# Price–quality relationship in the presence of asymmetric dynamic reference quality effects

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## Abstract

The purpose of this study is to examine the relationship between price and reference quality and their combined effect on profits. An analytical modeling approach aimed at solving the optimal solution for the profit maximization problem under these conditions is developed, enabling the exact path of the optimal price and quality over time to be depicted. Based on separating the effects of price and reference quality on demand, this analysis also provides insight into the contribution of these two effects to the steady-state solution through elasticities. Our results show that a monotonic inverse relationship exists between price and quality, such that a steady-state level is obtained where the quality–price ratio is lower when reference quality effects exist than when such effects do not exist. In other words, consumers obtain higher quality for a higher price but with a lower price per unit of quality. Overall, accounting for reference quality effects will increase a firm’s profits.

## Keywords

Reference quality Price elasticity Optimal pricing Differential games Equilibrium## Notes

### Acknowledgement

This research was supported by The Israel Science Foundation (grant No. 285/07)

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