Following new legislation the Swedish electricity market is about to be deregulated. The new system is designed to ensure competition in production and supply. The main motive for deregulation is to increase competition and thus achieve lower market prices. A possible threat to this outcome is the high degree of concentration on the seller side that characterizes the Swedish electricity market. In this paper we show that given the current structure of firms on the supply side, deregulation is not a sufficient condition for lower equilibrium prices in the electricity market. We use a numerical model to explore the quantitative relation between the Cournot-equilibrium price, the number affirms, and the size distribution affirms in the Swedish electricity market. We compute equilibrium electricity prices and a welfare measure in order to quantify the effect of asymmetric marker concentration on competition.