恳求大虾，给个思路也好，感激涕零：

1. The principle is risk neutral and agent has the following utility function:

u(c,a)=1000-1/c-a, c>0

Both principle and agent agree that the outcome is exponentially distributed with mean a, which is the action to be taken by the agent.

(a) give the complete first-order conditions for the agency problem implied by the above information;

(b) show that the optimal compensation plan is concave.

2. Consider the following agency problem:
Principle: RIsk neutral
Agent: u(c,a)=Lnc - square(a)
Beliefs: f(x|a)=(x*exp[-x/a)])/square(a) (i.e., Gamma of order 2)

Assume that x=y+e, where y and e are independetly distributed with exponetial distributions with mean a. Hence,
f(x|a)=(x*exp[-x/a])/square(a)

In the following questions, consider the case where both x and y are reported.

(a) compute f(x,y|a);
(b) Find the optimal compenstation plan c(x,y);
(c) show either that y is or that it is not informative in the Holmstrom sense;
(d) given an intuitive explanation of your result. It is a general property of aggregate/disaggregate information?