Continuity of a model with a nested CES utility function and Bertrand competition

In recent years models with a nested constant elasticity of substitution utility function and heterogeneous firms involved in some form of competition have become popular in the international trade literature. This paper considers one particular model of this class — with firms competing in prices — and shows continuity of the model as the elasticity of substitution between goods goes to infinity. This result contrasts with the conjecture of prior literature. Continuity of the model ensures consistency of its outcomes when the elasticity of substitution approaches infinity. Therefore, researchers who were reluctant to use this model because of the lack of proof of continuity can now rely on this paper’s result to employ the model in their research.