Trade-In and Cash-Out Strategies from Perspective of Dynamic Pricing Model

In recent years, scientific and technological development has made trade-in programs for innovative electronic products more and more popular. Many of these innovative companies that continue to launch new products offer trade-in and cash-out sales strategies to stimulate purchase. This paper studies when a company launches these two sales strategies and how to ensure optimal pricing that maximizes profits, while taking into account the degree of the consumer’s strategy, the degree of the new product’s innovation, the residual value of the old products, and the cost. We construct a two-period dynamic pricing joint optimization model with four core decision variables and derive the closed-form optimal solution through strict mathematical derivation including Hessian matrix analysis and KKT condition verification. We have adopted a dynamic pricing strategy that conforms to the actual market. The results show that this study provides new mathematical insights for dynamic pricing research, and reveals the substantive rule that companies are more likely to gain greater benefits when the degree of product innovation is not high and the consumer’s strategy degree is moderate. Statistics show that companies are more likely to gain greater benefits when the degree of product innovation is not high and the consumer’s strategy degree is moderate.

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Publication Details

Journal
Mathematics
Published
2026-04-16
DOI
https://doi.org/10.3390/math14081340
Primary Topic
Innovation Diffusion and Forecasting
Type
article
Field-Weighted Citation Impact
0.00

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article

Trade-In and Cash-Out Strategies from Perspective of Dynamic Pricing Model

Jiqiong Liu, Xiang Li
Mathematics
Innovation Diffusion and Forecasting
article

Trade-In and Cash-Out Strategies from Perspective of Dynamic Pricing Model

Jiqiong Liu, Xiang Li
article en

Abstract

In recent years, scientific and technological development has made trade-in programs for innovative electronic products more and more popular. Many of these innovative companies that continue to launch new products offer trade-in and cash-out sales strategies to stimulate purchase. This paper studies when a company launches these two sales strategies and how to ensure optimal pricing that maximizes profits, while taking into account the degree of the consumer’s strategy, the degree of the new product’s innovation, the residual value of the old products, and the cost. We construct a two-period dynamic pricing joint optimization model with four core decision variables and derive the closed-form optimal solution through strict mathematical derivation including Hessian matrix analysis and KKT condition verification. We have adopted a dynamic pricing strategy that conforms to the actual market. The results show that this study provides new mathematical insights for dynamic pricing research, and reveals the substantive rule that companies are more likely to gain greater benefits when the degree of product innovation is not high and the consumer’s strategy degree is moderate. Statistics show that companies are more likely to gain greater benefits when the degree of product innovation is not high and the consumer’s strategy degree is moderate.

MathematicsVol. 14(8)
Fuyang Normal University (CN), Logistics Management Institute (United States) (US)
Fuyang Normal University, Doctoral Foundation of Fuyang Normal University, Division of Graduate Education
Industry, innovation and infrastructure
Openalex Percentile: Top 19%
Innovation Diffusion and Forecasting
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