Unlocking the Secrets of Mathematics and Economics
The Math in Economics We Never Knew

What happens to the interest rate if I cancel my savings account midway?
Why are the taxes paid different depending on the tax base?
Can consumer satisfaction be expressed in numbers?
How much should production be increased if the store is successful?

Our lives are a series of choices.
Among them, making wise economic choices is essential to living a successful life.
From comparing savings and deposit interest rates to calculating year-end tax deductions and seeking investment information, the economy influences many aspects of our lives.
Moreover, as economic freedom emerges as a new life goal and the era of uncertainty continues with low growth, making rational choices has become increasingly important.
"Minimum Mathematics for Making Economics Easy" proposes a "mathematical way of thinking" as a method.

Author Oh Kook-hwan, a high school mathematics teacher, was in charge of the newly introduced "Economic Mathematics" course in the 2015 revised curriculum when he realized the value of mathematics as a language for explaining the complex human world.
While there wasn't much new material to teach in terms of mathematics, a variety of economic concepts emerged. I had to study them one by one, as if I were digging a well, to understand the context. In the process, I opened my eyes to the intersection between the fundamental question, "What is mathematics?" and the ever-changing realities of the economy.
Based on that experience, I decided to write this book and present it to the world, with the goal of providing an experience of 'understanding and expressing various complex economic phenomena through the lens of mathematics and in the language of mathematics to solve problems.'

This book gives us the courage to believe that 'economics' and 'mathematics' are not the exclusive domain of experts, but that we can experience the joy of knowledge and solve problems when economic and mathematical thinking meet in our daily lives.
Han Jin-soo, Professor of Social Studies Education, Gyeongin National University of Education, author of "Economics Essays for Youth"

This book, consisting of four chapters, presents a minimum mathematical thinking method that will serve as a guide for understanding the economy.
Through the framework of 'change and regularity (sequence),' 'relative size (ratio and proportion),' 'modeling (mathematical model),' and 'rational choice (optimization),' we examine everything from the problem of calculating the changing value of money to methods of maximizing the profits of market participants.
The author repeatedly emphasizes that mathematics is like a 'language', meaning that just as written language concretizes abstract ideas and enables high-level communication, mathematics, too, serves as a language that expresses the complex world and helps us think beyond intuition.
By exploring economic issues, sometimes broadly and sometimes deeply, through the language of mathematics, by the time you finish the book, you'll be able to discover the mathematical thinking hidden within even the most complex tasks—whether choosing a banking product, considering installment payments or lump sum payments, or even leaving a star rating review—and solve the problems on your own.

To make rational decisions that take into account the changing value of money, we need to go beyond the abstract understanding that "money is growing."
That means you need to be able to think specifically about how the value of money increases or decreases, how the value of money changes over time, and how the size of the principal affects interest.
The first thing to understand is ‘interest’.
This is because the interest rate, depending on the size of the principal or the period of borrowing, changes the value of money.
---「1.
- Interest: In search of the principle by which money makes money

This function represents the difference between the time it takes for your money to actually double and the time it would take for the rule of 72 to predict.
If we represent it as a graph, it is as follows.
As you can see from the graph, this function has the smallest error when it has a degree value.
This means that the Rule of 72 is most effective when you have a return of around 8%.

---「1.
- From "Economic Literacy: How Realizable Is the 'Rule of 72'?"

When calculating based on present value, the amount to be repaid is the same as the principal.
Since the calculation is based on the present, you can think of the loan as not having accrued interest yet.
Instead, if the monthly payment is in won, then the discount rate should be applied to each won.
Because the value of the won I will pay in a month will be less than the won I pay now.
Naturally, the further in the future you plan to pay, the smaller the discount rate will be applied.
Therefore, when calculating based on present value, you can calculate it by applying a discount rate to each monthly payment and adding them all up so that the current loan amount is the same.
---「1.
- Loans and Installments: How much do you want to pay per month?

The fundamental reason why these problems are difficult to solve is because they involve the concept of 'infinity'.
What I'm saying is that the problem contains parts that are difficult to solve intuitively.
To solve this, the solution to the infinite geometric series problem is to bring the problem to a point where it can be intuitively understood.
In other words, the original problem of finding the sum of infinitely many terms is changed to the problem of finding the sum up to the terms, and after making it into a form that is easy to imagine infinity (), we imagine what the value will be when this becomes infinitely large.
This is also the idea of ​​solving a problem by reducing it to a smaller scale when it is difficult to think about the whole picture, and then using the result to solve the original problem.

