[tromp]

Besides inequality in individual ownership of Bitcoin, there is also inequality of acquisition cost. The two are related since lower costs make it much easier to acquire large amounts as demonstrated by Satoshi himself. While we cannot reliably compute individual ownership inequality, all we need to compute cost inequality is the price history of Bitcoin.

Let d_0..d_n be all days in Bitcoin history sorted by price on day d_i. So d_0 is launch day, when Bitcoin was worthless, and d_n is the day when price last peaked.

Plot a graph where x coordinate is Sum 0<=i emission(d_i) and y coordinate is Sum 0<=i emission(d_i)*price(d_i).

If Bitcoin were a stable coin then this would produce a straight diagonal line. But not only did the price go up exponentially, at the same time the emission went down exponentially. The extent to which the graph lies below that line is the Gini index of Bitcoin price inequality.