Real Income = (Nominal income) / CPI (as decimal, or CPI/100)
The Correct Answer and Explanation is:
Correct Answer
- Real Income in 2009: $21,296.73
- Real Income in 2010: $21,933.96
- Change in Real Income from 2009 to 2010: An increase of $637.23
Explanation
This problem requires the calculation of real income for two different years and the change between them. Understanding the distinction between nominal and real income is crucial. Nominal income is the face value of money you earn, such as a salary of $45,000. However, its actual value can change over time due to inflation. Real income adjusts for these price level changes, providing a more accurate measure of purchasing power.
The tool used for this adjustment is the Consumer Price Index (CPI), which tracks the average cost of a standard basket of goods and services. The formula provided, Real Income = Nominal Income / CPI, effectively deflates the nominal income to reflect its value in constant base year dollars.
Step 1: Calculate Real Income for 2009
First, we calculate the real income for 2009 using the given figures.
- Nominal Income (2009): $45,000
- CPI (2009): 2.113
- Real Income (2009) = $45,000 / 2.113 = $21,296.73
This means the purchasing power of the $45,000 salary in 2009 was equivalent to $21,296.73 in the CPI’s base year.
Step 2: Calculate Real Income for 2010
Next, we perform the same calculation for the year 2010.
- Nominal Income (2010): $46,500
- CPI (2010): 2.120
- Real Income (2010) = $46,500 / 2.120 = $21,933.96
In 2010, the person’s purchasing power was equivalent to $21,933.96 in base year dollars.
Step 3: Calculate the Change in Real Income
Finally, to find the change in purchasing power, we subtract the 2009 real income from the 2010 real income.
- Change = Real Income (2010) – Real Income (2009)
- Change = $21,933.96 – $21,296.73 = $637.23
This positive result indicates that the individual’s real income increased by $637.23. Although their nominal income rose by $1,500, a portion of that gain was offset by inflation (the CPI increased from 2.113 to 2.120). Nevertheless, their pay raise was greater than the rate of inflation, resulting in a tangible increase in their ability to purchase goods and services
