Reference Price Effects Research Articles

Process improvement under the reference price effect

Cost-reducing process improvement, leading to price reductions and consequently sales growth, is becoming increasingly relevant in today’s uncertain economic environment. However, existing process improvement studies involving sales growth typically assume that consumers only consider the current price of a product when making a purchase. In reality, sales growth also often stems from the reference price effect, where consumers factor in both the current and past prices. By incorporating the reference price effect, we examine the process improvement investment decisions and pricing strategies in a decentralized supply chain. We develop a two-period game-theoretic model, where the supplier invests in process improvement to reduce production costs, and the supplier and the retailer set their prices. This approach differs from existing reference price effect literature, where prices are predetermined exogenously in a decentralized supply chain. We find that the reference price effect stimulates process improvement investment, making both firms more profitable. However, a more prominent reference price effect may significantly decrease supply chain efficiency in the presence of process improvement, resulting in lower profits that move away from what an integrated firm would achieve. When firms set their own prices, the reference price effect intensifies competition for profits and worsens misalignment caused by process improvement. This outcome contrasts with existing studies, which usually argue that the reference price effect increases efficiency. Therefore, managers should consider consumer responses to price changes when making process improvement investment decisions and analyze their impacts on both supply chain profitability and efficiency.

Dynamic policies with reference-price effects and reference-quality effects

Dynamic policies with reference-price effects and reference-quality effects

The Art of Balancing Price and Plug: Developing a Theoretical Model for Dynamic Pricing in the Electric Vehicle Market

This study presents a novel approach to understanding the complex dynamics of the electric vehicle (EV) market through the lens of differential game theory. We developed a comprehensive model that captures the strategic interactions between EV manufacturers and charging network operators, while incorporating the effects of consumer behavior, market uncertainties, and reference price effects. Using differential game theory, we examined the impact of reference price effects and the charging network’s influence on pricing strategies, focusing on three distinct approaches: basic pricing, static pricing considering reference price effects, and dynamic pricing strategies. Our model offers new insights into consumer behavior and price expectations in the rapidly evolving EV market. The key findings reveal that under static or dynamic pricing strategies, the optimal pricing for EV manufacturers is positively correlated with the initial reference price. When the initial reference price is high (low), the optimal pricing strategy resembles skimming pricing (penetration pricing). As the effort level of charging network operators increases and their influence on consumers’ purchase decisions grows stronger, EV manufacturers tend to set higher prices. Notably, while dynamic pricing strategies can optimize EV manufacturers’ profits, the profits of charging network operators may decrease compared with static pricing strategies. This integrated approach significantly contributes to the field by bridging gaps among market dynamics, pricing strategies, and the infrastructure’s development in the context of electric mobility, providing a comprehensive framework for understanding and optimizing the EV ecosystem. Ultimately, this study advances sustainable business models that balance profitability, consumer behavior, and the infrastructure’s growth in the rapidly evolving EV market.

Optimizing Pricing Strategies for Product Lines and Value‐Added Services: Accounting for Reference Prices and Network Effects

ABSTRACTCustomer choice behavior is increasingly influenced by the reference price effect and negative network effect as customers become more rational and personalized. This study, considering customers as pivotal stakeholders for enterprise development, employs the multinomial logit (MNL) model and develops pricing and strategy optimization models for pure bundling and mixed bundling strategies of an enterprise's product line. The main focus is to analyze how these effects impact optimal pricing and strategy selection. The results indicate that stronger effects lead to lower enterprise profits, and ignoring them can cause substantial losses. Generally, mixed bundling strategies yield higher profits.

