Nuku has an unemployment rate of 12%. There are 10,307 people who are working or have work. How many people are in Nuku's labor force? Round to the nearest whole number.

Principles of Economics 2e
2nd Edition
ISBN:9781947172364
Author:Steven A. Greenlaw; David Shapiro
Publisher:Steven A. Greenlaw; David Shapiro
Chapter21: Unemployment
Section: Chapter Questions
Problem 16RQ: Assess whether the following would be counted as unemployed in the Current Employment Statistics...
icon
Related questions
Question
**Labor Force Calculation in Nuku**

Nuku has an unemployment rate of 12%. There are 10,307 people who are working or have work. 

**Question:** 
How many people are in Nuku's labor force?

**Instruction:** 
Round to the nearest whole number.

---

To determine the total number of people in Nuku's labor force, we need to understand the relationship between the unemployment rate, the number of employed individuals, and the total labor force.

Here's a step-by-step process:

1. **Identify the Given Data:**
   - Unemployment rate = 12%
   - Number of people who are employed = 10,307

2. **Understand the Unemployment Rate:**
   The unemployment rate is the percentage of the total labor force that is unemployed.

3. **Formula:**
   \[
   \text{Unemployment Rate} = \frac{\text{Number of Unemployed People}}{\text{Total Labor Force}} \times 100
   \]

4. **Rewrite the Formula for Purpose:**
   \[
   \text{Unemployment Rate} = \frac{\text{Total Labor Force} - \text{Number of Employed People}}{\text{Total Labor Force}} \times 100
   \]

5. **Solve for Total Labor Force:**
   Let \( L \) be the total labor force.
   \[
   12 = \frac{L - 10,307}{L} \times 100
   \]
   
6. **Simplify:**
   \[
   12 = 100 \times \left(1 - \frac{10,307}{L}\right)
   \]

7. **Isolate \( L \):**
   \[
   0.12 = 1 - \frac{10,307}{L}
   \]
   \[
   \frac{10,307}{L} = 0.88
   \]
   
8. **Solve for \( L \):**
   \[
   L = \frac{10,307}{0.88}
   \]
   \[
   L \approx 11,714.77
   \]

9. **Round to the Nearest Whole Number:**
   \[
   L \approx 11,715
   \]

Therefore, the total number of people in Nuku's labor force is **11,715**
Transcribed Image Text:**Labor Force Calculation in Nuku** Nuku has an unemployment rate of 12%. There are 10,307 people who are working or have work. **Question:** How many people are in Nuku's labor force? **Instruction:** Round to the nearest whole number. --- To determine the total number of people in Nuku's labor force, we need to understand the relationship between the unemployment rate, the number of employed individuals, and the total labor force. Here's a step-by-step process: 1. **Identify the Given Data:** - Unemployment rate = 12% - Number of people who are employed = 10,307 2. **Understand the Unemployment Rate:** The unemployment rate is the percentage of the total labor force that is unemployed. 3. **Formula:** \[ \text{Unemployment Rate} = \frac{\text{Number of Unemployed People}}{\text{Total Labor Force}} \times 100 \] 4. **Rewrite the Formula for Purpose:** \[ \text{Unemployment Rate} = \frac{\text{Total Labor Force} - \text{Number of Employed People}}{\text{Total Labor Force}} \times 100 \] 5. **Solve for Total Labor Force:** Let \( L \) be the total labor force. \[ 12 = \frac{L - 10,307}{L} \times 100 \] 6. **Simplify:** \[ 12 = 100 \times \left(1 - \frac{10,307}{L}\right) \] 7. **Isolate \( L \):** \[ 0.12 = 1 - \frac{10,307}{L} \] \[ \frac{10,307}{L} = 0.88 \] 8. **Solve for \( L \):** \[ L = \frac{10,307}{0.88} \] \[ L \approx 11,714.77 \] 9. **Round to the Nearest Whole Number:** \[ L \approx 11,715 \] Therefore, the total number of people in Nuku's labor force is **11,715**
Expert Solution
steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Unemployment
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, economics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Principles of Economics 2e
Principles of Economics 2e
Economics
ISBN:
9781947172364
Author:
Steven A. Greenlaw; David Shapiro
Publisher:
OpenStax
Essentials of Economics (MindTap Course List)
Essentials of Economics (MindTap Course List)
Economics
ISBN:
9781337091992
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics (MindTap Course List)
Principles of Economics (MindTap Course List)
Economics
ISBN:
9781305585126
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Macroeconomics (MindTap Course List)
Principles of Macroeconomics (MindTap Course List)
Economics
ISBN:
9781285165912
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Brief Principles of Macroeconomics (MindTap Cours…
Brief Principles of Macroeconomics (MindTap Cours…
Economics
ISBN:
9781337091985
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning
Principles of Economics, 7th Edition (MindTap Cou…
Principles of Economics, 7th Edition (MindTap Cou…
Economics
ISBN:
9781285165875
Author:
N. Gregory Mankiw
Publisher:
Cengage Learning