Question

Smith earned \(40,000\) in 2003 and \(50,000\) in 2004 The CPI was 184.0 in 2003 and 188.9 in \(2004 .\) Using the data presented, how can Smith figure out whether his earnings went up by more than, less than, or equal to the change in prices?

Short answer

Smith's earnings increased by more than the rate of inflation. Hence, in real terms, he earned more in 2004 than he did in 2003.

Step-by-step solution

Calculate the Rate of Change in Earnings

Smith's earnings increased from $40,000 in 2003 to $50,000 in 2004. The rate of change can be calculated by subtracting the initial amount from the final amount and then dividing the result by the initial amount. In this case, it would be: \((50000 - 40000) / 40000 = 0.25\). So, Smith's earnings increased by 25%.

Calculate the Rate of Inflation

The consumer price index (CPI) rose from 184.0 in 2003 to 188.9 in 2004. The rate of inflation can be calculated by subtracting the initial CPI from the final CPI and then dividing the result by the initial CPI. Thus, \((188.9 - 184.0) / 184.0 = 0.0266\). So, the inflation rate was about 2.66%.

Compare the Changes

Finally, comparing the percentage increase in Smith's earnings of 25% with the inflation rate of 2.66%, it can be seen that the rise in his earnings was greater than the rise in prices. Hence, in real terms, his earnings went up.

Key concepts

Understanding the Rate of Inflation

The rate of inflation is a measure of how much the general level of prices for goods and services is rising over time, and subsequently, how purchasing power is eroding. Inflation is usually expressed as a percentage, indicating the change in the Consumer Price Index (CPI) over a specific period.

Consider the exercise where we examine the CPI in 2003, which was 184.0, and in 2004, it rose to 188.9. To calculate the rate of inflation between these two years, we use the formula: \[ \text{Rate of Inflation} = \left(\frac{\text{New CPI} - \text{Old CPI}}{\text{Old CPI}}\right) \times 100 \% \]When you insert the given values for the CPI, the calculation for the rate of inflation is as follows: \[ \left(\frac{188.9 - 184.0}{184.0}\right) \times 100 \% \]The result is approximately 2.66%, indicating the average level of price increase for consumer goods and services from 2003 to 2004.

It's crucial for individuals and policymakers to monitor the inflation rate. If incomes do not increase at least at the same rate as inflation, people's real incomes will fall, meaning they can buy fewer goods and services with the same amount of money. But if incomes rise faster than inflation, as in the case of Smith, real incomes rise.

Calculating Real Income

The concept of real income refers to the amount of goods and services that can be bought with one's earnings, taking into account the effect of inflation. To maintain the same standard of living, one's income must increase at least as much as the inflation rate.

In our exercise, Smith's income increased from \(40,000 to \)50,000. To calculate the real increase in earnings, one must account for the rate of inflation. The formula for calculating the rate of change in earnings is: \[ \text{Rate of Change in Earnings} = \left(\frac{\text{Final Income} - \text{Initial Income}}{\text{Initial Income}}\right) \times 100 \% \]When applied to Smith's earnings, the calculation is: \[ \left(\frac{50000 - 40000}{40000}\right) \times 100 \% = 25\% \]Smith's earnings increased by 25%, outpacing the inflation rate of 2.66%. This means that not only did Smith's nominal income rise, but his real income did as well. He is now able to afford more goods and services than before, even after accounting for the increase in prices due to inflation.

Performing a Purchasing Power Analysis

Purchasing power analysis involves understanding how changes in income and inflation affect the amount of goods and services one can buy. It is an important concept because it reflects the real value of money as affected by inflation.

In Smith's case, we've established that his income rose by 25%, whereas inflation was 2.66%. To understand the impact on his purchasing power, we compare these percentages. Since his income increase has exceeded the rate of inflation, his purchasing power has effectively increased. In other words, Smith can buy more with his income in 2004 than he could in 2003.

This analysis shows that not only can Smith afford to buy the same basket of goods and services he previously could, but he can also afford additional items or save the surplus. However, if his income increase was less than or equal to the rate of inflation, his purchasing power would have remained stagnant or even diminished, leading to a potential decrease in his standard of living.