A dozen eggs cost 0.88 dollar in January 1980 and 1.77 dollar in January 2018 . The average hourly wage for production and nonsupervisory workers was 6.57 dollar in January 1980 and 22.36 dollar in January 2018 . a. By what percentage did the price of eggs rise? b. By what percentage did the wage rise? c. In each year, how many minutes did a worker have to work to earn enough to buy a dozen eggs? d. Did workers' purchasing power in terms of eggs rise or fall?

Understanding how to calculate percentage change is essential for analyzing economic trends over time. Let's use a simple example with egg prices to illustrate the concept. To calculate the percentage change in the price of eggs from January 1980 to January 2018, we subtract the original price of \(0.88 from the new price of \)1.77 to get the change in price, which is \(0.89. This difference is then divided by the original price of \)0.88, yielding a result of approximately 1.011. Multiply that by 100 to convert to a percentage, and you have a 101.1% increase in the price of eggs over this period. The formula we've used is:

\[ \frac{{\text{{New price}} - \text{{Original price}}}}{{\text{{Original price}}}} \times 100\% \]
\[ \frac{{1.77 - 0.88}}{0.88} \times 100\% \approx 101.1\% \]
This method allows for quick assessments of economic changes, a crucial skill in fields like finance, business, and economics education.

Inflation analysis involves comparing how prices and wages alter over time relative to each other. Let's continue with our eggs and wages example. Using the percentage change calculation, we can assess how wages have also shifted. From January 1980 to January 2018, the average hourly wage increased from \(6.57 to \)22.36. The percentage rise in wages is calculated using the same formula as we did for the price of eggs. This results in a 240.2% increase in the hourly wage.

Using the calculated percentages, we can analyze the effects of price inflation and wage inflation. There's a clear appearance of wage growth outpacing the price increase of eggs, which would suggest an improvement in purchasing power. However, this conclusion can't be drawn until we conduct a real income comparison, considering the broader market, to understand whether this wage growth adequately compensates for overall inflation in the cost of living.

Comparing real income is paramount when evaluating economic wellbeing. This involves adjusting nominal income by the inflation rate to assess purchasing power changes over time. With our scenario, we have already determined that the price of eggs and wages increased by 101.1% and 240.2% respectively, from January 1980 to January 2018. However, to truly understand the worker's financial health, we calculate the time required to earn enough to buy a dozen eggs in both years.

In 1980, it took approximately \[ \frac{0.88}{6.57} \times 60 \approx 8.04 \] minutes of work to buy a dozen eggs. By 2018, this number decreased to \[ \frac{1.77}{22.36} \times 60 \approx 4.75 \] minutes. This numerical decrease indicates that, despite the sharp price increase, the even larger wage increase led to an improved purchasing power when it comes to eggs. Such comparisons serve as a real-world application of economics education, demonstrating how the abstract concept of real income affects everyday life.