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→Question B.2: Opportunistic sellers
*This page is included under the section [[BPP Field Exam]]
The 2008 field exam was on June 27th 2008. Reference material was permitted, communication was not. It was stated that grading would be based on the assigned times for each question.
===Question B.2: Opportunistic sellers===
Consider an economy with many identical Buyers that can each engage in a transaction with one of many sellers. For concreteness, imagine that there are more buyers than sellers and that the market for transactions must clear. The transaction can either succeed or fail. Each buyer’s value of "success" is 1 and of "failure" is 0.
There are two kinds of Sellers. A proportion <math>1 - \beta\,</math> are "good" and they succeed with probability <math>p > 0\,</math>. A proportion <math>\beta\,</math> are "opportunistic" and can choose some effort, <math>e \in [0,1]\,</math> at a personal cost of <math>c(e)\,</math> where <math>c'(0) = 0, c'(1) = \infinityinfty\,</math> and <math>c''(e) > 0 \;\forall e = 0\,</math>. The opportunistic types succeed with probability <math>ep\,</math>.
The economy operates for 2 periods. Sellers live for two periods but a new cohort of buyers is active in each period, and second period buyers can observe the first period outcome of transactions.