Pricing Strategies for O2O Catering Merchants Considering Reference Price Effects and Unconditional Coupons

Coupon marketing is an important promotion model for the O2O catering supply chain. As a well-known catering O2O platform in China, Meituan provides its members with the opportunity to buy unconditional coupons at low prices, and it is very popular with consumers. It is worth studying how catering merchants develop pricing and promotion strategies considering consumers’ reference price effects in two scenarios: participating and not participating in coupon stacking (S-PICS/S-NPICS). In order to explore the pricing mechanism of meals, two models using Stackelberg games are established considering some exogenous variables, such as commission rate, reference price, and sensitivity of consumers to coupon prices. The results show that (1) the reference price has a great influence on the maximum profits of catering merchants, varying in different scenarios; (2) in S-NPICS, the merchants’ maximum profit increases with an increase in the reference price, while, in S-PICS, an increase in the reference price leads to a decrease in merchants’ maximum profit; (3) the profit of merchants in S-PICS is higher than that in S-NPICS, indicating that merchants can benefit from coupon stacking; (4) when the commission rate of the coupons increases, the merchants in both S-PICS and S-NPICS should raise their online meal prices to obtain higher profits. This study provides a balanced reference for pricing strategies and coupon promotion strategies in different scenarios through the use of deduction and simulation methods, which is conducive to the sustainable development of the O2O catering supply chain. As consumers enjoy using these coupons, including unconditional ones, it is suggested that merchants and Meituan should focus on coupon promotion and develop better dining pricing strategies.

Models for dual-channel remanufacturing supply chain with reference price effect under static and dynamic games

With the diversity of shopping styles, reference prices have become a consideration in consumers’ purchasing decisions. It is critical to understand how manufacturers and retailers make optimal decisions based on consumer behavior. To this end, we develop a manufacturer-led Stackelberg (M-Stackelberg) game model to investigate the impact of consumer proportion, reference price effect (RPE), and the channel preference coefficient on the decision of the remanufacturing supply chain (RSC) in dual-channel structures. Through comparing different game scenario models, we find that when the reference price coefficient is relatively small, the optimal decisions for the manufacturer and the retailer are the same regardless of whether the RPE is considered. The manufacturer and E-tailer always benefit from RPE, while the traditional retailer (T-retailer) is uncertain. The numerical analysis revealed that the profits of supply chain members are inversely proportional to the proportion of consumers. The smaller the proportion of primary consumers, the more favorable the supply chain. In particular, the higher the channel preference coefficient, the higher the profits of the manufacturer and E-tailer, while the lower the benefit of the T-retailer. Further, in the dynamic game, the total supply chain profit is highest when the T-retailer prices earlier than the E-tailer.

An Empirical Study on the Retail Price Threshold of Pork in the Chinese Market

This study aimed to identify warning thresholds that can guide sellers in achieving reasonable profits while reducing buyer payment costs. Monthly price data from January 2009 to June 2023 and the two-regime threshold regression model were used for an empirical analysis of the asymmetric effects of the changes in household consumption under different pork price fluctuation levels to verify that the changes in household consumption have significant pork price fluctuation thresholds and threshold effects. It was found that as the fluctuation of pork prices approached the threshold, the temporary price-intervention policy (e.g., reference price) effect of adjusting prices diminished. An empirical analysis was conducted from the perspective of asymmetric effects of the upstream (feed and piglets), midstream (live pigs), and downstream (pork) of price transmission. The impacts of the products in the upstream and midstream of the industry chain on pork prices declined gradually, and among the products, the impact of the prices of feeds for fattening pigs on pork prices was found to be the weakest. Thus, the price intervention policy (e.g., reference price) based on the pork price threshold suggests that strengthening the supervision of the price fluctuations of midstream products (e.g., controlling the profit margin) when the pork price fluctuation is near the threshold (8.24%) would have more significant effects on all sides.

The government subsidy design considering the reference price effect in a green supply chain.

