The One Lesson Model

Economic models can be pretty simple

[Warning: this article is a bit more technical than most, so don’t worry about skipping over the details near the end if they seem too complicated. But if you know a bit about mathematical modelling, I hope you’ll appreciate them.]

What’s a model anyway?

Here’s a slightly frivolous definition to start with:

A model is a small imitation of the real thing.

So why would you make one? Well one good reason is to test an idea before committing a lot of resources to it. Maybe you’ve come up with an idea for a new aircraft design which you think will be more efficient, but you’re not absolutely sure, so you don’t want to spend a fortune building a full-size version until you’re a bit more confident. In that case, you can try making a much smaller version — a model — and putting it in a wind tunnel to see how it copes. If it turns out that your idea doesn’t work, you haven’t wasted too many resources. And even if it does work well, you’ve probably got a better idea of how to make the real thing.

Models aren’t usually just scaled-down versions of the real thing. They’re also simplified. If every single component of a real aircraft had to be shrunk down to the right size for the model, it would be extremely difficult and expensive to build. Instead, you focus on what you believe are the most important features, such as the overall shape of the body. And you probably wouldn’t bother to paint it either, even though it would look very different from the final product.

There are lots of very different examples of this sort of thing. From building small architectural models of buildings to check they’ll be strong enough to drawing a storyboard for a feature film.

Another type of model is a mathematical model. It’s a description, using precise language, of how something in the real world works. It helps you to understand the real world better, and perhaps even to predict the future. The real world is very complex, and to make sense of it, it’s a good idea to make the model simpler — again by concentrating on what you believe are the most important features.

One example of this type of model is the one described by Newton’s laws of motion. It’s an extremely simple model of the whole universe:

1. Every physical object is treated as a single point with momentum (mass × velocity), and

2. There are forces (it doesn’t explain where these come from) which change the momentum of these objects.

Some people might think that this extreme level of simplification couldn’t tell us anything useful, but it’s enough to accurately predict the motion of objects on Earth, as well as the motion of planets around the Sun¹. Don’t assume that simplifying something means it’s less accurate! When done well, simplifying is about concentrating on what really matters, and ignoring irrelevant details (like the colour of an aircraft when you want to know how well it’s going to fly).

Talking of very useful extreme simplifications, let’s look at the model of the One Lesson. It basically describes balance sheets. Here’s how it’s represented in “OMT” notation². Boxes represent types of “object” (person, product, debt, etc.), and lines represent how those objects are related to each other. I’ll describe it step-by-step below.

The object model for the One Lesson

Here’s what the diagram says. First of all the objects:

1. There are objects which we’ll call “entities”. (Don’t get put off by the abstract word. An entity is just someone or something which has a balance sheet i.e. it can own, be owed, or owe things).

2. The line below “Entity” which splits in two at a triangle shows that there are two different types of entity: people, and corporations.

3. There are objects which we’ll call “products”.

4. There are objects which we’ll call “debts”.

Objects have properties, which are shown below the dividing line in the box:

1. An entity (whether a person or a corporation) has a property called “raw net worth³” (RNW for short).

2. A product has two properties: “unit” and “quantity”. This could be “strawberry” and “50” respectively. It represents something which an entity can own in the real world.

3. A debt has the same two properties. It represents a promise made by one entity to transfer something to another entity at some time in the future.

Finally, there are relationships between objects, represented by the lines which link them:

1. Following the line from Entity to Product: each entity (person or corporation) can have (own) multiple products. (The black ball means “zero or more”). Following the line in reverse, each product has a single owner.

2. Following the line up then left from Entity to Debt: each entity can have multiple debts as assets (i.e. the debt is owed to the entity). Following the line in reverse, each debt has a single creditor (the entity to whom the debt is owed).

3. Following the line left then up from Entity to Debt: each entity can have multiple debts as liabilities (i.e. the debt is owed by the entity). Following the line in reverse, each debt has a single debtor (the entity who owes the debt).

Even though the diagram’s quite colourful (to make it more pleasant to look at), this is a formal, rigorous mathematical model of the economy. And combined with the table of the 7 economic actions below (described here), which describe how the model changes over time, this is a coherent and extremely useful dynamic model of the economy. All economic activity is made up of these economic actions, which affect what each entity owns, is owed and owes.

Summary

I thought it was about time I included a formal model for the One Lesson. I hope it’s clear that:

1. It’s very simple, as far as economic models go.

2. The ideas of the model correspond closely to things which we understand intuitively from the real world.

3. It describes all economic activity (unlike many economic models, which often ignore important ideas like production, consumption, insolvency, money(!), (other) debts, etc.

4. The arrow notation for economic actions closely corresponds to our intuition of how the economy works.

If you have any experience of creating mathematical models, whether about economics or anything else, please leave a comment below to let me know what you think!

1. With the exception of Mercury, which needs an adjustment for the effects of general relativity because it’s so close to the Sun.

2. See Object Oriented Modelling and Design by J. Rumbaugh et al.

3. Someone’s raw net worth (RNW) is what they own plus what they’re owed minus what they owe (i.e. their assets minus their liabilities). It is a “heterogeneous” sum/difference, which just means that things of different types are added and subtracted, not monetary “values” which have been assigned to them. If the idea is new to you, this article explains it with examples.