BEE Partner, South Africa Economy Watch

The endogenous determination of the interest rate

In a boom, banks will lend more and will seek to create new deposits or issue additional notes. To support these activities, they will have to attract additional reserves. This will lead them to bid up interest rates, as they seek to attract idle reserves from one another and from hoards. In a slump, they will issue less and lend less, and will seek to shed reserves, lowering interest rates. In other words, while long-term average rates are determined by costs and competition, current interest rates reflect the balance of supply and demand in the market. They move pro-cyclically.

This is illustrated by a simple model. On the one hand, the rate of interest (in relation to the rate of profit), is likely to affect investment inversely, and investment, in turn, will have an impact on prices and employment. Changes in prices and employment will call for changes in reserves. (Even in the conditions of the craft economy, the monetary system and the real economy cannot be separated — the classical dichotomy does not hold). On the other hand, shortages or surpluses of reserves will lead to market pressures driving interest rates up or down. Monetary adjustments do complement and reinforce the stabilizing effects of the price mechanism.

Interest rates, investment, and the demand for reserves

The origin will represent the normal position, assumed to be the average over the cycle. Here the rate of profit will be at its normal level, and the rate of interest will be just sufficient to cover the expenses of the banking system, allowing just enough profit for it to grow at the same rate as the rest of the economy. The vertical axis will represent increases of the interest rate above and below the normal level. The horizontal axis will show the level of reserves, similarly above and below the normal level.

First we have the relationship between above or below normal interest rates and investment, which translates into demand for reserves.

Taken together, these propositions tell us that if interest is low, for example, investment will be high. The resulting demand pressure will drive up prices in relation to money wages, lowering the real wage and increasing employment (and output), raising profits, and thus, savings; this will go on until savings has risen to match the high level of investment. The process works in reverse: If interest rates are high, investment will be low, and prices will fall relative to money wages. So with real wages high employment will fall, and profits and savings will be down. So savings adapts to investment, in a Keynesian fashion. But savings depends on profitability and employment, and not on the interest rate, so the latter cannot be determined here.

The preceding implies that the required level of reserves depends on the money value of output, therefore on prices and employment. Thus, required reserves will be large when interest rates are low, and small when they are high. Banks start out with a ‘normal‘ level of reserves; this will have to be adjusted as the interest rate changes. So the curve passes through the origin, falling from the left to the origin and continuing through it. Higher than normal interest rates mean low investment, output and employment, and consequently, lower than normal demand for reserves. Lower than normal interest means higher activity and higher required reserves.

Interest rates and the supply of reserves

To complete the simple diagram, we must show that reserves will be increased when interest rates are raised and that, when interest rates are lowered, reserves will be reduced. That is, the supply of reserves varies positively with interest rates. This needs careful explanation.

Since g has risen, it might seem that gold output would rise pari passu. If so, things would be simple. Gold producers would expand mining and processing, and so increase their purchases of capital inputs by an amount necessary to raise gold output to the higher level necessary to ensure that new gold/existing gold stock will equal the new higher growth rate, g₁. But the increased purchase of capital inputs would mean an increase in the supply of gold; reserves would therefore increase. The increased purchase of capital inputs/normal purchase of capital inputs would equal the new growth rate, assuming equilibrium ratios. Hence gold reserves would expand in the necessary ratio. But what incentives would lead gold producers to this?

Consider this: The pressure of the boom will tend to bid up prices (relative to money wages), which would seem to reduce the value of money, whereas a rise in the value of money is needed to induce mining. That is, there should be a shortage of money relative to goods, as would be expected with a rise in employment and output in a boom; this would call for more output from the mines. But the rise in prices suggests an increase in money relative to goods!

This would mean a lower value of money (monetary gold), which would hardly be an inducement to produce/supply gold. However, gold producers do not necessarily have to sell gold. They could hold it and deposit it with the banks in return for interest. In equilibrium, the rate of interest should equal the rate of profit. So gold producers should be indifferent as to whether they are investing new gold — (for example, plowing it back into the business, that is, selling gold to buy capital inputs to earn the rate of profit) — or lending it to earn the rate of interest. They will sell enough to keep the supply of gold in circulation at the level required, and will lend enough to keep the rate of interest at the equilibrium level.

