Is the Interest Rate Inflationary?

This is a post I probably shouldn't write given the previous two ones on banking (here and here). It is, nevertheless a question, or more often, a "conclusion" I usually get when when a discussion on inflation arises. As most people have developed a somewhat irrational, deeply rooted fear of inflation perhaps instilled by the extreme rates of the 1980's, anything that appears it might assist in an increase in inflation scares them deeply. It is a reaction which runs deep in human psyche: if the extreme hurts us, then we do not even accept an infinitesimal quantity out of fear of escalation. Even so, truth is that the interest rate paid on loans is anything but inflationary. Allow me to demonstrate:

Suppose we have an economy where a bank has 60 units of currency in cash (not deposits, this is a very simplistic model). At a given time 0, a worker borrows the 50 units and builds a lemonade stand to sell his homemade lemonade from lemons he gathers at home (making his cost, other than personal labour, 0 units of currency). Lemonade is the only good for human consumption sold in this simple economy. The worker uses the proceeds from the stand to repay the loan; given that the bank wants to make a profit from the loan, it charges the worker an additional 10 units. If the loan duration is 10 years, then the total amount to be paid would be 60 units, or 6 units per year. Thus, the bank is making a profit of 1 units per year, while the worker is forced to pay half a unit per year as the cost of borrowing. 

At first, this might appear as unsustainable: how is the worker ever going to earn 6 units per year in such an economy? This most straightforward of questions, represents one of the parts of economics most people fail to see; the inability to comprehend the full circle of money, results in incomplete models and flawed understanding. The better question here is what the worker does with the money he borrows. If he could just build the stand and equipment on his own what would the point of borrowing be? He could just chop wood on his own, manufacture the screws, the nails and the hammers needed, create the juicer and cups he would need and make some boxes to keep his lemons in and have no need for extra money, just extra time. Yet, our worker cannot do all that; more so, he does not have to do all that because he purchase them and that is why he is borrowing the money.

The worker, goes to the manufacturer's shop, where, using the 50 units he just borrowed, he buys everything he needs and goes down the road to set up his shop. Although the manufacturer can create all these goods and sell them, does produce any lemonade; either because she does not have the time, the expertise, the raw material or even because she is just bored to do so since she can simply purchase it with the 50 units of currency she just got from selling her merchandise. She thus breaks the total amount to 10 annual purchases of 5 units' worth of lemonade.

Let's now consider the bank: the bank currently has 10 available units, expects to get an additional 6 every year. Yet how does the bank consume? The answer is rather simple if one considers all that exists in a bank branch. It has to pay for its employees, rent, electricity, office supplies and other equipment. For simplicity, we assume here that the bank only has to pay an employee, with a salary of 1 unit per year, with the employee spending the money in the only available good for consumption in the economy, i.e. lemonade.

The transactions for each of the 4 involved in the economy in year 1 looks like this (total money means total money available for spending):

In year 2, the same chain of  even would again unfold:

Finally, at year 10, the balances would become:

Note that here, the amount of money in the economy, as stated at the beginning, is not customers' deposits. If they were, the reader will remember from here, that when a new loan is issued, money in the economy is increased and from here, that when that loan is repaid the amount of money is reduced back to its original levels, until the amount is again re-lent. In this model, where the bank just lends out cash, money is not reduced with debt repayment, yet although the interest rate appears to create money out of thin air, all it does is in essence re-distribute money in the economy.

When a loan is repaid, the bank's income is the spread (i.e. the difference) between the deposits and loans interest rates. This money is nevertheless not withheld from the economy: they are either paid as salaries and wages to employees, or spent for equipment, rents, etc. These are all included in the bank's costs one might suggest. True, but even if we use just net profit as a measure, money is almost never left sitting idly in a safe-box. The part employed as retained earnings is used to facilitate expansions, upgrades and other stuff which will make the bank more competitive in the future. This is nothing else but consumption, albeit under a different name. Even if retained earnings are not used for consumption and are just put in marketable securities, it really makes no difference, since even marketable securities are a form of consumption (they are, in essence, a short-term loan). How about the rest of the money? Well, we shouldn't forget about dividends right? Banks pay dividends to their shareholders who are able to employ that money as they please, meaning either spending or investing it. When interest is charged, nothing leaves the economy as many would like to believe; it is just distributed differently, just like when you and I decide to spend or save.

An increase in the money supply and thus in inflation, occurs only when new loans are issued and not when the repayment means that the borrower will have give back more money (in nominal terms always) than he borrowed. The conclusion is that money does not really stay in a bank's box when the latter charges interest and receives its profit: it is mere re-distribution. Obviously, whether this re-distribution is the optimal from the society's point of view is something completely different and certainly beyond the scope of this article.

Note: The same situation would also hold if the bank was lending customer deposits, yet the amount repaid would have to be re-lent at the same time to keep money supply stable. This does not mean that the interest rate would have any different function: it would again be just a re-distribution of funds.