Product × Finance × AI: Financial Products in the Age of AIPart One From 0 to 1中文
Chapter 1

One person, one year's harvestIncome and consumption do not happen at the same time

The first problem finance has to solve already appears in a world with only one person: income and consumption do not happen at the same time. The harvest comes once, in autumn, but one must eat in all twelve months of the year; one can work when young but not when old. Keeping today's goods for tomorrow is saving. Saving is worthwhile because the same amount of grain, spread evenly across the months, gives more satisfaction than eating it all in a few months. Saving is difficult because grain spoils, and keeping it as seed, though it brings a larger harvest next year, means eating one portion less today. This is as far as one person can go.

1. One person, one year's harvest

Imagine an island with only one person, who farms one plot of land. Every autumn he harvests 12 portions of grain and has no other income for the rest of the year. He must eat every month, and 1 portion a month is just enough. Here is the plainest of facts: income arrives at a single point in time, while consumption is spread over every day.

If he eats as much as he likes, he eats well for the first few months and goes hungry later. If he spreads the grain evenly over twelve months, every month has just enough. Both ways use up the same amount of grain; the only difference is how it is distributed over time. Turn the question around: if there were a harvest every day, or if people did not need to eat, there would be no problem of saving. The first problem of finance comes from the mismatch in time between income and consumption.

Today's counterpart. Most people are paid monthly and spend monthly, so the mismatch looks small. But a year-end bonus comes once a year, income stops during illness or unemployment, and wages end at retirement. Once the mismatch spans decades, it becomes the problem of retirement.

One harvest, twelve months of eating

The autumn harvest brings 12 portions of grain, and 1 portion a month is just enough. Switch between two ways of eating: the total eaten is the same, but its distribution over time differs.

Eaten that monthHungry monthsGrain left in the granary

Illustrative: "Eat as much as he likes" assumes at most 3 portions a month.

2. Why smooth: each extra portion is worth less

Even distribution is better because satisfaction grows at a diminishing rate. The first bowl of rice after a day of hunger brings far more satisfaction than a third bowl after one is full. The more grain one has, the less satisfaction one more portion brings; the less grain one has, the more satisfaction is lost by giving up a portion.

As long as satisfaction grows at a diminishing rate, dividing the same amount of grain evenly between the first and second halves of the year gives the greatest total satisfaction: moving one portion from the fuller half to the leaner half loses less satisfaction than it gains. This is the case for smoothing consumption. The same reasoning extends from one year to a lifetime. If a person could foresee the harvests of his whole life, the best arrangement would be to decide how much to eat each month according to his lifetime harvest, rather than eating more in good years and less in poor ones.

Diminishing marginal utility: why even distribution is better

Divide 12 portions of grain between two halves of the year. Drag the slider to change the split and see the total satisfaction of the two halves; satisfaction is the logarithm of the grain eaten.

First half
Second half
Total satisfaction

Illustrative: satisfaction = ln(portions eaten), the logarithm used by Bernoulli (1738). Any curve whose growth diminishes leads to the same conclusion.

3. Storage has a cost: grain spoils

Keeping grain until tomorrow is not free. Grain gets damp, breeds insects and is eaten by rats. Suppose a certain share is lost for every month in storage. Then the return on storage is negative: 1 portion kept today leaves less than 1 portion next month.

Losses change the best arrangement. Since the longer grain is kept the more is lost, it pays to eat a little more just after the harvest and less and less as time goes on: the consumption path tilts towards the front. The larger the losses, the steeper the tilt and the more grain is wasted. A better means of storage, a store of value that does not lose value and may even grow, is therefore valuable.

Today's counterpart. Cash does not get damp or breed insects, but inflation erodes its purchasing power. Keeping money for a long time somewhere that pays no interest amounts to a form of storage that loses something every year.

The return on storage is negative

Drag the monthly loss rate. The bars show the best way to eat at that rate: more just after the harvest and less as time goes on. The dashed line shows eating the same amount every month.

Lost over the year
First month / last month

Illustrative: 12 portions of grain, with satisfaction measured as a logarithm. The best way to eat satisfies the condition "the satisfaction of one more mouthful this month equals the satisfaction of that mouthful kept until next month, net of losses", so monthly consumption falls by a factor of (1 − loss): 1 portion in the first month, a little less each month after.

4. Seed: one portion less today, several more next year

Grain has another use: it can be kept as seed. Sow 1 portion of seed and next year's harvest brings back more than 1 portion. This is the first positive return, and it comes not from anyone's promise but from production itself.