So when a boom develops, the growth rate will rise, and prices will be driven up relative to money wages, raising profits. That is, goods prices measured in the actual circulating medium — paper and credit — will rise, relative to wages in that medium. By itself, this would appear to lower profits in gold, since gold’s command over goods would be less; but the boom is fueled by an excessive issue of paper and credit. So paper and credit will fall in relation to gold. Thus new gold can be exchanged for more paper than the invested gold commanded earlier. In current terms the rate of profit will be unchanged.

The banking system will be pressed to find reserves to back the new issues of paper and credit. Its efforts will drive up the interest rate. When the growth rate rises, a boom develops. As new paper and credit are issued, existing reserves come to be inadequate; so, in order to back their issues, banks will compete to borrow reserves from one another. (There will always, normally, be periods in which a given bank’s reserves will temporarily be excessive, making them willing to lend.) This will engender a widespread increase in borrowing pressure, driving up interest rates. This may somewhat increase reserves, as it will attract ‘hoarded’ gold from inventories. But why would a rise in interest rates lead directly to a rise in mining?

Mining will increase because the higher rate provides gold producers an opportunity to increase earnings. Their normal output will continue to be sold as before. But if they increase their output, they can deposit the additional gold with the banks, and collect interest at the higher rate. (This is equivalent to selling the gold for goods. That is, the interest rate must mirror the relation between the spot price of gold and its price for delivery at a later date. A rise in the interest rate must be reflected in a rise in the discount applied to the delivery price of gold.)

Thus adjustments in the interest rate will tend to attract or release reserves so that the actual level on hand will be brought into line with that required by the level of activity. Higher prices and output call for higher reserves; to attract more reserves, a higher interest rate will be needed, but this will also tend to reduce investment and so bring about lower levels of output and employment. A lower interest rate, in turn, would tend to release reserves, but it would also tend to stimulate investment, increasing activity and thus raising the demand for reserves. At some intermediate level of the interest rate, the level of reserves attracted should just match the level required. This will be the temporary equilibrium level, as determined by market forces.

Putting the two functions together, with the normal equilibrium at the origin, we see that a shift upward in investment — due, perhaps, to boom psychology — will raise the demand for reserves (upper dotted line). This will now intersect with the supply at a higher rate of interest and a higher-thannormal level of reserves. A slump would lead to just the reverse (see lowerdotted line).

As in the case of supply and demand for circulating funds, by the conventional account, this should be a stable market. If actual reserves are inadequate, those demanding reserves will be willing to pay higher interest charges, and the higher interest will attract more reserves. But note that if there are delays or time lags, the reactions could take the form of a ‘cobweb.’ With a steep demand function and a moderate supply function, the cobweb might well be divergent. In that case, government would be needed to maintain stability by adjusting the interest rate. The policy of the central bank would be ‘to lean against the wind’ in order to move the interest rate in the right direction. But the bank can also ensure that the changes will be large enough to have the desired impact.

^{In a modern system, however, the rate of interest is not determined by demand and supply for reserves. Reserves are arbitrary and can be manipulated, reserve ratios can be evaded, and above all, reserves are not a special kind of money, like gold. They are just accounts at the central bank — accounts that can be created by the central bank. As a result, there is no independent supply function.}

^{The chief reason for the shift from gold and convertible paper to modern bank money was that gold and real reserves could not be quickly adjusted. The quantity in circulation adjusted through the price mechanism; but as the economy shifted to mass production, employment became highly variable; the wage bill would fluctuate with layoffs and re-hiring. The wage bill, however, (together with spending on investment) provided the chief market for bank lending, which would now have to adjust quickly to changing demand. But a gold-based system could not expand without first increasing reserves, which had to be attracted by higher interest rates. In a slump leading to extensive layoffs and reduced demand for loans, reduced lending would leave banks with excess reserves — an unnecessary expense — leading to reductions in rates and efforts to shed reserves. The counter-cyclical movement of the interest rate certainly helped to stabilize the economy, but it put a great strain on the banking system.}

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