This paper deals with flexible electrical devices that, on the basis of a broadcast price signal, schedule their individual power consumption in order to minimize their energy cost. If the devices population is sufficiently large to be described as a continuum, it is possible to provide necessary and sufficient conditions for the existence of a Nash equilibrium in the energy market. This is done by comparing two functions which characterize, respectively, the valley capacity of the inflexible demand and the global properties of the appliances population. The equilibrium conditions, which do not require any iterative procedure to be applied, are finally tested in simulations.