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. The objective of creditors (owners) is to maximize their income (bank interest paid). The objective of debtors is to minimize their cost (bank interest earned).

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".

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 using 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.

Given the definition of a pure bank, the following relations are absolute. 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".

reserved        = borrowed - loaned
interest-earned = interest-rate * loaned
depreciation    = interest-rate * reserved
interest-paid   = interest-earned

For the pure bank, reserve ratio, capital ratio, and creditor rate of return are each functions of the amount borrowed, loaned and the uniform interest rate.

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

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

Notice that return on borrowed capital is lower than interest by the amount depreciation of the reserve. This is a consequence of liquidity required to support the money substitute (i.e. demand withdrawal).

By substituting capital ratio for interest rate, return rate can also be expressed 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