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## Marginal Utility and Interest Formation

07/03/2007

We have seen that the law of diminishing marginal utility is the key in the process of forming prices of present goods. This law is also the foundation for the establishment of the rate of exchange between present and future goods. This rate of exchange is also known as interest.

The essence of the phenomenon of interest is what a lender or an investor receives for having given up present consumption.

For instance, John the baker has produced four loaves of bread. The four loaves are John's means that he wants to employ to attain various goals. Let us say that John plans to use his first loaf to accommodate his most important need, which is the consumption of bread. With the second loaf John is planning to reach his second most important end, which is to have five tomatoes. The third loaf is planned to secure the third most important end — a shirt. The fourth loaf is aimed at the fourth (and least) most important end — securing a piece of chocolate.

• Five tomatoes
• Shirt
• chocolate

Irrespective of whether an individual exchanges present goods for present goods or present goods for future goods, he pays a price by entering an exchange. The individual gives up the marginal end in return for a much higher end. Remember that the loaves are interchangeable: when John exchanges a loaf of bread for a shirt, he sacrifices a loaf of bread, which is valued in accordance with his fourth and least important end, which is having a piece of chocolate. As a result of the exchange John makes a gain and improves his living standard — he exchanges something that he values less for something that he values more.

In the exchange of a present good for a future good there is also going to be a cost, which is the sacrifice of the marginal end. In order to be able to assess the cost that is made at present with future returns we have to add to the cost a premium for the time factor. The more we have to pay in terms of time to secure a good, the higher the cost that an individual endures. The cost refers to not being able to improve his well-being for the duration of waiting. Conversely, the less we pay in terms of time the more benefits we secure as far as life and well-being are concerned. On this Menger wrote,

To the extent that the maintenance of our lives depends on the satisfaction of our needs, guaranteeing the satisfaction of earlier needs must necessarily precede attention to later ones. And even where not our lives but merely our continuing well-being (above all our health) is dependent on command of a quantity of goods, the attainment of well-being in a nearer period is, as a rule, a prerequisite of well-being in a later period. …All experience teaches that a present enjoyment or one in the near future usually appears more important to men than one of equal intensity at a more remote time in the future.

Likewise according to Mises,

Satisfaction of a want in the nearer future is, other things being equal, preferred to that in the farther distant future. Present goods are more valuable than future goods.

Hence an individual will undertake the act of investment only if the return on investment will be in excess of the cost of investment adjusted for the time factor. (In short, the overall cost then is the sacrifice of the marginal end and the price of time.)

Let us say that John has agreed to exchange one loaf of bread for 1.2 loaves in one year's time. This means that 1.2 future loaves are expected to secure more benefit to John than the present one loaf of bread. Benefits that the 1.2 loaves of bread are going to secure in one year's time are valued more highly than the benefit from the marginal end that was given up as a result of lending the loaf of bread.

The introduction of money is not going to alter the essence of what has been said so far. Instead of trading bread for various goods, John will exchange his loaves of bread for money and then use the money to secure things he wants. Let us say that he has exchanged the four loaves of bread for four dollars. He can now exchange his dollars for goods he wants. So when he decides to lend a dollar, John still gives up the marginal end — having a piece of chocolate. In return he will be paid in one year's time \$1.20, or an annual interest of 20%. With \$1.20 John holds that he could improve his life and well being in the future to a greater extent than by not engaging in lending.

Note again that John agrees to lend at above a certain positive level of the interest rate. As we have already shown, this level of the interest rate must be above a figure that in addition to the incurred cost (giving up a marginal end) also incorporates a premium for the time factor. Let us say that below 15% John will not agree to become a lender. This means that his cost of funding is 15%. This cost emanates from sacrificing the marginal end and the time factor. From this we can infer that, once the rate of interest falls to below 15%, John may find it attractive to become a borrower. He can now secure resources at below cost.

As John's pool of resources expands, all other things being equal, the cost of lending for John will fall. Note that with more resources, all other things being equal, he would have to sacrifice less important ends than before the increase in the pool of resources. Consequently, he could afford to charge a lower interest rate. Also, if he wants to lend out more of his resources than before, he would have to lower his interest rates, all other things being equal.

We can thus see that a baker in his particular setup, has concluded that he will be ready to lend one dollar — which he has secured by selling one loaf of bread — for a borrowers promise to repay \$1.20 in a one year's time. His cost coupled with a time premium factor is less than 20%.

Similarly a shoemaker in his particular setup has concluded that he will be a willing borrower at this rate of exchange. His cost coupled with a time premium factor is above 20%. In short, once the deal is accomplished, both parties have benefited. The baker will get \$1.20 in one year's time that he values much more than his present one dollar. For the shoemaker the value of the present borrowed dollar exceeds the value of \$1.20 in one year's time.

Note that the baker has exchanged the one loaf of bread for money first, i.e., one dollar. He then offers to lend the one dollar for \$1.20 in one year. The asked interest rate is 20%. Whether or not the baker's offer is going to be successful is dependent on the existence of willing borrowers. We can conclude that while the lender sets the interest rate, it is the borrower who must provide the final approval for the rate that the lender has set. We have seen that the shoemaker has accepted the rate of exchange asked by the lender, John the baker.

Observe that without the existence of money — the medium of exchange — the baker isn't able to establish how much of future goods he must be paid for his loaf of bread that would comply with the rate of return of 20%.

In a world without money, all that one would have are the rates of exchanges between various present and future real goods. For instance, one present apple is exchanged for two potatoes in a one year's time. Or, one present shirt is exchanged for three tomatoes a year. Again all that we have here are various ratios. There is, however, no way to establish from these ratios what the rate of return is for one present apple in terms of future potatoes. It is not possible to calculate the percentage since potatoes and apples are not the same goods. Likewise we cannot establish the rate of return on a shirt in terms of future tomatoes. Only in the framework of the existence of money can the rate of return be established.

So if the rate of return cannot be established in the real economy apart from money it also cannot be established in the world of money apart from real goods — after all the role of money is to facilitate the exchange of real goods and services.

Consequently, there cannot be any separation between the real interest rate and the financial market interest rate — there is only one rate. Hence, the commonly accepted practice of calculating the so-called real interest rate by subtracting percentage changes in the consumer price index from the market interest rate is erroneous.

#### Increase in money supply and interest rates

An increase in money supply resulting from loose monetary policy benefits the earlier receivers of money. With more money in their possession they have more resources at their disposal. As a result of the increase in the pool of resources of the earlier recipients of money, their cost of funding has fallen — this enables them to lower interest rates. Borrowers who previously had to pay a higher interest rate will find the lower interest rate more appealing, all other things being equal. In short, the lowering of interest rates will enable the lender to lend out a greater amount of money at his disposal.

As time goes by, loose monetary policy undermines real wealth formation — this is manifested by a general increase in prices of goods and services. Because of the erosion in real wealth formation, the cost of lending has increased (fewer ends can now be accommodated with fewer resources—leads to a higher marginal end). Borrowers discover that with a general increase in prices they require more money. All this puts upward pressure on interest rates.

#### Conclusion

We can thus see that the law of marginal utility is not only instrumental in establishing the prices of present goods but also in establishing the rate of exchange between present and future goods. The essence of the phenomenon of interest is the cost that a lender or an investor endures. This cost stems from the fact that the lender or the investor has given up some present benefit. The cost is the value of the least important end adjusted for the time factor that the lender or investor must give up in order to secure benefits from future goods.

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