Henrique Costa

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In today's post, I want to start a discussion about the use of
mathematics and statistics in economics, and with this shocking
sentence:

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When a person studies economics for the first time, it is likely that
they will not encounter "crazy" equations that go beyond basic
mathematics. There is a lot of content to learn the various conceptual
definitions such as price, supply, demand, costs, profit, etc., in
addition to the various market structures.

As you delve deeper into the subject, you realize there is more to it
than just simplistic theories and newspaper chatter. So, what would be
the best way to explain the concepts of price, quantity of product sold
and production cost without referring to a single example without using
mathematics?

This *paper*:

> *KATZNER, Donald W. [Why mathematics in
> economics?](https://www.jstor.org/stable/4538849?seq=1). Journal of
> Post Keynesian Economics, v. 25, n. 4, p. 561-574, 2003.*

makes a very convincing defense of the use of mathematics in economic
science.

Although economics is technically recognized as a social science,
students who embark on a "nebulous" adventure (undergraduate course) in
this field receive (or should receive) a solid foundation in
mathematics. Because determining how scarce resources can be reallocated
requires a minimum understanding of mathematics, to calculate what the
distribution cost will be and evaluate (quantitatively) among other
measures. Thus, the field of economics is full of mathematical equations
and applications.

What is learned in teaching economics are mainly linear algebra,
calculus and statistics. These are the basis for achieving the infamous
econometrics. In algebra it is taught about total cost and total
revenue. In calculus the objective is to find the derivatives of
indifference and utility curves, profit maximization curves, cost
minimization and growth models.

In statistics, economists learn about predictive models and how to
determine how likely a certain event is to occur. Econometrics, for some
peculiar reasons, is called *"economentira"* for the use of models in
which the final objective is to estimate and predict a certain variable.

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As you progress through related topics, you will find examples such as
market demand curves (sum of several individual demand curves) or
changes in the supply and price of a *commodity* or calculating the
price elasticity of a commodity. consumption, each concept is validated
using mathematics. Definitely, a mathematical and statistical approach
is needed to have clarity when we arrive at the long-awaited "solution"
to the problems proposed to professionals in this area.

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<p><a href="./img/econometria.jpg" class="lightbox"
data-gallery="quarto-lightbox-gallery-2"
data-glightbox="description: .lightbox-desc-2"
title="A typical review for the basic econometrics final exam"><img
src="https://hcostax.com/blog/maths_economics/img/econometria.jpg"
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alt="A typical review for the basic econometrics final exam" /></a></p>
<figcaption>A typical review for the basic econometrics final
exam</figcaption>
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It has been noted that in the 19th century mathematics was considered as
a means of achieving truth; (rational) logic made it imperative to use
mathematics to prove any theorems. Many problems posed in economics are
therefore motivated to be solved by mathematics. Have these problems
really been solved?

Analyzes and studies carried out in the field of applied economics help
to explain the interdependent relationship between different variables.
An example is trying to explain what causes an increase in the price of
a product, such as the price of beef, or an increase in the unemployment
rate, or even a drop in inflation and a reduction in the basic interest
rate. Mathematical functions are used as a logical tool through
**models** from which these phenomena of everyday life can become more
understandable.

In fact, there is an exhaustive discussion about the importance of
relevant applied work and the uses of these metrics in economic science.
It is interesting to know that several economists have been awarded the
[Nobel
Prize](https://pt.wikipedia.org/wiki/Pr%C3%A9mio_de_Ci%C3%AAncias_Econ%C3%B3micas_em_Mem%C3%B3ria_de_Alfred_Nobel)
for applying mathematics/statistics to economics, including the first
awarded in 1969 to [Ragnar Frisch and
JanTinbergen](https://www.jstor.org/stable/1402316?seq=1). The most
interesting thing is that [Leonid
Kantorovich](https://pt.wikipedia.org/wiki/Leonid_Kantorovich) he won a
Nobel Prize in 1975 in economics for his contribution to the theory of
optimal resource utilization and he was a mathematician!

