14. good versus bad news Ralph is now thinking about evaluating and compensating his manager based on output and on a monitor. The setting is familiar: low

(L) versus high (H) input, Ralph desires high input and the manager desires low input. Output will be x1 or x2 and the monitor y will report g or

b, and this signal will be observed at the time output is observed. The probability structure is given below.

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

π(x, y|H) .25 .05 .60 .10

π(x, y|L) .35 .35 .15 .15

(a) Why would an optimal contract pay more for high (x2) as opposed to low (x1) output? Why would it pay more for monitor report g than for monitor report b?

(b) Suppose instead the probability structure is as given below.

What happens to the good (g) versus bad (g) news interpretation of the monitor’s report? Explain g/x1 b/x1 g/x2 b/x2

π(x, y|H) .15 .15 .35 .35

π(x, y|L) .05 .65 .25 .05