Credit expansion is the multiplication of credit against money, resulting from lending. When a loan is issued the lender and borrower both appear to hold the same money. Due to the apparent inflationary nature of credit expansion, it is commonly treated as an adverse effect on people holding the money. Because banks are the most visible lenders this effect is often attributed to banking itself. There is a theory that Bitcoin can eliminate the effects of fractional banking and thereby eliminate credit expansion.

Saving encompasses hoarding and investing. Hoarding implies ongoing depreciation, which is actual consumption. Investing is lending to production, and implies no depreciation as products must exist before they can depreciate. Investment includes both debt and equity contracts as the distinction is strictly financial, having no economic significance.

The distinction between hoarding and investment is essential to the understanding of credit expansion. Hoarded money is under the control of its owner, as if in a vault, buried in the back yard, or stuffed in a mattress.

This is inherent in the meaning of ownership. The lender of money is not the owner of the money, even though a loan is considered savings.

A lender requires liquidity to operate, and as such must hoard a certain fraction of savings. When a loan is created the borrower owns the amount lent. The borrower also requires liquidity, and so hoards a certain fraction of the loan. Any remainder of the loan is necessarily invested. This implies that the borrower has become a lender. The process continues until all capital that exists is hoarded.

The amount hoarded is sometimes referred to as the owner's "reserve", but properly it is the owner's hoard, a fraction of that owner's total savings. This use of the word reserve should not be confused with its use in the state money context of reserve currency (i.e. foreign exchange reserves). The term “fractional reserve banking” is a reference to the ratio of a bank’s hoard to its issued credit (money accounts).

The total amount of U.S. Dollars in circulation is referred to as "M0". This includes all tangible currency ("vault cash") plus intangible bank balances in Federal Reserve accounts. These two forms are considered interchangeable obligations of the Fed. The intangible obligations are money that is accounted for but not yet printed. As reported by the Fed, the total of U.S. Dollars is:

M0 plus all bank account money is referred to as "M3". This is no longer published by the Fed, but is estimated at $17,682,335,000,000. The total amount of credit extended in U.S. Dollars can be estimated from the sum of Dollar-denominated money accounts, bonds, public equities and private equities.

From the table:

• The total ratio of money to credit is ~3.46%, or credit expansion of 29.9 x money.
• Bank reserves of $1,400,949,000,000 indicate a bank reserve ratio of ~11.11% against bank credit, or credit expansion of 9.0 x money. This is slightly above the required reserve ratio, which is no more than 10%.
• Reserve of remaining money (i.e. excluding bank reserves) relative to bond and equity markets (i.e. the ratio of M0 minus bank reserves to the sum of bonds and equity) is ~2.08%, or credit expansion of 48.0 x money.

Eliminating credit expansion requires elimination of credit, and therefore production. All credit is subject to default. However the theory holds that bank credit is different in the presumption of being "risk free". This presumption arises from the fact of taxpayer insurance of the credit. This is not a consequence of banking but of state intervention in banking. To the extent the presumption is attributed to free banking, the theory is invalid. All classes of business are subject to failure, and in doing so free banking eliminates this misperception.

The distinction between a money market fund (MMF) and a money market account (MMA) is informative. Both are intended to maintain a one-to-one equivalence with money, yet both are discounted against money due to settlement and risk costs (e.g. some people accept only money, rejecting the higher costs of credit card and cheque transactions). The distinction (apart from taxpayer insurance of the latter) is in the treatment of investment risk and of insufficient reserve.

In the case of a MMF, investment failure is reflected in unit pricing. While the fund attempts to maintain sufficient net asset value (NAV) to allow exchange a unit of the fund for one of the money, a sufficient drop in NAV will be reflected in unit price. In the case of a MMA, such losses are absorbed by money reserves. If there is insufficient reserve, either because of an unexpected level of withdrawal, or because of investment losses, the MMA fails. Failure of a MMA manifests as a bank run, where some people are repaid and others not. Insufficient NAV of a MMF manifests as a uniform drop in unit price.

The advantage of the MMA is that its units are more fungible, though still discounted against money. The advantage of the MMF is that losses are evenly spread. It is not surprising therefore that MMAs are typically insured by the taxpayer, more tightly regulated by the state, and accounted for as bank credit. It is rare for a MMF to "break the buck" but of course it can and does happen. Bank failures also happen but are hidden by taxpayer insurance.

Bank credit is not truly fungible. This can be seen in everyday use of credit cards and checks. There is a material risk of failure to settle associated with each. While this risk is generally attributed to the account holder (e.g. in the case of a MMA), it is a non-distinction to the person accepting the credit. One might imagine therefore that the acceptance of credit cards and checks against MMFs to be treated similarly. The credit would circulate as a money-equivalent while more evenly distributing risk across those who are benefiting from its investment return. Free banking has the option to adopt either model to whatever extent people desire, but in any case credit will expand against money, risk will exist, and money substitutes will exist.

The decision to hoard vs. invest is based strictly on each person's time preference. Time preference is not derivable from any condition. It is, as the name implies, a human preference. Human preferences change and therefore so does time preference. Time preference determines the economic interest rate which can also be considered the cost of capital. An increase in the cost of capital resulting from increasing time preference causes credit available to contract, and a decrease has the opposite effect. With infinite time preference all capital would be hoarded for consumption, ending all production.

It matters not whether a lender is referred to as a "bank", all investment implies the same behavior. If banks operated with a 100% hoard they would not be lenders. This does not imply any reduction in lending, as the rate of lending is determined by time preference alone. Bitcoin can be lent and does nothing to limit credit expansion. The theory is therefore invalid.

Eliminating credit expansion is equivalent to the condition of infinite time preference, an infinite interest rate, no capital available for production, and no products available for consumption. In states where credit is limited or prohibited by statute (usury laws), investment moves to equity instruments, loan sharking, or an end to production.