Is there any economic value contributed by humanities faculty?
A response from Neo-classical economics:
If there are for-profit companies hiring graduates from these faculties, then yes, they do produce value. The sum of their wages is their contribution in terms of value-added to GDP.
Same applies to economists. If they are hired by companies, then their production is valuable. I see no particular difference between economists and any other degree, and I do not see why you make such an a-priori distinction, other than an implicit view of economists as superior (widespread in the field, btw).
Now, the argument about the value of graduates that is allocated to non-profit organisations, including the state, universities, NGOs, and etc, goes exactly in the same way. Consider Greenpeace. If donors of Greenpeace consider it's activity as valuable, and Greenpeace wants to hire economists and artists, then their production has value, because some people benefit from Greenpeace activities. As such, there is no reason why you would not value the contribution of all these careers. Again, the argument applies to both economists and non-economists.
The only situation where you could argue that there is no value produced is when a degree is producing graduates which are then hired to run those same degrees, in a perpetual circle. I am afraid that economics is just as likely to suffer from this than any other discipline.