Many students who are looking to pursue a career in economics are
advised to take a Mathematics course, as applied studies are covered in
mathematics. The use of mathematical models and applications in this
area has been notable in the last two decades.

[Economics --- the science that stopped being
dark](https://valor.globo.com/eu-e/noticia/2012/10/23/como-a-teoria-economica-deixou-de-ser-uma-ciencia-sombria.ghtml)(In
Brazilian Portuguese) , with advances in [Alfred
Marshall](https://pt.wikipedia.org/wiki/Alfred_Marshall), with the
well-known marginalist revolt that embraced the use of mathematics as an
integral part of the economy, now more intensive than ever. Mathematics
plays the main role in many sciences like physics, chemistry, etc. And
it's really the backbone of the modern economy.

Mathematics in economics is an important tool in decision making.
Economists are hired by companies or governments to investigate and
estimate the risk or likely outcomes of an event. Economists who work
for companies in the financial market make mathematical calculations
(models) to assess whether the risk of investing in a certain asset
outweighs its potential benefits.

Economists use their mathematical "skills" to find ways to reallocate
money, even in counterintuitive ways. Using a profit-maximization chart,
economists can advise a venue to sell only 75% of available tickets,
rather than 100%, a strategy to maximize its profit. If the company
lowers ticket prices to attract new concert-goers and fill the stadium
to capacity, it could make less money than selling just 75% of the
tickets at a much higher price.

Economists also use mathematics to determine the long-term success of a
business, even when some factors are unpredictable. For example, an
economist working for an airline uses forecasting based on econometric
models to determine the price of fuel for two months ahead. The company
uses this data to block fuel prices or to protect the fuel, the famous
*"hedge"*. Bijan Vasigh, author of the book ["Introduction to Air
Transport
Economics"](https://www.amazon.com/Introduction-Air-Transport-Economics-Applications/dp/1409454878),
explains that the [Southwest Airlines](https://www.southwest.com) gained
a financial advantage over other operators due to its fuel hedging
strategy.

However, not everything is rosy, much less a bed of roses, there are
limitations to what can be done using econometric models in the economy.
Economists perform mathematical calculations with imperfect information.
Their economic models are useless in times of natural disasters, union
strikes or any other catastrophic event. Furthermore, mathematics rarely
helps economists predict irrational human behavior. A fundamental
assumption of economics is that humans act rationally. However, humans
often make irrational decisions based on choices and preferences, or
even pure fear or love. These two factors cannot be accounted for in an
economic model.

But there are already some techniques, including in the field of
*Machine Learning* that try to solve such problems. But that is the
subject of another post that I will make soon.

But the potential of these methods is recognized and therefore extremely
useful, and economists are reviewing the way calculations are carried
out to account for intangible effects, such as pollution. Mathematical
models are necessarily based on simplifying assumptions, so they are not
likely to be perfectly realistic. Mathematical models also lack the
nuances that can be found in narrative models. The point is that
mathematics is a tool, but it is not the only tool or even the best tool
that economists should use.

So, what is your opinion regarding the use of mathematics and statistics
in economic science? Is it possible to think about economics without at
least mathematizing it?

Adapted from
[original](https://medium.com/the-empirical-mode/o-uso-da-matem%C3%A1tica-na-economia-6d6de2e39dab).

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[CC BY 4.0](https://creativecommons.org/licenses/by/4.0/){rel="license"}

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## Citation {#citation .anchored .quarto-appendix-heading}

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For attribution, please cite this work as:
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Costa, Henrique. 2018. "The Mathematization of Economics." September 21,
2018. <https://doi.org/10.59350/tvp77-8gp37>.
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In today’s post, I want to start a discussion about the use of mathematics and statistics in economics, and with this shocking sentence:  When a person studies economics for the first time, it is likely that they will not encounter “crazy” equations that go beyond basic mathematics.

Messaggi di Rogue Scholar

The mathematization of Economics