This paper constructs a green supply chain with a manufacturer and a retailer. Taking into account the reference price effect of consumers based on the mental accounting theory, we investigate the following government incentive policies: R&D (research and development) subsidy, consumption subsidy, and dual subsidy. For manufacturer-led (M-led) and retailer-led (R-led) supply chains, we evaluate the optimal wholesale price, sales price, green degree of product, and the optimal subsidy of the government aiming to improve the environmental benefit or social welfare. We find that the government goal, power structure and reference price effect impact the design of subsidy mechanisms significantly. First, for M-led supply chain, the government concerned with the environmental benefit goal should only provide R&D subsidy for the manufacturer when the reference price effect is low; otherwise, the government would offer subsidy both for the manufacturer and consumers. However, the government will only offer R&D subsidy when the social welfare goal is adopted. Second, for R-led supply chain, the government aiming to improve the environmental benefit prefers dual subsidy when the reference price effect is low; otherwise, consumption subsidy is preferable. Surprisingly, under the social welfare goal, no subsidy for R-led supply chain tends to be the best option. Intriguingly, embracing the social welfare goal can result in more economic and environmental benefits for M-led supply chain, although the subsidy strategy is less effective than the environmental benefit goal. Our research can provide inspirations and references for designing government subsidy mechanisms in practice.

Dynamic pricing of differentiated products under competition with reference price effects using a neural network-based approach

Dynamic pricing of differentiated products under competition with reference price effects using a neural network-based approach

The impact of reference price effect on pricing decisions

PurposeThe paper attempts to discuss the impact of reference price effect on pricing decisions.Design/methodology/approachWith the growth of the Internet and e-commerce, more and more customers purchase products in through online channels and choose products by comparing different prices and services, and the reference price effect has an impact on pricing decisions. To investigate the impact of consumers' reference price effect on the dual-channel supply chain, the authors establish a basic model consisting of a single dominant manufacturer and a single downstream retailer, and analyze the optional decisions under different situations and discuss the influence of reference price effect. Finally, a number case verifies the validity and rationality of the proposed model.FindingsThe results show that (1) the reference price effect has varying effects on the price, channel demand and income of manufacturers and retailers in the channel depending on the role of customers' channel preferences. (2) The manufacturer's online channel demand and profits always increase with the reference pricing effect, whereas the retailer's offline demand and profits always decline. (3) When the proportion of consumers preferring offline is higher, the manufacturer's network price and wholesale price increase with the reference price effect, while the retailer's retail price decreases with the reference price effect; when the proportion of consumers preferring offline is lower, the opposite is true, and the centralized decision results are consistent with the decentralized decision results.Practical implicationsThis paper can clarify the impact of consumer reference price effects on the operation of dual-channel supply chains, and help inform pricing decisions of manufacturers and retailers in dual-channel supply chains.Originality/valueThe proposed approach can well analyze the impact of consumer reference price effect and give channel their optional decisions.

Dynamic pricing in the presence of social externalities and reference-price effect

This paper considers the pricing of a new product in the face of sophisticated consumer behaviors. At the individual level, consumers are forward-looking, whereby they may wait strategically for better purchasing opportunities. Additionally, and in line with prospect theory, consumers might also look back to form a reference-price point with which they can compare the current price. Consumers are assumed to be loss averse where losses resonate more than gains. Moreover, we account for the role of social influences in the form of externalities in consumers’ adoption decision. We develop progressively different nested models to examine the impact of each behavior. Two types of pricing regimes, that is, preannounced and responsive pricing, are utilized where the firm commits to the price path from the outset in the former while it does not in the latter. We find that a penetration pricing strategy can be both strengthened or weakened by forward-looking consumer behavior depending on the underlying dynamics. Our results also suggest that the superiority of the firm’s profit under committed pricing depends heavily on the consumer behaviors.

