When money first arises, agents must find a way to economize on cash balances. Agents can hold on to commodities, but this is a risky practice. Commodity money may deteriorate or be lost or stolen. Theft was especially a problem for those making long trips through the countryside. Holding on to cash balances is costly. Early on, agents realize this. Those with enough wealth begin to keep their money with a trusted third party. Historically, when gold came into use as money, agents left their gold at a warehouse in exchange for a deposit slip. These deposit slips served a role as a medium of exchange. If the warehouse has multiple branches, the deposit slips might be exchanged at another branch, thus increasing the marketability of the slips by diminishing agents’ incentive to discount the them. These slips are part of a more general class of money known as fiduciary currency (the root of the word fiduciary comes from the Latin word for “faith”). These are promises to repay.
Eventually, the keepers of the warehouses realize that they can lend the money entrusted to them so long as depositors do not rush all at once to retrieve their commodity money. This is fractional reserve banking. Banks hold some portion of their reserves (the money lent to them) while lending the remainder. This allows cash to be employed when it would otherwise sit in reserve. For depositors, this diminishes the cost of holding cash balances. In a gold standard world, for example, instead of holding and exchanging in actual gold, agents can exchange deposit slips. Meanwhile, they earn interest on the money that they have temporarily relinquished to the bank. This creates a tendency for the total money stock, which in our example is the total gold plus the total amount of deposit slips to fluctuate due to changes in demand to hold currency. We measure the relative size of the total money supply by comparing the base money stock to the total amount of money in circulation.
MB= MT / MM
MM = MT / MB
MM = MT / MB
MT = Total Money Stock (MB + Liquid Credit Instruments)
MB = Base Money
MM = Money Multiplier
The money multiplier is intimately related to the reserve ratio of a banking system. Collectively, banks form an aggregate reserve ratio. It is defined by the amount of currency they have on hand divided by their total liabilities. Monetary dynamics fall out of this identity. When banks extend credit on net, the reserve ratio drops. When banks contract credit on net, the ratio increases. When agents deposit currency on net, the ratio increases. When agents withdraw currency on net, the ratio falls (Hawtrey 1919).
We might also think of the reserve ratio as its inverse: the money multiplier. This represents the ratio of total currency to base currency. The ratio of currency to deposits plays an important role in this identity as it allows us to observe the effect of a change in currency or deposits on the money multiplier.
Mt = C + D
Mb = C + R
Mt/Mb = (C + D) / (C + R)
Mt/Mb = (C/D + 1) / (C/D + r)
Mt / Mb = Money Multiplier
C = Currency
D = Deposit
*Other variables defined as above
Notice that the numerator is larger than the denominator as long as r < 1. This means that as C increases, the denominator grows at a faster rate than the numerator. The money multiplier falls under this scenario. Likewise, as the total stock of currency shrinks, the money multiplier grows. Similarly, as the amount of deposits increases, the denominator, C/D + r, falls at a faster rate than the numerator. The money multiplier increases. As deposits falls, the money multiplier falls.
Unspent Margin: Cash Balances, Money on Account, and Substituting for Available Credit Lines
Agents respond to the incentives of this relatively flexible system. We assume that agents economize on cash balances. That is, they decide to hold cash for several reasons. Agents receive income in discrete units, so they must build up reserves in preparation for periods where income has yet to be received. Agents also hold currency or deposit balances in order to hedge for risk. Last, agents deposit their currency in discrete quantities. (This was more important before the development of direct deposit and electronic quasi-monies.) Agents may economize on cash balances by leaving their money on deposit to collect interest. They may also choose to allot some wealth to long-term investments where it collects more interest than an ordinary demand deposit account. They may also choose to substitute an available credit line for balances of cash or deposits. By doing this, an agent may collect a higher yield from long-term investments while still having ample liquidity to deal with fluctuations in their own demand for money.
The unspent margin serves as analytical proxy for demand for money. First we must identify the unspent margin. “The unspent margin is equal to all the cash, whether in circulation or in the banks, plus the net interest bearing assets of the banks (Hawtrey 1919).” The unspent margin represents portfolio demand for money. In a world where credit influences the money stock, a net increase in loans by the banks will first have the effect of increasing the unspent margin. When credit is expanded without being exchanged for goods, the credit represents an increase in the money stock with an offsetting expenditure. Demand for money increases (velocity falls) as a result. A contraction of credit represent a fall in demand for money. Demand for money falls as agents relinquish cash to the bank and the bank fails to offset the decrease in liabilities. In either case, prices must adjust to in order to facilitate the exchange despite a change in the money stock.
It is from this pattern that Hawtrey made an observation concerning the relation between incomes and changes in credit.
Apart from this shuffling of debts, all the credit created is created for the purposes of being paid away in the form of profits, wages, salaries, interest, rents – in fact, to provide the incomes of all who contribute, by their services or their property, to the process of production, production being taken in the widest sense to include whatever produces value. It is for the expenses of production, in this wide sense, that people borrow, and it is of these payments that the expenses of production consist. So we reach the conclusion that an acceleration or retardation of the creation of credit means an equal increase or decrease in people’s incomes.
In the world that we have constructed thus far, exchange only occurs when both agents expect to profit. This implies an expectation of the lender that the borrower has or will earn the means to repay the loan at a later date. The borrower will typically produce goods or provide services in order to raise the income required for repayment. In a world of voluntary exchange, then, incomes rise and fall with increases and decreases of the credit stock as this reflects changes in the expected value of production.