# Exercise 2 of Microeconomics I

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).

1. What is the optimal contract in these circumstances?
2. 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?
3. 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 e0 is given. Analyze graphically the possible payment mechanisms {w(x),w(y)} when:

1. Both the principal and agent are risk lovers.
2. 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).

1. What is the optimal contract in these circumstances?
2. 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?
3. Do you think that this explains the existence of a fund for guaranteeing salaries (Fondo de Garantía Salarial)? What problems this fund may create?