As opposed to the traditional supply-follow-demand approach, demand response is seen as an effective solution to improve efficiency of electricity system. In demand response, dynamic pricing schemes are believed to have significant potential to fully exploit the flexibility of shiftable energy consumptions. Most existing work on dynamic pricing schemes, however, falls short on consideration of price discrimination over different types of consumer groups. In this work, we propose a bilevel game theoretical Stackelberg model between a price-making utility company (a leader) and price-taking consumer groups (followers) in a discriminated dynamic pricing environment. We show under price discrimination producer surplus is monotonically increasing as energy consumption capacity of consumer groups increases. Numerical simulation validates our theoretical analysis and also shows that without price discrimination the social welfare may decrease against the energy consumption capacity of consumer groups. Moreover, social welfare can be higher under price discrimination.