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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.
-What is the amount of compensation H and L) that will solve this problem?
A)H=$2,000 and L=$150
B)H=$2,500 and L=$50
C)H = $3,025 and L = $25
D)H = $3,600 and L = $0
E)H = $3,600 and L = $25

Question

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.
-What is the amount of compensation H and L) that will solve this problem?
A)H=$2,000 and L=$150
B)H=$2,500 and L=$50
C)H = $3,025 and L = $25
D)H = $3,600 and L = $0
E)H = $3,600 and L = $25

Quizplus · Accepted Answer

In order to solve this problem, we need to find the expected profit of the i.p. from producing information and from not producing information. 
If the i.p. produces information, the expected profit is:
(0.6)(H-5)+(0.4)(-5)
Simplifying, we get:
0.6H-3-2=0.6H-5
If the i.p. does not produce information, the expected profit is:
(0.5)(L)+(0.5)(30)
Simplifying, we get:
0.5L+15
Therefore, the i.p. will only produce information if:
0.6H-5>0.5L+15
which simplifies to:
0.6H-0.5L>20
In order to make sure that the i.p. produces information, the asset owners must offer enough compensation such that the i.p.'s expected profit from producing information is greater than or equal to his expected profit from not producing information. 
Setting the two expected profits equal to each other, we get:
0.6H-5=0.5L+15
which can be rearranged to:
0.6H-0.5L=20
Now it is simply a matter of plugging in answer choices for H and L until we find the values that satisfy the equation. Using answer choice C, we get:
0.6(3025)-0.5(25)=1800-12.5=1787.5
This is greater than the i.p.'s minimum acceptable compensation of $30, so he will produce the information. Therefore, the answer is choice C, with H=$3,025 and L=$25.

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