prior informed manager Ralph wants to hire a highly skilled manager. The venture will succeed (output x2) or fail (output Xl). The diffieulty is the manager might be a high-skill type or a low-skill type. The probabilities are listed below:

Notice the high-skill type has a higher probability of success. For simplicity there is no eoncem over the quantity of input supply. There is coneem, however, over the skill of the supplier. Two managers populate the labor market. Both are known to have a utility function defined over weaIth of U(W) = -exp{-rW>., with r = .0001.
One is high skilled and one is low skilled. They know their own skill, but have no way of convincing Ralph of any such claim. The high-skille d type has a next best altemative that delivers a utility of U(M) with M = 10,000, while the low-skilled type faees M = 5,000. (In a sense, the suppliers privately know their respeetive costs.)
a] Loeate a pay-for-perfonnance aITangement that will entice the high-skille d type to apply for Ralph's job, but the low-skille d type to shun Ralph's job. Provide an intuitive explanation for how this "separating" contraet works.
b] The contraet in la] above entices the high-skilled type to seek out Ralph, as desired, but at the added cost of productive risk being bome by the risk averse party.
An altemative is to not separate the type s, i.e., simply offer a wage of 10,000 and flip a coin to seleet between the applieants. What is the implieit cost of this approaeh?AppendixLO1

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X1 X2 input from high-skill type 1/3 2/3 input from low-skill type 2/3 1/3