Monopolistic Competition and Optimum Product Diversity

Dixit & Stiglitz

AER, 1977

Abstract

The Dixit/Stiglitz monopolistic competition model has been widely adopted in various fields of economic research such as international trade. 本文表明在利用规模经济与满足多样化偏好之间，存在 trade-off.

说明

1. The paper^[1] actually contains three distinct models, yet economic literature has mostly taken up only the first one (constant elasticity of substitution case) and its market equilibrium solution. 本文仅推导这一部分。

2. Modeling 规模经济 & 多样化偏好

   • Modeling 规模经济：\(C(x_i)=a+cx_i\)，总成本可分为固定成本和不变的边际成本，则平均成本随产量增加而下降。

   • Modeling 多样化偏好：D-S Utility Function

     • \(U[x_0,V(x_1,x_2,⋯,x_n)]\)，\(V(\cdot)\) 中的 \((x_1,x_2,⋯,x_n)\) 代表一个部门，\(x_0\) 是另一个部门。\(U(·)\) 满足 separable¹、homothetic，并拥有 convex 无差异曲线。
     • 忽略收入分配。即假定 \(U(\cdot)\) 为社会效用函数或代表性消费者的效用函数的加总。

3. 本节假设：部门内替代弹性为常数（CES）；部门间替代弹性未知。

4. 后人继续简化的典型 “Dixit-Stiglitz lite²” 在上述假设的基础上，还规定了以下三个特征，从而使数学处理变得简单许多。

   • symmetry of \(V(\cdot)\)
   • CES specification for \(V(\cdot)\)，如 \(\left(\sum_{i} x_{i}^{\rho}\right)^{1 / \rho}\)
   • Cobb-Douglas form for \(U(\cdot)\)

参考文献

[1]

DIXIT A K, STIGLITZ J E. Monopolistic competition and optimum product diversity[J]. The American Economic Review, 1977, 67(3): 297–308.

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1. separable 意味着可以使用两阶段最优化的方法。With weakly-separable utility functions, the MRS (and thus the elasticity of substitution) of two goods from the same group is independent of the quantities of goods in other sub-groups (see Gravelle and Rees, 2004, 67).↩︎

2. lite, 简化物。(used after a noun) used to say that a thing is similar to sth else but lacks many of its serious or important qualities.↩︎