In this paper, we propose variational inequality models for electricity markets with time-of-use (TOU) pricing. Demand response is dynamic in the model through a dependence on the lagged demand. Different market structures are examined within this context. With an illustrative example, the welfare gains/losses are analyzed after an implementation of TOU pricing scheme over the single pricing scheme. It is intended that the proposed models would be useful: 1) for regulatory bodies in jurisdictions to assess market power; 2) to forecast future TOU prices; and 3) to examine welfare changes in electricity markets that change to TOU pricing from single pricing.