On the Dixit-Stiglitz model of monopolistic competition
重新审视迪克西特和斯蒂格利茨的垄断竞争模型，指出宏观经济学中常用的变体与原版有显著差异，并分析了不同变体对近似方法有效性的影响。
Our purpose in this note is to revisit the popular monopolistic-competition model of Avinash K. Dixit and Joseph E. Stiglitz ( 1977) and to stress the fact that the variant of this model used in the recent macroeconomic literature is significantly different from the original. In particular, by taking n as the number of active monopolists, the recent discussion of Dixit and Stiglitz (1993) and Xiaokai Yang and Ben J. Heijdra (1993) about the the advantages of neglecting terms of the order 1/n in the computed elasticities, is significantly affected by the choice of the variant of the model. The basic presented in Section I, has been used from the start by Dixit and Stiglitz to study optimum product diversity. It is a simple general equilibrium model with n monopolistic goods and a numeraire good, which can be interpreted as labor (or leisure) time or as the aggregation of all the other goods in the economy. The variant of the analyzed in Section II, was independently developed by several authors for different simple applications in macroeconomics.1 It is an model, that includes an additional good, interpreted as labor time but not taken as the numeraire. More importantly, the enlarged model does not lead to a general equilibrium analysis until the wage rate, taken as given in a first step, is adjusted competitively or strategically. It is for the basic model that Yang and Heijdra (1993) (YH) give an alternative computation method taking into account the priceindex effect of individual pricing decisions. This effect had been neglected in the original paper of Dixit and Stiglitz (1977) (DS), who were only concerned with the large n case (ensured by low fixed costs and imperfect substitution between the monopolistic goods). Limiting their model to the special case of a unitary elasticity of substitution between the monopolistic goods and the numeraire good, YH obtain an explicit solution. But YH's solution is still an approximation, because it neglects the indirect effects that feedback has on pricing decisions. We will show that, in the enlarged taking into account this income-feedback effect allows for an explicit solution and simplifies calculations. But in the variant, some meaningful cases are incompatible with free entry and thus prohibit the use of DS's approximation. However, as we conclude in Section III, this is not to say that their approximation should never be used. On the contrary, the approximation hypothesis is a very useful part of Dixit and Stiglitz's contribution.