Use the Following Information for Questions
Suppose There Are $0.5 \sqrt { H } + 0.5 \sqrt { L } \geq 25$

Use the following information for questions
Suppose there are assets whose owners wish to attract capital.Due to adverse selection problem, a cost must be incurred in order to learn the value of those assets.There are individuals who specialize in producing information about firms.It costs the information producer i.p. $5 to produce information.The i.p.is risk averse and has a utility function of where X is the i.p.'s wealth.Each i.p.has an alternative employment which provides a minimum level of expected utility of $30.Suppose that the owners of the assets approach the
i.p.directly, and assume that they can monitor the i.p.to learn if the i.p.has invested in information production.The monitoring is noisy and it says that the i.p.produced information with probability 0.6 and did not produce information with probability 04.If the i.p.did not produce information, the signal says that he did with probability 0.5, and that he did not with probability 0.5.Suppose the asset owners tell the i.p.that they will pay $H if the i.p.produced information and $L if he did not.
-To make sure that the i.p.has an incentive to produce information, his compensation must satisfy

A) $0.5 \sqrt { H } + 0.5 \sqrt { L } \geq 25$
B) $0.4 \sqrt { H } + 0.6 \sqrt { L } \geq 25$
C) $0.4 \sqrt { H } + 0.6 \sqrt { L } \geq 30$
D) $0.6 \sqrt { H } + 0.4 \sqrt { L } \geq 30$
E) $0.6 \sqrt { H } + 0.4 \sqrt { L } \geq 35$