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The evolution over time of the Consumer Price Index (CPI) is regarded as a key indicator of the general health and direction of any given economy. As the CPI continues to rise, the purchasing power of consumers decreases and their spending habits change significantly, making it imperative for policymakers to understand the underlying reasons that lead to such changes. A key component of the CPI basket is represented by the food and beverages items, within which eggs have undergone a significant price increase during the past years. Egg prices have a significant impact on consumers, given that eggs are a staple product, serving as the lowest cost protein alternative. This paper analyzes the long term behavior of the average egg price (cost per Dozen) in the U.S. by looking at the statistical properties of the series and using a methodology based on the concept of fractional integration. The primary goal is to determine whether the average egg price exhibits traits of long memory or mean reversion. Long memory describes the scenario where observations from a distant past have an influence on the present value of the series. Conversely, mean reversion refers to the phenomenon where data points eventually return to the long-term average after deviating from the mean for a certain period. The analysis also explores the relationship between egg prices and the Producer Price Index (PPI) through cointegration methods. Preliminary findings indicate that long memory takes place in both series and mean reversion in the PPI. Also, the two series seem to be cointegrated. This suggests the presence of a stable long-run equilibrium relationship between the Average Egg price and the Producer Price Index in the U.S., indicating a sustained co-movement between the two variables over time.