Suppose in 2009 the united states congress passes a minimum wage law that increases the minimum wage (the lowest legal wage) to 7.25 per hour and has a provision that increases the minimum wage at the beginning of each year based on the CPI for the previous year.
a.) If the CPI increases 3 percent for each of the next four years (so inflation rate is 3% for each next four years), find the minimum wage for 2010 and 2011.
b.) if the CPI overstates inflation by 1%, calculate a revised minimum wage for each year 2010 to 2011 removing the CPI bias
C.) How much does the CPI bias affect the minimum wage in 2010 and 2011
To answer these questions, we need to understand how to calculate the minimum wage based on the CPI and consider the given inflation rates.
a.) To find the minimum wage for 2010 and 2011 with an inflation rate of 3% for each year, we will use the following formula:
Minimum Wage = Previous Minimum Wage + (Previous Minimum Wage * Inflation Rate)
For the year 2009, the minimum wage was $7.25. Applying the above formula for each year, we get:
Minimum Wage for 2010 = $7.25 + ($7.25 * 0.03) = $7.25 + $0.2175 = $7.4675 ≈ $7.47
So the minimum wage for 2010 would be approximately $7.47 per hour.
Minimum Wage for 2011 = $7.47 + ($7.47 * 0.03) = $7.47 + $0.2241 = $7.6941 ≈ $7.69
Therefore, the minimum wage for 2011 would be approximately $7.69 per hour.
b.) If the CPI overstates inflation by 1%, we need to adjust our calculations by subtracting this 1% from the inflation rate.
Revised Minimum Wage = Previous Minimum Wage + (Previous Minimum Wage * (Inflation Rate - Overstatement))
Using the same formula as before, but with the revised inflation rate, we get:
Minimum Wage for 2010 = $7.25 + ($7.25 * (0.03 - 0.01)) = $7.25 + ($7.25 * 0.02) = $7.394 ≈ $7.39
Therefore, the revised minimum wage for 2010 would be approximately $7.39 per hour.
Minimum Wage for 2011 = $7.39 + ($7.39 * (0.03 - 0.01)) = $7.39 + ($7.39 * 0.02) = $7.536 ≈ $7.54
Hence, the revised minimum wage for 2011 would be approximately $7.54 per hour.
c.) To calculate how much the CPI bias affects the minimum wage in 2010 and 2011, we can find the difference between the original minimum wage and the revised minimum wage for each year.
Difference = Original Minimum Wage - Revised Minimum Wage
For 2010:
Difference = $7.47 - $7.39 = $0.08
So, the CPI bias affects the minimum wage for 2010 by $0.08.
For 2011:
Difference = $7.69 - $7.54 = $0.15
Hence, the CPI bias affects the minimum wage for 2011 by $0.15.