When Joe started his job at the laundromat five years ago, his wage was $5.50 an hour. Today, his wage is $6.50 an hour. If Joe started his job in the base year, and his real wage is the same as when he started, what is the Consumer Price Index (CPI) today? Round your answer to two decimals.
To calculate the Consumer Price Index (CPI), we need to compare the prices of a basket of goods and services in two different time periods. In this case, we are comparing the base year (when Joe started his job) with today.
To find the CPI, we need to calculate the inflation rate and adjust Joe's wage using that rate.
First, let's calculate the inflation rate:
Inflation Rate = (Current Wage - Base Wage) / Base Wage
Given:
Base Wage = $5.50
Current Wage = $6.50
Inflation Rate = ($6.50 - $5.50) / $5.50
Inflation Rate = $1.00 / $5.50
Inflation Rate = 0.1818 (rounded to four decimal places)
Now, let's adjust Joe's wage using the inflation rate:
Adjusted Wage = Base Wage * (1 + Inflation Rate)
Adjusted Wage = $5.50 * (1 + 0.1818)
Adjusted Wage = $5.50 * 1.1818
Adjusted Wage = $6.48 (rounded to two decimal places)
Since we are given that Joe's real wage (adjusted for inflation) is the same as when he started, his adjusted wage today is $5.50.
Now, to find the CPI, we can use the formula:
CPI = (Current Basket Price / Base Year Basket Price) * 100
We don't have the specific basket of goods and services, but since Joe's wage represents the average wage, we can consider it as a proxy for the overall price level. Therefore, we can assume that the wage represents the CPI.
CPI = $6.48 / $5.50 * 100
CPI = 117.82 (rounded to two decimal places)
Therefore, the Consumer Price Index (CPI) today is 117.82.