As energy systems transition towards renewable sources, creating challenges for grid stability, household demand-side flexibility has become a cornerstone of modern policy. Dynamic electricity pricing is one of the most prominent tools for activating this flexibility, yet the robustness of its effects and the heterogeneity of responses across socioeconomic groups remain under-explored. The study addresses these gaps by analyzing data from a large-scale randomized controlled trial in Norway, conducted from December 2020 to March 2021, involving 3,746 households. The study replicates the fixed-effects panel-data model used by Hofmann and Lindberg (2024), to verify the average treatment effect of variable hourly pricing and extends it with interaction terms to test whether household income moderates price responsiveness. The replication analysis successfully reproduces the original findings, confirming a statistically significant average peak-hour demand reduction of 2.92% (0.085 kWh/h). The subsequent extension reveals a strong and systematic inverse relationship between household income and price elasticity, with low-income households significantly reducing peak consumption by 12.05% (0.221 kWh/h), compared to negligible responses from high-income households, particularly during high-price events for shorter time periods. These findings confirm that dynamic pricing effectively elicits demand response but is disproportionately driven by financially constrained households. To ensure an effective and equitable energy transition, policymakers must adopt segmented pricing strategies that account for socioeconomic differences. Limitations, including the Norway-specific context, suggest caution in generalizing these results.