Question

In July 2014 , in the economy of Sandy Island, 10,000 people were employed, 1,000 were unemployed, and 5,000 were not in the labor force. During August 2014,80 people lost their jobs and didn't look for new ones, 20 people quit their jobs and retired, 150 unemployed people were hired, 50 people quit the labor force, and 40 people entered the labor force to look for work. Calculate for July 2014 a. The unemployment rate. b. The employment-to-population ratio. And calculate for the end of August 2014 c. The number of people unemployed. d. The number of people employed. e. The unemployment rate.

Short answer

a. Unemployment rate: 9.09% b. Employment-to-population ratio: 62.5% c. Number of unemployed: 890 d. Number of employed: 10,050 e. Unemployment rate: 8.14%

Step-by-step solution

Calculate the Unemployment Rate for July 2014

First, the total labor force in July 2014 is the sum of employed and unemployed people. The formula for the unemployment rate is given by \[ \text{Unemployment Rate} = \frac{\text{Number of Unemployed}}{\text{Labor Force}} \times 100 \] where the labor force = number of employed + number of unemployed.

Plug in the Numbers for July

Employed: 10,000, Unemployed: 1,000. \[ \text{Labor Force} = 10,000 + 1,000 = 11,000 \] \[ \text{Unemployment Rate} = \frac{1,000}{11,000} \times 100 = 9.09\text{\text{ %}} \]

Calculate the Employment-to-Population Ratio for July 2014

The employment-to-population ratio is given by \[ \text{Employment-to-Population Ratio} = \frac{\text{Number of Employed}}{\text{Total Population}} \times 100 \] Total Population = Number of Employed + Number of Unemployed + Not in Labor Force.

Plug in the Numbers for Employment-to-Population Ratio

Total Population: Employed (10,000) + Unemployed (1,000) + Not in Labor Force (5,000) = 16,000 \[ \text{Employment-to-Population Ratio} = \frac{10,000}{16,000} \times 100 = 62.5\text{ %} \]

Update the Employment and Unemployment Numbers for August 2014

Calculate the changes in employment and unemployment: - 80 people lost jobs and didn't look for new ones - 20 people retired - 150 unemployed people got hired - 50 people quit the labor force - 40 people entered the labor force Update counts for employed and unemployed accordingly.

Calculate the Changes

Initial numbers: Employed = 10,000, Unemployed = 1,000.Changes: - Employed: 10,000 - 80 - 20 + 150 = 10,050 - Unemployed: 1,000 + 40 - 150 = 890 - Total Labor Force = 10,050 (Employed) + 890 (Unemployed) + People not in the labor force changes (5,000 - 50 - 80 - 20 + 40 = 4,890).

Calculate New Unemployment Rate for August 2014

With new numbers: \[ \text{Labor Force for August} = 10,050 + 890 = 10,940 \] \[ \text{Unemployment Rate} = \frac{890}{10,940} \times 100 = 8.14\text{ %} \]

Key concepts

Labor Force

The labor force is an essential concept in understanding employment statistics. It includes everyone who is either employed or actively seeking employment. Essentially, it is the sum of employed and unemployed individuals, but it does not include those not actively looking for work, such as retirees, students, or discouraged workers.

• Employed: People having a job, whether full-time or part-time.
• Unemployed: People without a job but actively seeking work.

For example, in Sandy Island in July 2014, the labor force consisted of 10,000 employed people and 1,000 unemployed people, making a total of 11,000. Understanding the size of the labor force is crucial as it serves as the basis for calculating the unemployment rate. To reiterate, the labor force formula is:
\[ \text{Labor Force} = \text{Number of Employed} + \text{Number of Unemployed } \]

Employment-to-Population Ratio

The employment-to-population ratio is a measure of the working-age population currently employed. This ratio provides a broader picture of the economic health of a country or a region by considering the overall population, not just the labor force.

• Formula: \[ \text{Employment-to-Population Ratio} = \frac{\text{Number of Employed}}{\text{Total Population}} \times 100 \]

To calculate this ratio, you need to know the total population, which includes those employed, unemployed, and those not in the labor force. Using Sandy Island as an example: Total population is the sum of the employed (10,000), unemployed (1,000), and those not in the labor force (5,000), making it 16,000. The employment-to-population ratio here would be:
\[ \text{Employment-to-Population Ratio} = \frac{10,000}{16,000} \times 100 = 62.5\text{\text{ %}} \] This means 62.5% of the total population was employed in July 2014.

Unemployment Rate

The unemployment rate is a key economic indicator used to gauge the health of an economy. It represents the percentage of the labor force that is unemployed and actively seeking work. This metric provides useful insight but needs to be understood alongside other measures.

• Formula: \[ \text{Unemployment Rate} = \frac{\text{Number of Unemployed}}{\text{Labor Force}} \times 100 \]

To calculate this, divide the number of unemployed individuals by the total labor force and multiply by 100 to get a percentage. In the case of Sandy Island for July 2014:
Total labor force = 10,000 (employed) + 1,000 (unemployed) = 11,000
\[ \text{Unemployment Rate} = \frac{1,000}{11,000} \times 100 = 9.09\text{\text{ %}} \] This means that 9.09% of the labor force was unemployed.

By the end of August 2014, changes in the labor force would update these numbers. After calculations, with new figures indicating shifts in employment and unemployment, the updated unemployment rate would be calculated similarly. For August 2014, the updated labor force was 10,940 and unemployed 890, leading to an unemployment rate of:
\[ \text{Unemployment Rate} = \frac{890}{10,940} \times 100 = 8.14\text{\text{ %}} \] This decrease in the unemployment rate indicates an improvement in employment during that period.