We now turn to a different modification. As in the basic model there are only two possible
outcomes, R in the good state and 0 in the bad state, and if En provides eort the success
probability is pH < 1. However, we now assume that En is risk averse. That is, En obtains
utility u(Rb) if she is rewarded Rb, where u is an increasing and concave function. For simplicity,
we maintain the assumption that En gets private utility B if she shirks and B is added to the
utility she may get from her reward. Also, let E's reward be RSb and RFb in the good and bad
state, respectively. Finally, we impose limited liability for En, but not for the lenders.
Suppose first that u(Rb) = log(Rb) (log is the natural logarithm).

Exercise 3 Write up the program which the optimal contract must solve. Solve the program,
i.e. derive (RSb ;RFb ), and write up En 's (expected) utility, Ub.