Universitat Pompeu Fabra, 1998/1999

**Due October 14, 1998**

**1.** Consider a situation in which there are
two states of nature. State 1 occurs in probability *(1-p)*.
There are two players, a risk averse worker has the utility function *U(w)=ln(w)*,
where *w* is his salary, and a risk neutral employer.
The employer has to offer a contract to the worker
under the constraint that the employer's mean payoff is not negative.
The output of the worker would be *H* in state 1 and *L*
in state 2 (where *H>L*).

- What is the optimal contract in these circumstances?
- The employer knows that once the state of nature is revealed,
the more productive worker will receive an offer of
*H*from another firm. The worker can break the contract with no penalty, and change his job. The employer has to have a non-negative profit in any case, what is the optimal contract in these circumstances? Is the situation of the worker better or worse when he can break the contract? - Explain whether the above results are related to the restrictions in the contracts of soccer players (futbolistas).

**2.** Consider the benchmark model
with two states of nature and outcomes *X={x,y}*.
The principal and/or the agent are not necessarily risk averse.
Moreover assume that the effort level *e ^{0}* is given.
Analyze graphically the possible payment mechanisms

- Both the principal and agent are risk lovers.
- The principal is a risk lover and the agent is risk averse.

**3.** Consider a situation in which there are
two states of nature. State 1 occurs in probability *(1-p)*.
There are two players, a risk averse worker has the utility function *U(w)=ln(w)*,
where *w* is his salary, and a risk neutral employer.
The employer has to offer a contract to the worker
under the constraint that the worker
obtains a non-negative utility level.
The output of the worker is *H* in state 1 and *L* in state 2
(where *H>L*, *H>1, L<1*).

- What is the optimal contract in these circumstances?
- Assume that the employer may not loose money in any state of the world. What is the optimal contract in these new circumstances? Is the worker better off?
- Do you think that this explains the existence of a fund for guaranteeing salaries (Fondo de Garantía Salarial)? What problems this fund may create?