Consider the following version of the model of incentive pay with endogenous monitoringIn a Principal-Agent relationship, effort is not contractible. The Principal can however linkthe Agent's wage to a measure of Agent's performance which is correct on average butaffected by stochastic measurement errors. Specifically, denoting effort by e = 0, Agent's actual performance is given by pe, where p > 0is the productivity of effort.
The imperfect measure of Agent's performance is:z = pe + x, where x is the stochastic measurement error with E(x) = 0 and Var(x) = V. (As usual, E(.) andVar(.) denote the operators expected value and variance, respectively).
The Principal can invest in monitoring to improve the precision of the performance measure,according to the monitoring technology: CMV2? ,where CM = 0 denotes the investment in monitoring. The Principal is risk neutral, and sets both the optimal linear contract w = a + ßz and theoptimal investment in monitoring. The Agent is risk adverse.
Her preferences are such that the certainty equivalent wealth of arisky income, I, equals: ( )21CEW E(I) Var I A? ? .Given the contract, the Agent chooses effort to maximise the certainty equivalent wealth ofher income (wage) net of the cost of effort: C(e) =2(e) .a) Assume that p = 2.
Find the optimal incentive intensity of the contract, ß*, and the optimalvariance of the performance measure, V*, chosen by the Principal. [40%]b) Suppose now that p = 4.
Find the new corresponding values for the optimal incentiveintensity of the contract, ß*, and the optimal variance of the performance measure, V*. [20%] c)
Discuss your results at point (a) and (b), and provide aneconomic interpretation of the effect a higher productivity of effort exerts on ß*and V*.Discuss briefly the other determinants of the optimal incentive intensity and the optimalmonitoring intensity