As I understand it, the market cap of an asset is the marginal price times the quantity. But the total value is the integral of the marginal price * d(quantity)

As I understand it, the market cap of an asset is the marginal price times the quantity. But the total value is the integral of the marginal price * d(quantity). These can differ greatly. If I buy one Bitcoin on the market for $1, and then another Bitcoin on the market for $100, I now have two Bitcoins, with a market cap of $200, which I only paid $101 for. It's like $99 just appeared out of thin air! But that $99 might disappear again when I sell my bitcoins. After selling one of them, the market price might plummet back down to $1. When someone on your street sells their house for $1 million, the paper value of the neighbourhood might shoot up by $10 million, just from all the nearby houses being revalued at that latest price, despite only $1 million actually changing hands. The same can happen in reverse, too.