4. information arrives after manager acts Ralph is contracting with the usual (overly familiar) manager, in a setting where the manager’s input can be high (H) or low (L), with H desired. While Ralph is risk neutral, the manager exhibits constant risk aversion (ρ = .0001), a high input cost of cH = 5, 000 and the usual normalizations of cL = M = 0. The only contracting variables are output (x1 or x2) and a monitor (g or b). The monitor report is observed after the manager acts, but before the output is observed.

The probabilities follow.

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

π(x, y|H) .05 .25 .45 .25

π(x, y|L) .45 .25 .05 .25

(a) Find an optimal pay-for-performance arrangement that will implement the H input when only output can be used for contracting purposes.

(b) Repeat

(a) for the case where the monitor is publicly observed and both the monitor and output can be used for contracting purposes.

(c) Repeat

(b) for the case where the manager privately observes the monitor and communicates this observation; so output and the agent’s claim as to what the monitor is reporting can be used for contracting purposes.

(d) Carefully contrast your three solutions above.

(e) What happens in part

(c) above if the manager’s communication is delayed until after the output is observed?