The first aspect of the interest rate concerns the price of not waiting. If I am to have any incentive to choose to give up today’s consumption for the sake of a particular satisfaction tomorrow, then it must be the case that bringing closer to fruition the future good ranks higher on my values scale than the present good sacrificed. However, if I want to put a number on the interest rate, then I cannot deal with valuations alone, because those are ordinal: they form a hierarchy, a scale and cannot be divided by each other. Still less is it possible to obtain a numeric interest rate by comparing “present goods” with “future goods,” because no mathematical operations can be attempted on heterogeneous goods.
Therefore, the rate of interest is a monetary phenomenon.
How does time preference figure in the determination of interest? Let’s say I am thinking of buying a computer for $1,500. I can choose to have the computer from now to 5 years from now. Alternatively, I will agree to refrain from my purchase and give up the $1,500 for a year if someone were to give me an extra $500 at the end of the year. It so happens that a monitor and a printer together cost $500. My second choice is to have computer + monitor + printer from 1 year from now to 5 years from now.
The second choice pulls the enjoyment of the monitor and printer closer to me, while the first choice would postpone their purchase indefinitely. As a result, the disutility of waiting is smaller for the second choice at the expense of some immediate enjoyment, namely of the computer from now to 1 year from now.
My own personal interest rate then is 500 / 1,500 = 33%. Now answer: by how much must $500 + 1,500 be discounted a year from now to result in $1,500 now? The answer is, by 25%.
In general, if the interest rate is i per time period, then the rate of discounting is i / (1 + i) per the same period. We do not discount the future because it is uncertain or less important than the present. The future will be here soon enough.
The easiest way to see the essence of the trade-off is to contemplate some Crusoe economics. If Crusoe catches fish, then he has the option of consuming the entire catch every day. There is not enough time left in the day for him to do anything else. Even if he would like to, say, build a shelter, he can’t and ends up “waiting” for it forever. A choice is open him, however, to go somewhat more hungry yet save some fish. Having accumulated a cache of dry fish, Crusoe quits fishing for a time and works on the shelter project, sustaining himself with the savings. A month later, the glorious house is built, and Crusoe restores his consumption of fish.
The choice then for Crusoe is between 1) plenty of fish from now till forever and 2) just enough fish to survive from now to 2 months from now (1 month saving and 1 month investing into building the house) yet a shelter plus plenty of fish from 2 months from now till forever.
Going back to our computer, why would anyone offer me the $500? Well, on the loan market people with different time preferences benefit from each other’s existence. Maybe Crusoe has worked very hard the previous year and feels like indulging himself. He wants a few good meals, but has spend all of his savings. He can borrow the fish from Friday, increasing his present consumption at the expense of future goods, because the interest payments later on will diminish his disposable income. Friday does not care how to receive the benefits from his own savings. He can invest them into a project, say, weapons to protect him against the cannibals, just as Crusoe did with the shelter. But loaning the fish to Crusoe works just as well, if the price — the interest rate — is agreeable to both.
When Crusoe borrows, this increases both his present consumption and the disutility of waiting for future goods.
Time preferences determine the interest rate both on the consumer loan market and in regard to the world of business, investment, and production.