Network Effect Fallacy

There is a theory that the utility created by 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 one coin. The theory is an application of Metcalfe's Law.

This implies that an even 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.

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