What should I state for "expected salary" in a tenure-track job application? I am applying to a tenure-track assistant professor job in an applied math department,
for which the job posting states


  Applicants should state their current and expected salary in the application.


Questions:


Why does the department ask for "expected salary"?
Is it because they are trying to exploit my naiveté?
What number should I state in my application?
If I state a number that is on the low side,
will they use that to offer me a lower salary?


At the moment, I am thinking of just stating my estimate of the mean salary
for new assistant professors at math departments,
which according to a Tenured/Tenure-Track Faculty Salaries Survey
is $71,412.
I feel it's kind of obnoxious to ask for an expected salary, and it does raise issues of whether the answer could be used to lower the initial offer (or decrease the applicant's negotiating power).  I don't see anything wrong with giving a vague answer or just saying you are flexible.  If you specify a number, you should try to choose one that's representative of the type of school you are applying to, as Danny W. suggests.

As for why they do it, one reason is that salaries vary enormously.  A regional liberal arts college may pay less than half as much as a leading research university.  Some U.S. states scandalously underfund their state universities, so there can be dramatic salary differences between what you'd think are comparable institutions.  The net effect is that schools that aren't able to pay a lot worry about attracting candidates who have no idea how little they pay.  They don't want to waste time trying to hire someone who will never accept any amount they could plausibly offer.  One way to get around that is to announce a salary range.  However, some departments are hesitant to do that, perhaps because they don't want to publicly emphasize how little money they get (and thereby humiliate themselves or discourage applicants).  Instead, they ask for an expected salary and filter out anyone who names a figure far out of their range.  I don't like it, but it seems to work well enough that departments keep doing it.