Though it is generally believed that increasing competition improves social welfare, we are able to show with a Shubik–Levitan demand function for differentiated goods that this is not always the case. Under Cournot and Bertrand competition, market entry increases the equilibrium total output and lowers the equilibrium price in the case of substitutes, but it reduces the total output and raises the price in the case of complements. In the long run, the equilibrium number of firms is excessive and the equilibrium cannot achieve even the second‐best social welfare under either type of competition, regardless of product substitutability or complementarity.