Linearly, though I guess the fee isn't $X. Technically the fee is enough to attract capital of $X. So if X is $100 -- if you need to hold one U.S. dollar for every Bitcoin that you hold for customers -- and the expected return on capital is 20 percent, the fee for holding 100 Bitcoins would be $20 a year.
Maybe it's even required by New York law. That seems like the sort of thing that New York law would require. I have not checked.
The obvious parallel for the BitLicense rules is to customer segregation requirements at brokers, but those requirements are not nearly as absolute as the BitLicense rules seem to be. (As MF Global customers found out.) So for instance stock brokers can make use of securities and cash in margin accounts, for stock-lending and other purposes. And all sorts of money-transfer and intermediary activities make similar uses of float to earn some money.
The great Izzy Kaminska has much to say about this, e.g.:
"The Austrian obsession with intrinsic worth leads me to another observation about the crypto currency faithful. Not sure if this is an Austrian theory per se (in fact I don’t think it is at all) but it’s certainly something I keep hearing about in the crypto forums and at crypto debates. What they ultimately desire is a no-debt society. I find this strange since it runs contrary to the intended evolution of Bitcoin that you read about on the Bitcoin wiki. This very much envisages a lending market in Bitcoin once the supply cap is reached. The only difference with conventional lending is that it prohibits dreaded fractional reserve lending. Only what exists can be lent."
(Related thoughts here, etc., just read her whole blog.) Here is the Bitcoin wiki on fractional reserve banking. Here is John Carney arguing that "There's nothing about Bitcoin that means you can't have fractional reserve banking," which is entirely correct but bear in mind that he's arguing against libertarian Bitcoin supporters who view the absence of fractional reserve banking as a desirable feature of Bitcoin. Here is a post from Libertarian News that begins, "I recently got into an argument over on the Reddit Bitcoin boards where I held the position that fractional reserve banking with Bitcoins was not possible," which sounds fun; he recants that view but does make what I think is a very valid point:
The one thing that would NOT be possible under Bitcoin banking would be the creation of a central bank or FDIC type “insurance” scheme to backstop bank reserves. This is because there is no way for new Bitcoins to be created other than the mining process and because people directly conduct transactions using Bitcoins themselves.
Fractional reserve banking is possible without a lender of last resort who can print money. But it's not, like, a great idea.