With an eye to finding the reasons behind high journal subscription costs: do journals / publishers make outrageous margins, or are prices truly justified by the costs to run journals? In other words, how does their budget look like?
tl;dr: it is a distorted market. Open-access models involve cross-subsidy. Subscription models offer inflated profit margins to large publishers (and some small, very specialist publishers).
Those market distortions mean that suppliers' budgets will conceal as much as they reveal.
You'll find a little sympathy for the devil, here. Things are rarely pure, never simple, sometimes ugly.
As with most questions of the form "why does this thing have this price?" the answer is: supply and demand. It's that price because that's the price at which buyers and sellers agree on a quantity of supply.
But is it a fair market?
Is there an oligopoly?
There are very low barriers to entry: pretty much anyone with a computer and web connection can start a journal and get an ISSN for it.
Some profit margins at the big publishers (Elsevier, Taylor & Francis), do suggest oligopolistic pricing - 25-35% margins look suspicious. While any sensible profit margin analysis would also look at returns on capital employed, none of the critiques of the large publishers that I've seen have done so. There are claims is that Elsevier and Taylor & Francis, and possibly others, have used bundling (selling large numbers of titles as a group subscription) to inflate their margins. Some universities tackle this by subscribing journal-by-journal.
So yes, there are indications of oligopolistic practices that inflate prices and margins.
Is there a monopsony or oligopsony?
Well, those high margins would suggest not, and indeed, there are many many hundreds of competing universities each paying publishers on their own behalf, so the demand-side looks competitive. No, there is no oligopsony
There are three primary models of publishing business.
The first model is the open-access charity model, where everything is begged, borrowed or donated. So the costs are still there - and it's typically academics and universities paying - but the costs are concealed: effectively, the donators of resources are cross-subsidising the publishing, perhaps as an investment in reputation and/or impact. This model is very rare, because it's practically impossible to build a reputation from zero without any investment. Journals that I'm aware of that use this model, inherit reputation from predecessors that used one of the other two business models.
A second model - open access, author pays - is also along the lines of academia pays, readers from industry and commerce get the research for free, just like the open-access charity model. A large number of low-quality predatory journals are able to use this model, because of the pressure on many academics to "publish or perish".
The third model, the traditional journal subscription model, is that only organisations and institutions who access the papers, pay. This is the only model where academia does not have to subsidise industrial and commercial access to research. Some low-quality predatory journals use this model, though less sucessfully than the open access-author pays model, because the subscription model has much less demand-side pressure. But this model is also how large-scale scientific publishing got established, and it's how reputations of most academics, editorial boards, weighty titles, and many conferences got established. This is the least fashionable and most successful model.
Three of the four biggest academic publishers are publicly held (Informa, Wiley, and Elsevier) which means their profit margins can be searched for in their annual reports. Links to their websites: Informa, Wiley, Elsevier. Note that Informa and Elsevier especially are multi-faceted businesses so the profit margin they report might include their other businesses. All three companies also publish books, which has a different profit margin compared to journals (book margins are usually lower).
As of time of writing (2018):
Informa's academic publishing division reported revenue of 530.0m GBP and operating profit of 154.1m GBP for an operating profit margin of 29% (note operating profit doesn't include taxes).
Wiley reported journal revenue of $901.5m and a "contribution to profit" of $275.5m (this includes an unknown contribution to profit from Atypon, which is a publishing platform). Taking Atypon to contribute $0, this is a profit margin of 30.56%.
Elsevier didn't break down their academic division's revenue, so the reported 2,478m GBP figure includes numbers from Scopus, ScienceDirect, ClinicalKey, and a lot of other stuff. Notably they said 19% of their revenue was from print with the other 81% from electronic sources. Total reported adjusted operating profit was 913m GBP or 36.84% adjusted profit margin. Caveat: adjusted operating profit is non-GAAP. Based on page 186 of that same report, their real profit is significantly lower.
Something else that might be interesting: OMICS, a publisher widely-held to be predatory, reported $11.6m in revenue and $1.2m in profit in 2016, for a profit margin of 10.34%.
Small update: here is an analysis of the fifth-biggest publisher MDPI's profit margins: about 1-6% per paper, after tax. The APC is about $1500, and the cost per paper is about $1400.
Many of the commercial academic publication companies have massive profit margins. In the age of the internet, profit is by far the main reason for high costs---and many of the other costs are essentially just ways of enhancing profit, such as marketing expenses. The actual costs of running a journal can be very low, given that many (including high cost journals) depend entirely on volunteer service by academics for editing and reviewing. Some disciplines have dealt with this by embracing electronic publishing: see for example, the Journal of Machine Learning Research which is high impact and entirely free (in a related discussion, JeffE independently provided a link to an excellent article analyzing its finances)
Do journals / publishers make outrageous margins,
Yes, e.g. from this post in Nature (ironic publishing venue for this kind of article...):
Elsevier's reported margins are 37%, but financial analysts estimate them at 40–50% for the STM publishing division before tax. (Nature says that it will not disclose information on margins.)