When rich people work less, does it help the poor? A simple model

For my brother, Maximilian Wilson

Economic explanations are often about simplifying things to illustrate an essential principle. So we make a simple world:

1) No fossil fuels or resource depletion concerns
2) No unemployment
3) Prices are fixed

Consider poor people as a group. Give them each a sum of money, and let them spend it without taxes. Does any of this money leave the group? In the real world, poor people as a group lose money to rich people as a group in two main ways.

First, poor people who live in the same country as rich people lose money because these poor people must pay higher prices for things like rent and medical care. The existence of rich people is the reason these prices are high, and rich people are also the owners of property and capital, so they get the profits.

Second, poor people who live in poor countries, and so have low costs for rent and so on, lose money when they buy things from rich countries. This can be luxury products, because even in a poor country there are relative degrees of rich and poor, or it can be things like reliable machinery that is manufactured using high technical expertise. (In the real world, we might also include fossil fuels here.)

So we can expect poor people as a group to lose money to rich people. What about the other way around? Well, it's common for people to talk about rich people wanting there to be more poor people to work as their corporate slaves. Whether it's poor people assembling luxury products like iPhones that sell for expensive prices, or poor people picking fruit or building giant mansions, if poor people are working for rich people it means that there is some money going from the group of rich people to the group of poor people. This means that despite poor people losing money to rich people, the group of poor people is never entirely drained of all of its money.

We now have an understanding of what kind of interactions we need in our simple world.

We make two types of people: rich people, and poor people.

We make three types of goods: Good Bananas, Medium Bananas, and Bad Bananas.

Each person who makes bananas can make enough for one other person. In a slightly more complex model, we could add a second category of good (perhaps a different cultivar of bananas), also available in Good, Medium, and Bad varieties, and each person chooses during childhood whether to specialize in bananas or this second type of good, so we can ensure that some trading goes on and people don't just eat the bananas they make themselves. But we're not worrying about who eats the bananas, just the total number of bananas of each type being made.

Anyone can make Bad Bananas. But making Medium Bananas requires a license that costs $1, with this profit going to a corporation that is owned by rich people. People prefer Medium Bananas over Bad Bananas, but their production is limited by the amount of money that the group of poor people earns from the group of rich people.

Rich people can make Good Bananas, which are so expensive that only other rich people can afford them. (There might be a license fee, but since rich people would be paying it to themselves, it doesn't matter.)

Bananas are not necessary for survival, but people prefer having bananas over having nothing.

In the very simplest model, we don't add any special way for money to go from the group of rich people to the group of poor people: rich people make Good Bananas for each other and consume them. Poor people don't have any money, so cannot afford a license for Medium Bananas, so they only make Bad Bananas for each other.

What happens if a rich person decides to work less? Suddenly, the group cannot make as many Good Bananas as the group wants to eat. Somebody, perhaps the rich person who is working less, must buy some other type of banana. The first time this happens, perhaps they buy a Bad Banana, but after that the group of poor can afford a license for Medium Bananas and make and sell these to the rich person instead.

The details after this depend on the fixed prices, but suppose that Bad Bananas sell for $1, Medium Bananas sell for $5 profit + $1 license fee ($6 total), and Good Bananas sell for "if you need to ask for the price, you can't afford it". When a single rich person decides to buy Medium Bananas, they are spending $6, which is enough for six poor people to afford the license fees to make Medium Bananas.

One of these six will be selling to the rich person. The other five are selling Medium Bananas to other poor people: people who otherwise would only be able to consume Bad Bananas.


In this simple model, we use a license fee in order to be able to easily calculate the effects of the group of poor people receiving more money. If the way that money leaves the group of poor people is through purchasing luxury products made by rich people, then we have to balance the production by rich people with the change in demand and the model becomes more complicated. We might have to start allowing prices to change or allow people to produce more goods than a single other person can use, which could force us to include unemployment and stop treating poor and rich people as homogeneous groups.

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notes:
written 09 Sep 2024

People are confused by "rich people", and prefer "high earners" as a term which can potentially include themselves.

Adding unemployment makes it easier to show that higher earners working less helps low earners. One could, for example, eliminate Bad Bananas from the model and just start with the poor people as all being unemployed.