Defining better the equation between unemployement and national output part 2

Posted by: admin 1 week, 2 days ago

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Let’s break down the equation \( u = 1 - \frac{Y}{L} \) in a very simple way.

### What It Means:

- **u** = Unemployment rate. This tells us what **percentage of people** in the workforce don’t have jobs.
- **Y** = Output. This represents how much stuff (goods and services) the economy is producing. In simple terms, it’s related to **how many people are working** to produce things.
- **L** = Total labor force. This is the **total number of people** who can work, which includes both people who have jobs and people who don’t.

### Simple Explanation:

1. **1 - Something**:
In this equation, the number 1 represents **all the people** in the labor force (both those working and not working). When you subtract something from 1, you’re looking at the part of the labor force that **isn’t working**—which is the **unemployment rate**.

2. **Y / L**:
This part, \( \frac{Y}{L} \), is the **fraction of the labor force that has jobs** and is working to produce output. It tells us how much of the labor force is being used to produce goods and services.

3. **Putting It Together**:
So, the equation \( u = 1 - \frac{Y}{L} \) is saying:

- **Unemployment (u)** is what’s left after you subtract the people who are working (represented by \( \frac{Y}{L} \)) from the total labor force.
- If **more people are working** (meaning \( Y \) goes up), then unemployment goes **down** because a larger part of the labor force is producing stuff.
- If **fewer people are working** (meaning \( Y \) is lower), unemployment goes **up** because fewer workers are producing goods.

---

### Example:

Imagine there are 100 people in the labor force (L = 100):
- If 90 people are working to produce goods (Y = 90), the unemployment rate is:
\[
u = 1 - \frac{90}{100} = 1 - 0.9 = 0.1 \text{ or } 10\%
\]
This means 10% of the people in the labor force are unemployed.

- If only 70 people are working (Y = 70), the unemployment rate is:
\[
u = 1 - \frac{70}{100} = 1 - 0.7 = 0.3 \text{ or } 30\%
\]
Now, 30% of the people in the labor force are unemployed.

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### Easy Summary:
- The equation \( u = 1 - \frac{Y}{L} \) shows that **unemployment** is the part of the labor force that **isn’t working**.
- The more people working (higher Y), the **lower the unemployment**.
- The fewer people working (lower Y), the **higher the unemployment**.

It’s like saying: "Unemployment is whatever is left over after we account for all the people who are working."

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