Ralph is trying to finish a rush job for a favored customer. The schedule is tight and Ralph can…

Ralph is trying to finish a rush job for a favored customer. The schedule is tight and Ralph can save 8,000 in overtime cost if part of the job is turned over to a local subcontractor. The subcontractor’s cost is either 4,000 or 6,000. The subcontractor knows its cost, but Ralph is uninformed. Let α be Ralph’s probability the subcontractor’s cost is low (i.e., 4,000). Ralph is risk neutral; time is critical and Ralph must make a take-it-or-leave-it offer to the subcontractor.

(a) Suppose α = 0, so the subcontractor is a high-cost type and Ralph knows it; what should Ralph do?

(b) Suppose α = 1, so the subcontractor is a low-cost type and Ralph knows it; what should Ralph do?

(c) Determine Ralph’s optimal strategy for all possible values of α. Why does Ralph forego trade with the subcontractor on occasion, even though it is common knowledge such trade would be mutually beneficial?

(d) The strategy you determined in (c) above can be interpreted as one where Ralph designs a contract in which trade will take place at known terms, depending on what the subcontractor claims the cost is; and the subcontractor is motivated to candidly reveal that cost. Provide such an interpretation. Why does Ralph commit to “underutilize” the subcontractor’s revelation?

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