Say that a financial intermediary is hired to make a transaction “go forward”. The intermediary can do a good job that costs the intermediary $5,000, or do a bad job that costs the intermediary zero. If the intermediary does a good job the transaction will go forward. If the intermediary does a bad job the transaction will go forward with probability 0.8, and will fail with probability 0.2. The customer can’t observe the intermediary’s job choice and simply pays the intermediary $X if the transaction goes forward and pays $0 if it fails. What is the minimum X the customer must pay in order to persuade the intermediary to do a good job?
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