4. an old friend Return to one of your favorite illustrations, Example 13.5, where the following probability structure was assumed:

x1 x2

π(x|H) .5 .5

π(x|L) 1 0 Further recall the optimal pay-for-performance arrangement used I1

= 5,000 and I2 = 12,305.66

(a) Now suppose both parties observe the manager’s input. The firm acquires this information before the output is observed.

The catch is the parties cannot contract on their joint observation of the manager’s input. This might be due to "contracting costs" (though hardly believable in this simple story) or the impossibility of a third party ever verifying the manager’s input.

Consider the following arrangement: initially set the above pay-for-performance arrangement in place; then, if the firm sees input H, offer to exchange the manager’s risky compensation for its certainty equivalent of 8,000. Is this scheme incentive compatible for both the manager and the firm? Does it, in equilibrium, allow for use of the input observation by the parties? Would Ralph be pleased? What is the explanation?

(b) Now suppose the firm does not observe the manager’s input.

But it knows, under equilibrium behavior, that the original control system motivates supply of input H. So after the input has been supplied, why not simply offer to renegotiate the manager’s contract and exchange the risky pay for its certainty equivalent?

Will this scheme work? Explain.