We present a model of the electricity market which has a simple connection to the rest of the economy, due to a quasi-linear utility function.A key stochastic parameter shifts electricity demand between points of time.The correlation between these demand shifts and the variation of supply from variable renewable electricity (VRE) sources is crucial for the equilibrium price of electricity.Based on these equilibria we compute the value factors of VREs, as well as producer and consumer surpluses.An outcome of the model analysis is that value factors of VREs decrease as their penetration gets higher, which is also commonly found empirically, but only up to a point.