This is a continuation of problem 8 in Chapter 13. Everything remains as before, except Ralph now…

This is a continuation of problem 8 in Chapter 13. Everything remains as before, except Ralph now has an information source. For a cost of 4,000 the source will report, without error, whether the manager supplied input H or input L. If input H is reported, the manager will be paid IH = 15,000. If input L is reported, the manager will be fired, with a payment of IL = 0. (No negative payments are allowed.) This is certainly effective, but far too costly.

(a) Suppose Ralph can commit to buying the information only when output x1 is observed. Ralph will then pay 0 whenever the information is purchased and reveals input L was supplied and 15,000 otherwise. Will this motivate supply of input H? Will the manager have any compensation at risk, in equilibrium? Is this a good idea?

 (b) Now suppose Ralph can commit to buying the information only when output x1 is observed and only then with probability β. (Think of this as random monitoring.) Ralph will again pay 0 whenever the information is purchased and reveals input L was supplied and 15,000 otherwise. Find the lowest β that will motivate supply of input H. Is this a good idea?

(c) Next, consider a more elaborate plan. Set β = .20738. Pay 0 if the information is purchased and input L is reported. Pay 15,130.97 if x1 is observed, the information is purchased and reports input H; pay 13,909.36 if output x1is observed and the information is not purchased; and pay 15,098.98 if output x2 is observed. Is this a better idea? What is the explanation?

(d) Do you perceive any incentive problems on the part of Ralph at this point?

(e) Finally, notice all of the above presumes the lowest possible payment to the manager is 0. What happens if there is no such constraint, if the manager can be penalized with impunity?

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