# Loyalty and Consumption: A CES representation

執筆者 猪瀬 淳也 (東京大学) 2016年3月  16-E-058 持続的成長とマクロ経済政策

## 概要

また、この経済における企業活動を考えると、企業の生産性と収益の関係は一般的な独占的競争のモデル（Melitzモデル）と同様の関係を満たすことが示された。

## 概要（英語）

This paper offers a new interpretation of the elasticity of substitution in the constant elasticity of substitution (CES) utility function under discrete choice and separability. We model an economy with one discrete choice goods group and one composite good under diverse consumers. The results from our theoretical analysis illustrate the relation between the diversity of loyalty of each good and goods demands. Moreover, the origin of the elasticity of substitution of the CES utility function is described based on our assumptions. According to our results, the power index of the CES utility function does not change even if the diversity of loyalty differs by each good. On the other hand, coefficients of $$X_i^σ$$ vary according to each good's attractiveness. We also consider the production under this economy, and find that an increase in productivity leads to a decrease in price. This effect is the same as the standard Melitz model (monopolistic competition).