According to Statistics New Zealand, in the fourth quarter of 2014 , the labor force was 2,394,000 employment equaled 2,254,500 , and working-age population was 2,984,600 in New Zealand. Calculate the a. Labor force participation rate. b. Employment-to-population ratio. c. Unemployment rate.

The **Labor Force Participation Rate** is a key measure in labor economics. This metric helps us understand the active portion of the working-age population, including those working or actively seeking work.

To calculate this rate, you use the formula: \( \text{Labor Force Participation Rate} = \frac{\text{Labor Force}}{\text{Working-Age Population}} \times 100 \)

In our example, New Zealand's labor force in the fourth quarter of 2014 was 2,394,000, and the working-age population was 2,984,600. Insert these values into the formula: \[ \text{Labor Force Participation Rate} = \frac{2,394,000}{2,984,600} \times 100 \]

By performing the division and then multiplying by 100, you get the Labor Force Participation Rate. This calculation helps in understanding what proportion of the population is engaged or seeking to engage in productive activities.

The **Employment-to-Population Ratio** indicates the proportion of the working-age population that is employed. This ratio provides a snapshot of the true employment status within a country.

The formula to find this ratio is: \( \text{Employment-to-Population Ratio} = \frac{\text{Employment}}{\text{Working-Age Population}} \times 100 \)

Using New Zealand's data from the fourth quarter of 2014, with 2,254,500 people employed and a working-age population of 2,984,600, we substitute these into the formula: \[ \text{Employment-to-Population Ratio} = \frac{2,254,500}{2,984,600} \times 100 \]

Calculate the division and multiply by 100 to obtain the ratio. This measure gives a clear picture of the employment status among the working-age population, shedding light on the economy's ability to create jobs.

The **Unemployment Rate** is one of the most critical indicators of labor market health. It reflects the percentage of the labor force that is actively seeking work but remains unemployed.

To determine the Unemployment Rate, use the formula: \( \text{Unemployment Rate} = \frac{\text{Labor Force} - \text{Employment}}{\text{Labor Force}} \times 100 \)

From the exercise, with New Zealand's labor force at 2,394,000 and employment at 2,254,500 in the fourth quarter of 2014, we first calculate the number of unemployed: \[ \text{Unemployed} = \text{Labor Force} - \text{Employment} = 2,394,000 - 2,254,500 \]
Thus, there are 139,500 unemployed individuals. Now, insert these into the formula: \[ \text{Unemployment Rate} = \frac{2,394,000 - 2,254,500}{2,394,000} \times 100 \]
Finally, perform the calculations to get the unemployment rate.
This metric is essential for understanding the percentage of the labor force that is currently without work but actively seeking employment.