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doi: 10.3934/jimo.2021157
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## Equilibrium decisions on pricing and innovation that impact reference price dynamics

 1 School of Management, Hefei University of Technology, Hefei 230009, China 2 Naveen Jindal School of Management, University of Texas at Dallas, Dallas, TX 75080, USA 3 Belk College of Business, University of North Carolina at Charlotte, Charlotte, NC 28223, USA 4 Coordinated Innovation Center for Computable Modeling in Management Science, Tianjin University of Finance and Economics, Tianjin 300222, China

* Corresponding authors: Xiuli He and Xianjin Du

Received  February 2021 Revised  June 2021 Early access September 2021

Fund Project: This work is supported by the National Natural Science Foundation of China (NSFC) under Grant 72071065

Previous studies have confirmed that reference prices play an essential role in consumer purchasing decisions, and some researchers have suggested that reference prices are positively influenced by innovation. Therefore, we construct an interactive effect of innovation and reference price to study their combined impact on supply chain decisions. We model a supply chain, where a manufacturer determines the innovation level and the wholesale price while the retailer controls the retail price, as a dynamic Stackelberg game. We show that the interactive effect causes the steady-state wholesale and retail prices to increase, thus motivating the manufacturer to increase innovation investment. We see that the retail price and the level of innovation increase in reference price effect whereas they decrease in consumer memory. The centralized firm has a higher steady-state innovation level and innovation/price ratio and lower steady-state retail price compared to the decentralized supply chain. Consumers also benefit from the interactive effect as well as from centralization. Finally, we use numerical analysis to demonstrate our results and offer some managerial implications.

Citation: Shaokun Tao, Xianjin Du, Suresh P. Sethi, Xiuli He, Yu Li. Equilibrium decisions on pricing and innovation that impact reference price dynamics. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2021157
##### References:

show all references

##### References:
The trajectories of reference price and selling price in centralized decision-making
The comparison of $Q_{d-ss}^{IR}$ and $Q_{c}^{IN}$
The relationships between the steady-state profits and $\delta$, $\theta$, $\beta$
The comparisons of corresponding optimal profits under $'IR'$ and $'IN'$
Superscript and subscript annotations
 $IR$ the presence of an interactive effect $NR$ the absence of innovation $IN$ the absence of reference price c centralized decision-making d decentralized decision-making ss steady-state
 $IR$ the presence of an interactive effect $NR$ the absence of innovation $IN$ the absence of reference price c centralized decision-making d decentralized decision-making ss steady-state
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