We study the effect of Demand-Response (DR) in dynamic real-time electricity markets. We use a two-stage market model that takes into account the dynamical aspects of gen-eration, demand, and DR. We study the real-time market prices in two scenarios: in the former, consumers anticipate or delay their flexible loads in reaction to market prices; in the latter, the flexible loads are controlled by an independent aggregator. For both scenarios, we show that, when users are price-takers, any competitive equilibrium is efficient: the players' selfish responses to prices coincide with a socially optimal policy. Moreover, the price process is the same in all scenarios. For the numerical evaluation of the properties of the equilibrium, we develop a solution technique based on the Alternating Direction Method of Multipliers (ADMM) and trajectorial forecasts. The forecasts are computed us-ing wind generation data from the UK. We challenge the assumption that all players have full information. If the as-sumption is verified, then, as expected, the social welfare increases with the amount of DR available, since DR relaxes the ramping constraints of generation. However, if the day-ahead market cannot observe how elastic loads are affected by DR, a large quantity of DR can be detrimental and leads to a decrease in the welfare. Furthermore, the DR operator has an incentive to under-dimension the quantity of avail-able DR. Finally, we compare DR with an actual energy storage system. We find that storage has a faster response-time and thus performs better when only a limited amount is installed. However, storage suffers from charge-discharge in-efficiency: with DR, prices do concentrate on marginal cost (for storage, they do not) and provide a better welfare.