Introduction:
Cost of living index numbers are used to measure the changes in the cost of living over time. These indexes are calculated by comparing the prices of goods and services in a particular region to the prices in a base period. The result is an index number that reflects the relative change in the cost of living over time.

Real Wages:
Real wages are the wages that an employee receives after adjusting for inflation. They represent the purchasing power of an employee's earnings. In other words, real wages are the wages that can actually buy goods and services.

Process:
The process of finding real wages using cost of living index numbers involves the following steps:

1. Determine the nominal wage: The nominal wage is the wage that an employee receives in current dollars.

2. Determine the cost of living index: The cost of living index is calculated using the prices of goods and services in a particular region. This index reflects the relative change in the cost of living over time.

3. Adjust the nominal wage for inflation: The nominal wage must be adjusted for inflation to determine the real wage. This is done by dividing the nominal wage by the cost of living index.

4. Calculate the real wage: The real wage is the result of the nominal wage divided by the cost of living index.

Example:
Suppose an employee earns a nominal wage of $20 per hour in 2020. The cost of living index in 2020 is 120. In 2021, the employee's nominal wage increases to $22 per hour and the cost of living index increases to 125. To find the employee's real wage in 2021, we follow these steps:

1. Determine the nominal wage: The employee's nominal wage in 2021 is $22 per hour.

2. Determine the cost of living index: The cost of living index in 2021 is 125.

3. Adjust the nominal wage for inflation: $22 / 125 = $0.176 per index point.

4. Calculate the real wage: $0.176 x 120 = $21.12 per hour.

Therefore, the employee's real wage in 2021 is $21.12 per hour, which is less than the nominal wage of $22 per hour due to inflation.