13. subtle points Suppose we face a contracting problem as studied in this chapter, including but two output levels, two inputs, two possible signals, etc.

The manager is specified by ρ = .0001, cH = 5, 000, cL = 0 and M = 0. Input H is of course desired. The probabilities are given below, where 0 ≤ α ≤ 1.

x1/g x1/b x2/g x2/b

π(x, y|H) .6(1 − α) .4(1 − α) .6α .4α

π(x, y|L) .25 .25 .25 .25

(a) Does the second information variable, y = g or

b, satisfy the informativeness criterion? Explain.

(b) Determine an optimal solution for the case α = .9. Is the second information variable useful? Explain.

(c) Repeat

(b) for the case α = 1. Why can a variable satisfy the informativeness criterion and yet not be useful? Can it be useful without satisfying the informativeness criterion.

(d) What happens here as α becomes small, say approaches .6?
(Hint: read note 3.)