ECON5323代写、代写Python/c++程序

日期：2022-10-27 08:39

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 payo?.

The principal’s utility function is, as usual: Up = y w where y = e. The agent has

payo? function Ua = w + Up 12e2, where 0 < < 1/2. So, the agent is altruistic: he

prefers outcomes where the principal gets a higher payo?, 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 o?ers 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.

1. For step 3, given the principal’s o?er (w = y), write down the agent’s maximization

problem, and calculate his payo?-maximizing e?ort choice e? as a function of . How does

the agent’s e?ort choice change with his altruism for a given level of ?

2. For step 1, write down the principal’s maximization problem, and calculate his payo?-

maximizing choice of incentive scheme (). Does the principal o?er stronger or weaker

incentives (?) to an agent who is more altruistic (higher )?

3. Show that the e?ort level of the agent does not change with his altruism.

4. In words, why does the e?ort 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?

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

person.

1

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” e?ect: the agent’s

e?ort in one task reduces the agent’s marginal cost of e?ort in the other task.

There are two tasks (task 1 and task 2). The principal benefits from the agent’s e?ort in

both tasks: Up = y1 + y2 w where y1 = e1 and y2 = e2. The agent has payo? function

Ua = w 12(e21 + e22 e1e2).

(Note that the agent may choose negative e?ort 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 o?er the agent an

incentive scheme of the form w = ?+ x, where x = e1.

The timing is as usual:

Step 1. Principal o?ers agent an incentive scheme w = ?+ x.

Step 2. Agent may accept or reject the o?er. 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 = ?+ x.

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

1. For step 3, given the principal’s o?er (w = ?+ x), write down the agent’s maximization

problem, and calculate his payo?-maximizing e?ort choices e1 and e2 as a function of ?

and .

2. For step 1, write down the principal’s maximization problem, and calculate his payo?-

maximizing choice of incentive scheme (? and ).

3. What e?ort levels does this incentive scheme induce in the agent?

4. Calculate the ecient e?ort levels (i.e. the e?ort levels e1, e2 that maximize total payo?s

Up + Ua).

5. Explain, in words, why your answers to (3) and (4) di?er (if they indeed di?er).