Pure Bank

The concept of a pure bank can be useful in demonstrating lending behavior generally.

A pure bank provides only the following services:

• borrows money (debt from creditors)
• lends money (credit from debtors)
• hoards money (reserve)

The material differences from a real bank are:

• no state intervention (free bank)
• uniform interest (efficient market)
• no cost of operation (efficient operations)

The bank is owned by its creditors in proportion to their credit, as is the case with any company. There are existing major banks that are owned by their account-holders, such as USAA and Vanguard, so this is not a distinction from a real bank. Neither a pure bank nor a real bank has "own capital" to lend, as all capital is borrowed from investors in one form or another. The objective of creditors is to maximize their income (return). The objective of debtors is to minimize their cost (nominal interest).

Creditor accounts are money substitutes. The money substitute may be either a demand deposit or a money market fund. The distinction is in the allocation of insufficient reserve, with the former being "first come, first served" and the latter "breaking the buck" (i.e. negative rate of return).

The lack of state intervention is the common concept of free banking, where there is no statutory control, no state insurance, no discount capital, and no seigniorage. The bank uses commodity money unless otherwise specified, which simplifies calculations by eliminating the need to offset price inflation or price deflation with the Fisher Equation.

Perfect operational efficiency differs from a real bank only in the amount returned to owners, as nothing is consumed in operations. A perfectly efficient market implies uniform interest, and that all earning is a consequence of time preference.

Reserved capital is the money in which credit and debt are settled (zero maturity). Depreciation is the opportunity cost of it not being loaned, also known as "cash drag". Interest relations assume a single compounding period with the rate of interest over that period. Given the definition of a pure bank, the following relations are absolute.

reserved         = borrowed - loaned
depreciation     = interest-rate * reserved
nominal-interest = interest-rate * loaned
return           = nominal-interest

For the pure bank, the reserve fraction determines reserve ratio and capital ratio.

Reserve Ratio

reserve-ratio = reserved / borrowed
reserve-ratio = (borrowed - loaned) / borrowed

Capital Ratio

capital-ratio = reserved / loaned
capital-ratio = (borrowed - loaned) / loaned

Rate of Return

Creditor rate of return is additionally a function of the nominal interest rate. The creditor's rate of return is less than the debtor's nominal interest rate due to cash drag, the necessary cost of demand withdrawal. To reduce this cost, time constraints are typically included in real bank contracts. For example, by law any withdrawal from an interest-bearing U.S. bank account can be delayed for seven days. The creditor can only eliminate cash drag by holding the debt with no settlement assurances.

return-rate = interest-earned / borrowed
return-rate = interest-rate * loaned / borrowed

By substituting capital ratio for interest rate, a return rate can also be represented by borrowed and loaned capital.

return-rate = interest-rate * loaned / borrowed
return-rate = capital-ratio * loaned / borrowed
return-rate = ((borrowed - loaned) / loaned) * loaned / borrowed
return-rate = (borrowed - loaned) / borrowed
return-rate = reserve / borrowed

The bank's capital ratio does not cause its nominal interest rate, as that is determined on the market. But it is the expression of the individual bank's time preference. There is no distinction between accepting market rates until time preference is satisfied and accepting any positive market rate for the fraction of money not preferred for liquidity.

Not only is the capital ratio the nominal interest rate, but the reserve ratio is the rate of return. Both ratios are established by time preference alone and expressed as the fraction of reserve.