Network Effect Fallacy

There is a theory that the utility of an economy varies with the square of the number of its merchants, assuming each merchant offers the same value of goods or services for sale in the coin. The theory is an application of Metcalf's Law.

This implies that a clean and equal split of the economy reduces combined utility by half. For example, if 20 merchants has utility 400 then 2 networks of 10 of these merchants has utility 200.

The theory fails to account for the fungibility and convertibility of money. The ability to exchange any units of one coin for the other collapses the utility of the two economies into a hybrid economy. The hybrid has lower utility than would a single economy, but cannot be comparable to loss of one of the two economies entirely unless the conversion cost is unbounded. The theory is therefore invalid.