As soon as there is a second person on the island who runs short of grain at different times from me, storage is no longer the only way to keep grain for tomorrow. I lend him what I cannot eat today, and he repays me after his own harvest. Grain that is lent out does not spoil in the granary, so lending benefits both sides. The further apart their times of shortage, the larger the benefit; if the times are exactly the same, lending cannot help. Interest is the price of time. It lies between the lowest return the lender will accept and the highest cost the borrower is willing to pay.
A second person arrives on the island. He grows a different crop and harvests in spring; I still harvest in autumn. In autumn my granary is full and his is empty; in spring it is the other way round.
If each stores his own grain, both of us keep grain in the granary for a whole year, losing some all the way. If in autumn I lend him part of what I cannot eat, and in spring he repays me from his harvest, then this grain is eaten by him during the half year it is on loan instead of spoiling in my granary; what I get back in spring is his newly harvested grain. For me, lending out is a form of storage without losses.
Today's counterpart. Being short of money before payday and having some left over after it is the same thing within a single person. Put many people together and someone always has a surplus while someone else is short. Seasonal businesses are a clearer example: they collect revenue in the busy season and pay rent and wages in the slack season, and what they need is exactly lending across mismatched times.
In autumn I have 12 portions of grain, and one more portion brings little extra satisfaction; he has only 1 portion left, and one more portion brings great satisfaction. In spring the situation is reversed. Move one portion from my autumn to his autumn, then from his spring back to my spring, and both of us are more satisfied. This is the same reasoning as one person smoothing consumption, except that the smoothing now spans two people.
How much to lend and how much to repay must be agreed between the two. If the repayment is too small, the lender would do better storing grain himself; if it is too large, the borrower would do better not borrowing. Any agreement between these two bounds leaves both better off than not lending at all.
Today's counterpart. The depositor is me, harvesting in autumn; the borrower is him, harvesting in spring. The depositor hands over money he does not need for now, and the borrower uses future income in advance.
Borrow one portion and repay more than one; the extra is interest. It is the price of today's grain expressed in tomorrow's grain. The interest rate is not arbitrary; it has a lower bound and an upper bound. The lower bound is set by the lender's other options. If storing grain himself loses a tenth each year, then getting back slightly less than he lent is still better than storage, and the interest rate can even be negative. If the grain could also be kept as seed, the lower bound is the return on seed. The upper bound is set by the borrower's circumstances: the more urgent his need, the more he is willing to pay. The two can strike a deal because the same portion of grain at the same moment is worth different amounts to each of them. A portion of grain in autumn is worth more to him, with an empty granary, than to me, with a full one. He is willing to exchange more of his spring grain for it, and I am happy to accept.
Writing lending and interest into rules has a long history. The Code of Hammurabi set the maximum interest rate on loans of grain at one third a year, and on loans of silver at one fifth (Homer and Sylla, 2005). The Code does not explain why the two differ.
Today's counterpart. Deposit rates and lending rates sit near these two bounds respectively: the deposit rate must exceed what savers could earn by putting their money elsewhere, and the lending rate cannot exceed what borrowers can bear. The law still caps lending rates today. For example, the judicial interpretation on private lending revised by the Supreme People's Court of China in 2020 sets four times the one-year Loan Prime Rate as the upper limit for judicial protection.
The simulator adds a second person and the rule of lending. Each harvests 12 portions a year, and you can adjust the number of months between their harvests. With a six-month gap, lending keeps grain in the granary for the shortest time and both eat more; with no gap, both run short at the same time and lending does nothing at all. The benefit of lending comes precisely from the constraint this chapter introduces: shortages at different times.
Lending makes both people better off, and it also brings new problems:
Deposits and loans are, in essence, the transaction between this chapter's two people scaled up. Three implications follow. First, the value of lending comes from needs that fall at different times: a lending product serves the complementarity in time between the user's cash flows and other people's cash flows. Second, the return on a deposit comes from the borrower's future income; a promise can be kept only if the other party still has income in the future. Third, the interest rate has a lower bound and an upper bound: the lower bound is the saver's other options and the upper bound is the borrower's circumstances. The rate a product offers should be judged against these two bounds.
Two people who run short at different times lend to each other, so grain need not spoil in the granary.
If both run short at the same time, lending cannot help; with a half-year gap, the benefit is greatest.
The floor is the lender's other options, the ceiling the borrower's circumstances; when storage involves losses, the floor can be negative.
What is lent is today's grain; what comes back is a promise about the future, and it may not be kept.