Competition and the Regulation of Fictitious Pricing

Fifty years ago, the Federal Trade Commission stopped enforcing its fictitious reference pricing guidelines, emphasizing the search qualities of price and the belief that competition would drive out deceptive behavior. Yet this practice of posting false, inflated comparison prices alongside sale prices has proliferated. Building on prior analytic work and the documented effects of reference pricing on search behavior and consumer choice, the authors develop a descriptive model explaining why fictitious reference pricing has spread instead of being extinguished by competition. After summarizing the model with a series of generalizations, the authors consider potential regulatory solutions to the problem. They propose that disclosure of the true normal price charged may be the only solution that could plausibly influence both consumer and firm behavior. Then, based on the existing literature, interviews with practitioners and regulators, an analysis of other nations’ approaches, and the results of a laboratory study of 900 consumers to examine how they integrate “true normal price” information into deal evaluations, the authors develop a set of propositions about the likely effects of requiring firms to disclose recent selling prices for goods, identifying both potential benefits and challenges associated with such a requirement.

Joint pricing and inventory control with reference price effects and price thresholds: A deep reinforcement learning approach

The literature has recognized that the consumers’ purchase behaviour and retailers’ policies are significantly influenced by reference price effects, but has yet to provide flexible operational decisions on the threshold-based reference price. In this study, we consider an infinite-horizon joint pricing and inventory control problem in which the customers’ psychological behaviour is modelled as reference price effects and price thresholds. Specifically, there is a region of price insensitivity allowing for threshold effects around the reference price, which is formulated as a three-regime piecewise function with the consideration of gain, loss, and indifference. A resolution approach based on proximal policy optimization is proposed to address the combinatorial complexity of continuous domains in action-state spaces. Tested on eight different market environments, we demonstrate how the deep reinforcement learning (DRL) approaches the ground-truth algorithm and outperforms three other algorithms. Moreover, near-optimal strategies and convergence results are obtained with regard to initial states and price thresholds of the system. The results show that the order-up-to level is increasing in price thresholds and the sales price is decreasing in them, while the retailer’s profits suffer from the increase in thresholds. Besides, the sales price is increasing in the reference price. In the steady state of the environment, the average profits are higher than those in which the retailer ignores reference price effects with thresholds. Our study provides evidence that black-box DRL algorithms can effectively solve joint pricing and inventory control problems with psychologic and behavioural concerns.

Optimal pricing strategy for new products considering reference price effect in advance selling

Previous research has shown that retailers’ operations and consumers’ purchase choices are significantly influenced by reference prices. This study explores a retailer selling some new products to strategic consumers in advance selling, and addresses the impact of reference price effect on the advance selling strategy and corresponding pricing decisions. Consumers’ choices are determined by their purchasing utilities which are dependent on the selling price in current period and the reference price. We first drive optimal selling prices and corresponding profits of the retailer under the scenarios of no advance selling, advance selling without considering the reference price effect, and advance selling with considering the reference price effect, respectively. We find an advance selling strategy is not always beneficial for the retailer. Besides, results present that the retailer benefits from considering reference price effects only if the positive reference effect is relatively high. Finally, numerical studies show that dynamic pricing is dominated by price commitment, which reaches the maximum when positive and negative reference effects parameters are both the highest.

Dynamic Operational Strategies Incorporating Consumer Reference Price Effects and Enterprise Behavior: A Differential Game Approach

The continuous evolution of consumer behavior in the modern era of consumption has prompted enterprises to explore the underlying behavioral factors of consumers and cater to their particular needs. Moreover, developing a rational operational behavior model and responding effectively to the dynamic market environment have become critical concerns for businesses. This study examines the impact of consumer reference price effects and enterprise short-sighted behavior on strategic selection and performance, employing differential game theory to construct a game model between manufacturers and retailers. Utilizing Behrman's continuous dynamic programming theory, analytical solutions for various models are derived, followed by comparative analyses and numerical examples. The research reveals that: (1) manufacturers' behavior patterns are found to be dominant, favoring far-sighted behavior, which not only enhances profits but also enables consumers to access higher quality and cost-effective products; retailers should opt for collaboration with far-sighted manufacturers and exhibit a preference for short-sighted behavior. (2) In terms of overall system profit, the FM model emerges as the optimal combination. (3) When the reference price effect has a small impact on market demand, enterprises can make use of the reference price effect to actively promote marketing and gain profit; as the influence increases, intensifying the degree of influence effectively augments profits.

