APPENDIX TO CHAPTER 14A Principal-Agent
Model
Throughout this chapter, the principal-agent relationship has appeared in numer-
ous places: medical and Federal Deposit insurance, workers’ contracts, franchis-
ing policies, and executive compensation. Thus, it pays to build a formal
description of this relationship. We now describe and analyze a bare-bones model.
Suppose a risk-neutral principal hires a risk-averse agent to work (under-
take effort) to produce output . (We value output in dollar terms, so can be
thought of as the net profit generated by the agent.) The exact output realized
depends on the agent’s level of effort (e) and on other, uncertain factors beyond
the agent’s control. For instance, a salesperson might devote the same effort in
contacting clients in March as in February, but his or her actual sales results
might vary significantly between the months. We model output by the equation[14A.1]where the coefficient k represents the agent’s marginal product (output per unit
of effort) and u is the component of output (plus or minus) due to uncertain fac-
tors. The random factor u is taken to have a mean of zero and a variance of ^2.
The agent measures his welfare according to the wage (W) received from
the principal and the cost of the effort expended. We model the cost (or disu-
tility) of the worker’s effort as CE .5ce^2 , where c denotes a numerical coeffi-
cient and e is taken to vary between 0 (no effort) and 1 (100 percent effort).keu,626
c14AsymmetricInformationandOrganizationalDesign.qxd 9/26/11 11:03 AM Page 626