Gains from variety? Product differentiation and the possibility of losses from trade under Cournot oligopoly with free entry

In a free-entry Cournot oligopoly model with a quadratic utility function that yields differentiated products, it is shown that there are losses from trade when the trade cost is close to the prohibitive level. Although the total number of varieties increases, there is a reduction in consumer surplus. This occurs because trade leads to an increase in imported varieties where consumer surplus is low due to the high trade cost and a decrease in domestically-produced varieties where consumer surplus is high. This result is in contrast with results from the free-entry Cournot oligopoly models with homogeneous products of Brander and Krugman (1983) and Venables (1985); the monopolistic competition models such as Krugman (1980) and Venables (1987), and heterogeneous firm models such as Melitz (2003) and Melitz and Ottaviano (2008).