 3

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.

1 2 where ��₁ = ��₁ and ��₂ = ��₂. The agent has payoff function �� = �� − ₂ (��₁ + ��₂ − ��₁��₂).

(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 , where .