Empirical evidence on households' awareness of electricity prices and potentially divergent demand responses to price changes conditional on price knowledge is scant. Using panel data originating from Germany's Residential Energy Consumption Survey (GRECS), we fill this void by employing an instnunental-variable (IV) approach to cope with the endogeneity of the consumers' tariff choice. By additionally exploiting information on the households' knowledge about power prices, we combine the IV approach with an Endogenous Switching Regression Model to estimate price elasticities for two groups of households, finding that only those households that are informed about prices are sensitive to price changes, whereas the electricity demand of uninformed households is entirely price-inelastic. Based on these results, to curb the electricity consumption of the household sector and its environmental impact, we suggest implementing low-cost information measures on a large scale, such as improving the transparency of tariffs, thereby increasing the saliency of prices.