# Interpreting coefficient in the disutility function as disutility tolerance?

I am studying a model that relates incentives (money) and a set of actions.

Let $f(x) = k\frac{x^2}{2}$ be the disutility function of the agent, where $x$ is the level of effort that the agent is exerting and $k$ is set exogenously. I found that if $k > \theta$, $\theta$ is also set exogenously, then the incentive plays an insignificant role at determining the set of actions.

How should I interpret that?

My own interpretation is that the agent has low intention to exert a high level of efforts that even being compensated, they would not exert the necessary level of actions.

Am I right? How can microeconomics interpret the coefficient $k$? I understand that it is the marginal disutility, but it does not sound very practical. Can anyone please give me some reading/intuition behind the disutility function?

Updated: I am thinking of using the work: disutility tolerance but I cannot find any literature on the term.

• 1) What $\theta$ represents? More context is needed. 2) Why do you think that "it does not sound very practical"? Jul 19, 2015 at 2:18
• Also $f'(x) = kx$ so $k$ is not marginal disutility (instead, $f''(x) = k$). Jul 19, 2015 at 2:32
• What I mean by "practical" is that it really does not give me a plain intuition that I can explain to a person without intermediate knowledge of microeconomics. Even I did make a mistake in interpreting $k$ as the marginal disutility. My microeconomics course book does not cover this much so if you are aware of some good sources of reading, please let me know. Thank you!
– Khan
Jul 19, 2015 at 13:09
• Oh, yes. Thank for pointing out that. θ in my study is $\frac{1}{rσ^2}$ where r and $\sigma^2$ are mean and variance of idiosyncratic risk of the agent. The context is if k is high (enough to be higher than θ, the incentives play no role. How would I interpret that?
– Khan
Jul 19, 2015 at 13:33
• Is this a sub-component of a larger model where other goods provide utility and dis-utility? Is risk involved? Because the canonical statement about utility functions comes from Varian (1992), "The only relevant feature of a utility function is its ordinal character", and in a problem with a single good and without risk the magnitude of k has no ordinal consequences on preferences.
– BKay
Jul 20, 2015 at 19:15