---「1.
- Pension: The difference between 'thin and long' and 'thick and short'

GDP calculated this way has limitations in accurately representing a country's production capacity. Production and prices are variables in GDP calculations, so changes in commodity prices can affect GDP even if production remains unchanged.
So GDP is divided into nominal GDP and real GDP.
Nominal GDP is calculated by multiplying the production volume of the current year by the price of the current year, and real GDP is calculated by multiplying the production volume of the current year by the price of the base year.
By eliminating the impact of price fluctuations, we can accurately identify changes in production capacity.

---「2.
- Economic Index: Reading the Economy Through Ups and Downs in Numbers

Income tax should be applied at progressive rates.
If everyone is taxed the same amount of income tax, those with lower incomes will bear a relatively greater tax burden.
( ··· ) In our country, the tax base is divided into sections as shown in the table below, and tax rates are applied differentially according to the section.

There are two ways to apply progressive tax: simple progressive tax rate and excess progressive tax rate.
A simple progressive tax rate is a method of uniformly applying a high tax rate according to a high tax base, while an excess progressive tax rate is a method of dividing the tax base into sections and applying the tax rate for each section only to the excess amount and adding them together.

---「2.
- From "Taxes: If you can't avoid them, know them and use them"

In fact, we can roughly understand the meaning of articles that use complex economic indicators.
If you look at the vocabulary used in the text or the nuances of the text, you can see whether the economy is in crisis or boom.
The problem is that if you don't clearly understand the meaning of the terms, it's difficult to understand more information from the text or interpret it critically.
For example, if an article comes out saying that the exchange rate is rising and the economy is at risk, if you don't know how the exchange rate rises and falls in the first place, you won't be able to imagine how this economic risk will materialize and affect you.

---「2.
- From "Why we look at the economy by zooming in and out"

It is noteworthy that even when explaining the same phenomenon, different mathematical models or approaches arise when the assumptions change.
What marginal utility theory and indifference curves ultimately try to explain is the behavior of consumers when consuming goods or services.
To this end, marginal utility theory assumed that utility could be quantified, and indifference curves assumed that only the order of utility could be assigned.

Here, it might be worth considering that when approaching a theoretical mathematical model, we should keep in mind what assumptions are being made about the dog.
As in the previous example, mathematical models appear in different forms depending on what assumptions are made and how which variables are controlled.

---「3.
- Utility Function: Can Consumer Satisfaction Be Expressed Numerically?

Production does not increase proportionally as the amount of labor increases.
If you keep adding staff to your donut shop, your production will initially increase, but as time goes on, the shop will become more complex and less useful.
This is called the 'law of diminishing returns'.
On the one hand, as we continue to hire employees, various costs, including labor costs, increase rapidly.
Production volume is gradually decreasing while costs are increasing, so it is not a good situation for producers.
Ultimately, producers will strive to find a balance between production and costs that maximizes profits while maintaining an appropriate number of employees.

---「3.
- Production and Cost: How much should a producer produce and at what price?

When there is a good harvest, the supply curve shifts to the right, prices fall, and quantity traded increases.
However, in the case of agricultural products, the demand curve is inelastic, so the increase in transaction volume is not large compared to the large drop in price.
So, in the end, total revenue, which is calculated by multiplying price and production quantity, decreases.
On the other hand, when there is a famine, the supply curve shifts to the left, prices rise and quantity traded falls.
However, the trading volume does not drop significantly compared to the significant increase in price.
In this case, the total income will eventually increase compared to before.
Because of this principle, the farmer's paradox occurs, where total income decreases during good harvests and increases during bad harvests.
---「3.
- Economic Literacy: Is a Big Harvest Always Good? From "The Farmer's Paradox"

In general, when a consumer consumes multiple goods, utility is maximized when the marginal utility of each good per 1 won is the same.
This is called the law of equal marginal utility.
This rule is often explained using the situation of going to a buffet.
If you go to a buffet and keep eating only steak because the steak is good, you'll soon get sick of it.
Because the marginal utility of steak has declined.
If you insist on filling your stomach with only steak and leave the restaurant, you'll probably be left with some regrets. If you leave with the uneaten dessert lingering in your eyes, you won't be very satisfied with your meal.
So when you get hungry for steak, you need to find a new food with a higher marginal utility to increase your overall utility.
If you keep eating new foods like this, there will eventually come a point where no matter what you eat, it won't be beneficial.
Now, I don't have any regrets about what else I should eat.
Now that you're fully satisfied, you can leave the restaurant feeling good, right?

---「4.
- Utility Maximization: From “If You’re Going to Do It, Do It” Explained Through Differentiation