Keeping seed follows a law of diminishing returns. Land is limited. The first few portions of seed go into the best land and add the most to the harvest; the more is sown, the smaller the gain from each additional portion. How much seed to keep depends on weighing two things. One is how much he values today: the more eager he is to eat, the greater the cost of eating one portion less today. The other is how many extra portions next year will bring: the better the land the seed goes into, the more it adds. He will keep adding seed until the gain from the last portion just makes up for the cost of eating one portion less today. The grain that the last portion of seed brings back over and above the seed itself is the "natural rate of interest" on this island of one.

Today's counterpart. Education and vocational training are the modern way of keeping seed: give up part of today's income in exchange for higher income later. A company that puts its profits into a new production line makes the same trade-off.

Keeping seed: eat less today, harvest more next year

Set aside part of the 12-portion harvest as seed. The curve is the trade-off between what is eaten this year and what is harvested next year; drag the slider to see how much extra harvest the last portion of seed still brings.

Eaten this year
Next year's harvest
Return on the last portion of seed

Illustrative: next year's harvest = 12 + 4 × √(portions of seed). Land is limited, so the more seed is sown, the smaller the gain from each additional portion; the slope of the tangent is the return on the last portion of seed.

5. One person's lifetime: Civilization Simulator, version 1

Stretch the time from one year to a lifetime and the problem becomes more severe. Suppose he begins farming at 20, can no longer work the land after 60 and lives to 80. The harvests of his youth must feed him in old age, while the grain keeps spoiling throughout those twenty years.

Below is the first version of the Civilization Simulator. The world contains only one person and his land. You can choose among three ways of eating and adjust the monthly loss rate and the share kept as seed. You will see that as long as storage involves losses, the grain saved in youth has almost nothing left by old age; however carefully he plans, he will go hungry when old. This is as far as one person can go.

Civilization Simulator · Chapter 1: one person's lifetime

He begins farming at 20, can no longer work the land after 60 and lives to 80. Choose a way of eating, adjust losses and seed, and see how much he eats in each month of his life.

SavingSeedLending · Ch. 2Commitment · Ch. 3Insurance · Ch. 5
Eaten each month (left axis, portions)Grain in the granary (right axis, portions)Below 0.6 portions means hunger

Illustrative model: the harvest comes every autumn, with a base harvest of 12 portions; next year's harvest = 12 + 4 × √(seed kept last year). Satisfaction is the logarithm of the portions eaten each month, summarized as "equivalent steady monthly consumption over a lifetime" (the exponential of the average monthly logarithm; months with less than 0.05 portions count as 0.05). "Plan for a lifetime" recalculates at each harvest: monthly consumption from then on falls by a factor of (1 − loss), which is the best arrangement when storage involves losses, and the granary is guaranteed not to run empty before 80.

Today's counterpart. This is exactly the problem of saving for retirement. Saving for decades ahead alone, using only means of storage that lose value, is enormously costly. The deposits, bonds, funds and pensions on which people today rely for retirement do not exist in a world of one person.

6. What this step leaves open

In a world of one person, saving can only mean storing goods, and expanding production can only mean keeping seed. Several problems remain that one person cannot solve, and they are the constraints of the steps that follow:

  1. There is no grain in months of poor harvest or illness, and storage involves losses. If there were another person on the island whose months of shortage happened to differ from mine, could we lend to each other?
  2. There is no harvest in old age, so saving must span decades. Could one lend to someone else? Will that person still be there decades later?
  3. Harvests are uncertain, with good years and bad years. This chapter assumes the same harvest every year, which is a strong assumption.
  4. People do not necessarily act according to plan; eating too much in autumn is common. This chapter assumes he always follows the best plan.

What this step leaves open

Four problems that cannot be solved in a world of one person, each becoming the constraint of a later chapter. Choose a problem to see the assumption hidden in it.

One personSaving and seed

7. Implications for products

Every financial product today serves the same original need: rearranging consumption over time. Three plain implications follow. First, in designing any financial product, first ask when the user will need the money. Second, a store of value is valuable in itself: a means of storage that does not lose value already makes people better off. Third, positive returns originally come from production, not from trading; returns in financial markets, traced back to their roots, also depend on this.

Chapter summary: finance in a world of one person

Four conclusions, each corresponding to one mechanism in this chapter.

The need to saveFirst ask when the user will need the money

Income and consumption not happening at the same time is the first need every financial product serves.

Store of valueNot losing value is itself valuable

A means of storage that does not lose value already makes people better off, even if it earns nothing.

Where returns come fromPositive returns originally come from production

The return on seed comes from the extra grain the land grows, not from anyone's promise.

The limit of one personSpanning decades requires other people

Storage spoils and there is no harvest in old age: one person alone cannot save across a lifetime.

References