Dynamic Pricing with Parametric Demand Learning and Reference-Price Effects

In reality, sellers face challenges in obtaining perfect demand information. Demand is influenced not only by price but also by behavioral factors such as reference effects, which complicate optimal pricing for enterprises. To address this problem, we propose a dynamic pricing model that incorporates demand learning and considers consumer reference effects. Using the Bayesian method and based on historical sales and prices, sellers can learn about demand patterns. We analyze the model to determine the existence of an optimal solution and provide an algorithm to solve it. Our numerical simulation demonstrates that the total consumer demand and the impact of price on demand remain relatively stable over time. However, the factors influencing the reference effects exhibit greater variability. Sellers can also gain insights into market demand through their learning behavior in each phase and adjust production based on market size. For instance, our simulation shows an increase in market demand over time, allowing the seller to adjust the production plan according to the demand change.

How Do We Perceive Prices? A Three-category Taxonomy of Reference Price Effect on Consumers’ Price Judgments

Aims: Price is one of the pivotal determinants when consumers make purchasing decisions. An unresolved issue in extant literature regarding factors that affect price referencing remains. The difficulty is in identifying types of price references that consumers will use in any given purchasing situation. This study hence proposed a new scheme of three-category taxonomy of reference price model and can be used as a conceptual framework for examining the effects of various reference prices on consumers’ price judgments.
 Methodology: A literature review and theoretical background lead to propositions.
 Conclusion: This research not only fills the literature gaps of referencing prices on consumer price judgments but also a three-category reference price model is developed. The present study goes beyond previous work in this field and a comprehensive set of reference price cues that influence consumers’ final reference price formation. This new model gives future research a direction to test and refine relationships proposed in the present study.

Hiding or disclosing? Information discrimination in member-only discounts

E-commerce platforms commonly offer price discounts as a loyalty benefit for fee-based members. Some of them disclose the member-only discount, while others strategically hide the specific discount information from non-members, which can be seen as information discrimination between non-members and members. This paper constructs a stylized model to examine whether disclosing or hiding member-only discounts yields higher revenue. Our study also incorporates the two-sided reference price effects into customers’ utility formation to reveal how information discrimination works. By comparing the revenue gap between information disclosing and hiding strategies concerning exogenous and endogenous member-only discounts, we find that platforms that aim at the high-end market by charging a higher product price and membership fee and whose target customers hold higher negative but lower positive reference price effect should implement the information hiding strategy. The findings guide e-commerce platforms to improve revenue by strategically hiding or disclosing member-only discounts in fee-based membership management.

A dynamic analysis of a monopolist's efforts for improving product quality and process innovation with reference price effects under linear demand

AbstractThis paper examines a monopolist's innovation efforts for improving product quality and process innovation with reference price effects. Our main results show that the system can achieve saddle‐point steady‐state equilibrium; the two efforts increase with the increase of reference price; although the price is still determined by the monopolist, the price under the social planner regulation is higher than that under the monopolist decision‐making; there is always a negative relationship between the product quality and the price; and memory parameter affects the complementarity (substitutability) relationship between these two efforts.

Pricing and coordination in a green supply chain with a risk-averse manufacturer under the reference price effect

This paper considers a green supply chain using manufacturers and retailers as the research objects. The pricing and coordination strategy of the green supply chain, considering a risk-averse manufacturer, is investigated under the reference price effect. We establish centralized, decentralized, and cost-sharing contract decision-making models and then provide the optimal balancing strategy for each model. Further, we analyzed the optimal equilibrium strategy of different models. In the end, validate them through numerical simulation. We have found that the cost-sharing contract model is better than the decentralized decision model. Besides, manufacturers’ degree of risk avoidance affects the wholesale price, product greenness, retail prices, and profits of supply chain members. It is verified that the cost-sharing contract can coordinate the supply chain system to increase the profit of members of the supply chain.