We model the continuous-time power market as an optimal control problem where the demand and supply processes are governed by stochastic differential equations controlled by the price. We first analyze the efficiency of an intermittent supplier which is characterized by cheap production with high supply volatility. We show that for a sufficiently high intermittent supply volatility, the intermittent supplier negatively impacts the social efficiency. Next, we introduce a novel market mechanism for power markets: we define one price process for supply subject to friction and another price for frictionless ancillary supply with a marginal cost of production higher than that of the regular supply. We show that (i) the negative efficiency impact of the intermittent supplier due to stochasticity and uncontrollability can be offset with the new double price market mechanism, and (ii) the volatility of the price can be decreased with the new double price mechanism.