Suppose a risk neutral principal wants to hire an agent to do a project. The output .Y is either 1 (if successes) or 0 (if not). The probability of success depends on the agent's effort e ε [0, 1].
i. e., Pr(X = 1) = e.
The cost of effort is c(e) = 1/2e^2. Because the principal cannot directly observe e, he will write a contract on the outcome X, i. e., the principal pays the agent w_1 if it succeeds, and w_0 = 0 otherwise. The agent's monetary utility is u(w) = 3 w^1/3. The agent's outside reservation utility is assumed to be zero.
1. What's the first best effort level and contract?
2. Derive the optimal contract under moral hazard.

Answer for the question :

Suppose a risk neutral principal wants to hire an agent to do a project. The output .Y is either 1 (if successes) or 0 (if not). The probability of success depends on the agent's effort e ε [0, 1].

i.e., Pr(X = 1) = e.

The cost of effort is c(e) = 1/2e^2. Because the principal cannot directly observe e, he will write a contract on the outcome X, i.e., the principal pays the agent w_1 if it succeeds, and w_0 = 0 otherwise. The agent's monetary utility is u(w) = 3 w^1/3. The agent's outside reservation utility is assumed to be zero.

1. What's the first best effort level and contract?

2. Derive the optimal contract under moral hazard.

is given in the attachment.

Step-by-step explanation:

step-by-step explanation:

1. practice, practice & more practice

2. review errors

3. master the key concepts

do not try to memorise the processes.

4. understand your doubts.

5. create a distraction free study environment

6. create a mathematical dictionary

7. apply maths to real world problems.