Suppose in 2007 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 that the inflation rate is 3 percent for each of the next four years), find the minimum wage for 2008, 2009, and 2010.

b) If the CPI overstates inflation by 1 percentage point, calculate a revised minimum wage for each year 2008 to 2010 removing the CPI bias.

c) How much does the CPI bias affect the minimum wage in 2008, 2009, and 2010?

To answer these questions, we need to understand the calculation process for determining the minimum wage based on the CPI (Consumer Price Index). Let's go step by step and calculate the minimum wage for each year.

a) Calculating the minimum wage for each year (assuming a 3% CPI increase):
- In 2007, the minimum wage is $7.25 per hour (given).
- In 2008, we need to increase the minimum wage by 3%. To do this, we multiply the previous year's minimum wage by 1 plus the inflation rate (in decimal form).
Minimum wage in 2008 = $7.25 * (1 + 0.03) = $7.25 * 1.03 = $7.47 per hour.
- Similarly, we can calculate the minimum wage for 2009 and 2010:
Minimum wage in 2009 = $7.47 * (1 + 0.03) = $7.47 * 1.03 = $7.69 per hour.
Minimum wage in 2010 = $7.69 * (1 + 0.03) = $7.69 * 1.03 = $7.92 per hour.

b) Calculating the revised minimum wage for each year (assume CPI overstates inflation by 1%):
- Since the CPI overstates inflation by 1%, we need to adjust the inflation rate by subtracting 1%.
- Let's calculate the revised minimum wage for each year using the adjusted inflation rate of 2% (3% - 1%):
Revised minimum wage in 2008 = $7.25 * (1 + 0.02) = $7.25 * 1.02 = $7.41 per hour.
Revised minimum wage in 2009 = $7.41 * (1 + 0.02) = $7.41 * 1.02 = $7.57 per hour.
Revised minimum wage in 2010 = $7.57 * (1 + 0.02) = $7.57 * 1.02 = $7.74 per hour.

c) Calculating the impact of CPI bias on minimum wage for each year:
- To determine the CPI bias, we need to find the difference between the minimum wage using the actual CPI and the revised minimum wage using the adjusted inflation rate.
- Let's calculate the CPI bias for each year by subtracting the revised minimum wage from the actual minimum wage:
CPI bias in 2008 = $7.47 - $7.41 = $0.06 per hour.
CPI bias in 2009 = $7.69 - $7.57 = $0.12 per hour.
CPI bias in 2010 = $7.92 - $7.74 = $0.18 per hour.

So, the minimum wage for 2008, 2009, and 2010 would be $7.47, $7.69, and $7.92 per hour, respectively. The revised minimum wage, removing the CPI bias, would be $7.41, $7.57, and $7.74 per hour for the same years. The CPI bias affects the minimum wage by $0.06, $0.12, and $0.18 per hour for 2008, 2009, and 2010, respectively.