# Estimate the Utility function for the Principal-Agent problem (real case)

I have a company and I have to set the wage to my employer based on different levels of revenues. Examples

W_1 if Revenue = 100k

w_2 if Revenue = 200k

w_3 if Revenue = 300k

I know how to solve this problem analytically, but I don't know how, in practice I will estimate the Utility function of the agent. In book they say it's

$U(w,s) = \sqrt{w} - s$

where $w$ is wage, and $s$ is their efforts. How do I apply this in pratice?

• What do you have as data? Do you observe a wage and an effort multiple times? – GuiWil Jun 30 '16 at 14:32
• I have no data yet. Are there some documentation about the estimate of this kind of utility functions? – sparkle Jun 30 '16 at 14:38
• Maybe you should be more precise about what you want to estimate (a specific utility function?) and what you observe (wages, efforts?) because the estimation strongly depends on these conditions. Importantly, if you want to estimate the utility, the problem differs if you impose a structure on the utility function or not (parametric vs. non-parametric estimation). – GuiWil Jul 1 '16 at 11:50