mtbc | Pricing exchanges of cryptocurrency

At work, I had to learn about a particular distributed cryptocurrency exchange. Liquidity is provided by set of reserves that each contain coins of two different kinds, an equal value of each.

For pricing an exchange "from" the coin we hold "to" the coin we want, using one of these reserves of two different kinds of coin, we have:

r_f: how much of the "from" coin is in the reserve
r_t: how much of the "to" coin is in the reserve
a_f: how much of the "from" coin we want to exchange
a_t: how much of the "to" coin we are to receive
c_n: a constant determining the transaction cost
c_d: another constant determining the transaction cost, a little larger than c_n

It turns out that we decide how much currency users receive by,

a_t = (a_f × r_t × c_n) / (a_f × c_n + r_f × c_d)

I found this quite interesting. In my ignorance, I don't know if it's a standard approach for such currency exchanges. The formula seems to have some reasonable properties, in terms of things like how the price increases as one's swapping to a currency that there is now less of (or would be less of after the swap).

(Dreamwidth doesn't appear to allow <math> markup so I did what I could.)