When economists use maths to describe people, it’s somehow clearer when they’re less accurate. People tried to model the entire world and failed — but the logic of simple metaphors means … more.

Below is a good example.

The main question motivating the paper below is: would **school vouchers** improve the educational system, and would they **increase inequality**?

*A Complicated Endogenous Jargony Title* by G. Glomm and B. Ravikumar

**PAPER SUMMARY**

The paper studies the difference between private and public systems of education.

- The public system means that everyone pays taxes to finance schools and the quality of schools is the same for everyone.
- The private educational system means that people choose how much to pay for education and the quality of schooling depends on the amount of money a student’s parent puts into it.

The model used on the paper is an **overlapping generations model**. In the first period agents allocate a unit of time between studies (i.e. acquiring human capital) and leisure. In the second period agents get income equal to their human capital.

The main findings of the paper are the following:

- First,
**inequality declines**faster with the**public**system of**education**. - Second,
**private**education results in**higher**per capita**income**unless the initial inequality is not very high. - Third, if income distribution is skewed to the left, then majority voting will result in the choice of the public education system.

*end of excerpt*

**METAPHORS AND FAIRY TALES**

Alright, so what does that mean? We took a mathematical model which resembles reality. It is wildly inaccurate; much more inaccurate than assuming the sun is a point mass for instance. But … the conclusion still does seem to say something. But what? And what, precisely, can you do with the knowledge gained from reading the above? Does it prove anything about real school vouchers? Does it even make a valid suggestion about real school voucher policy?

It’s not exactly an if-the-world-were-like-this story and it’s certainly not a here’s-how-it-is-and-here’s-what-it-means story. More like a mathematical fairy tale? Or something.

This ambiguity and vagueness are actually what made me return to mathematics after years away from it.

It’s exciting to think that logic and maths might apply to relevant, contentious questions like political disputes. It’s also cool how economists rely on judgment to construct assumptions, “pure logic” to reach conclusions, and then judgment again to apply the conclusions.