October 28, 1998, Universitat Pompeu Fabra.

**1.**Consider the model with two effort levels
*E={e _{H},e_{L}}*. There are two possible outcomes:

- Is the principal risk averse, risk neutral or risk loving? and the agent?
- Find the optimal contracts for inducing high and low efforts.
- Write the equation that determines when the principal is
indifferent between inducing the high and the low effort levels.
(It may be a function of
*P*,*p*,*x*,_{H}*x*and_{L}).__U__

**2.** Consider the problem of moral hazard, where
**both the principal and the agent** have mean-variance
preferences. The agent's preferences are:
*EU _{A}=E(w)-½r_{A}Var(w)-½e^{2}*
and his reservation utility level is

- Find the optimal effort level the will be chosen under symmetric information.
- Assume that the contract has the form
*w(x)=A+Bx*. Find the optimal effort of the agent*e*. (Note that for any random variable^{*}*x*and non-random variables*a,b*, we have*V(a+bx)=b*).^{2}V(x) - Find the optimal contract under asymmetric information.