How is money exchanged in free banking?
Much the same as under the current banking system. Money will be used in buying goods and services. Some will be used, no doubt, to convert to the standard(s) e.g., gold and silver. Since each bank can print money, banks will exchange each other’s notes at par if they have confidence in each other. A bank that does not hold such confidence will have its note trade below par (or in the limit case, not at all) unless and until it can gain it. There would also be no limit to entry into the currency issuing market, so new banks could form and non-banks could issue currency as well.
