To model the observed slow response of aggregate real variables to nominal shocks, most macroeconomic models incorporate real rigidities in addition to nominal rigidities. One popular way of modelling such a real rigidity is to assume a non-constant demand elasticity. By using a homescan data set for three European countries, including prices and quantities bought for a large number of goods, in addition to consumer characteristics, we provide estimates of price elasticities of demand and on the degree of demand-side real rigidities. We find that price elasticities of demand are about 4 in the median. Furthermore, we find evidence for demand-side real rigidities. These are, however, much smaller than what is often assumed in macroeconomic models. The median estimate for demand-side real rigidity, the super-elasticity, is in a range between 1 and 2. To quantitatively assess the implications of our empirical estimates, we calibrate a menu-cost model with the estimated super-elasticity. We find that the degree of monetary non-neutrality doubles in the model including demand-side real rigidity, compared to the model with only nominal rigidity, suggesting a multiplier effect of around two. However, the model can explain only up to 6% of the monetary non-neutrality observed in the data, implying that additional multipliers are necessary to match the behavior of aggregate variables.