controllable versus conditionally controllable measure This is a continuation of problem 8 in Chapter 18. The basic story and preference speeifieations remain as hefore. Ralph owns a produetion funetion, recall; and randomness in the environment pIus labor input from a manager combine to produce output. The output is now one of two quantities: XI

Here, however, the parties ean contract on the observable output and on a monitor. The monitor will report what will he labeled good news (g) or bad news

(b). It is observed at the time the output is observed. Suppose the probabilities are as follows:

input H input L g;xI

.05

.40 b;xI

.05

.40 g;x2

.45

.lD b;x2

.45

.lD As a base case, suppose the parties cannot contract on what the monitor reports.

Their contracting is confined to the output. We should recaH from the earlier problem the optimal payment arrangement is II = 8,934.62 and 12 = 15,972.54 along with an expected wage of 15,268.75. (It will also become clear helow that throughout we maintain the same relationship between output and input as in the originai problem.)

a) Determine an optimal contract when both the monitor and output can be used.

Interpret your finding. Is the monitor controllable, in the sense the probability of what the monitor reports depends on the agent's supply of input? Is it conditjonally controllahle?

b) Repeat for the following probability structure:

e] Ineach ofthe fourcases carefully explain, in qualitative tenns, why the pay-forperfonnance arrangement selects the monitor/output combinations it does for high and for low reward. What connection do you see with the idea the monitor should be used if the agent can control it?AppendixLO1

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g;x1 b;x g;x2 b;x input H .00 .10 .90 .00 input L .00 .80 .20 .00 c] Repeat for the following probability structure: input H input L g;x b;x g;x2 b;x .06 .04 .54 .36 .32 .48 .08 .12 d] Repeat for the following probability structure: g;x1 b;x g;x2 b;x2 input H .01 .09 .49 .41 input L .35 .45 .15 .05