# Loyalty and Consumption: A CES representation

Author Name INOSE Junya (University of Tokyo) March 2016 16-E-058 Sustainable Growth and Macroeconomic Policy

## Abstract

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).