Back to Vol. 39, No. 2, 2025
Vol. 39, No. 2, 2025

Pricing Decision of a Gray Market System with Reference Price Effect and Consumer Heterogeneity

Title

Pricing Decision of a Gray Market System with Reference Price Effect and Consumer Heterogeneity

Author

FENG Ying; HE Wenhao; SONG Xin; ZHANG Yanzhi; LIU Manzhi

Abstract

Gray market refers to an “informal” market channel formed by selling the brand products in a certain area without the authorization of the brand owner. In the existence of gray market, there are often differences in the purchase decision behavior of consumers in the high-price market, that is, some consumers are strategic consumers, who will pay attention to the price difference between gray products and high-price authorized products (referred to as “high-price products”), thus forming an external reference price effect. However, the other ones are loyal consumers, who have absolute loyalty to authorized channel products. They only pay attention to the price of authorized products in the high-price market, and prefer to purchase authorized products. Based on the above background, this paper intends to explore the impact of the above factors on the pricing decisions and operations of the gray market system. The system is composed of a manufacturer and a gray market speculator, and we consider the heterogeneity of consumer purchase behavior and the two-way asymmetric reference price effect between the high price market and the gray market.Specifically, consumers are divided into strategic consumers and loyal consumers based on whether they are loyal to the authorized channel. Then, two Stackelberg game models are constructed under the conditions with and without reference price effect, respectively. The research shows that, in the case of with/without reference price effect, the system both has a unique game equilibrium solution, which is closely related to consumers′ willingness to pay for low-price products. When the willingness to pay changes, the gray market system will switch among the internal point/boundary equilibrium, gray market existence/absence, and other states.Several research conclusions are derived when the system achieves the interior-point equilibriums. In the benchmark situation without reference price effect, both the increase in the consumers′ preference for gray products and the proportion of strategic consumers can lead to the increase of gray products′ price directly, and the increase of the low-priced products′ price and the decrease of the low-priced market demand indirectly. Furthermore, the changes of the high-priced market demand, the gray market demand, and the manufacturer′s profit all have thresholds related to consumers′ willingness to pay in the low-priced market since the willingness to pay in the low-priced market directly affects the speculation space in the gray market. By comparing the values of different thresholds, we find that the threshold value of the manufacturer′s profit changes with each parameter always lags behind the high-priced market demand. This is because the manufacturer′s revenue is affected by the high/low-priced market demand and marginal profit simultaneously, then the threshold value of its change lags behind relatively. In the situation with reference price effect, the overall trend of each equilibrium result with the above two parameters is the same as that without reference price effect. However, the trend thresholds of the high-priced market demand, the gray market demand, and the manufacturer′s profit change. The threshold of manufacturer′s profit still lags behind the high-priced market demand.Comparing the interior-point equilibrium results under the situations with and without reference price effect, we find that the reference price effect will have a direct impact on the price and the market demand of gray products, and high-priced market demand, as well as an indirect impact on the price and the market demand of low-priced products. In order to reduce the negative impact of the reference price effect and curb the growth of the gray market, the manufacturer will reduce the space for gray market speculation by increasing the price of low-priced products and sacrificing the size of the low-priced market. The reference price effect does not necessarily benefit the speculator, nor does it necessarily harm the manufacturer, which is related to the consumers′ willingness to pay in the low-priced market. The introduction of reference price effect makes gray products more attractive, while it will also accelerate the manufacturer to resist them more strictly. For the manufacturer, the introduction of reference price effect increases consumers′ willingness to buy gray products. On the one hand, the development of gray market can promote the development of low-priced market and bring benefits to him in the low-priced market; on the other hand, it will also erode the space of his high-priced market.Furthermore, the numerical analysis of consumer surplus in the gray market system is carried out by introducing an example. We find that the reference price effect in the gray market environment will lead to the decline of consumer surplus, so the brand manufacturer should take corresponding measures to reduce the impact of reference price effect; In both cases, consumer surplus decreases with the increase of the proportion of strategic consumers. This is because the increase of strategic consumers will make the gray market more active, which will have a negative impact on the total consumer surplus. The increase of the strength of the reference price effect or the increase of the profit loss ratio will lead to the decline of consumer surplus when there is a reference price effect. However, consumer surplus will remain unchanged since it is not affected by the above factors when there is no reference price effect. On the one hand, the research conclusions of this paper can enrich the research achievements in the relevant fields of gray market, on the other hand, they can also provide better theoretical support for manufacturers on how to deal with the development of gray market in practice. In addition, this paper studies the situation of independent third-parties′ gray market speculation. Future research can be extended to the situation of distributors′ speculation, or other member enterprises′ speculation. This paper considers the situation where consumers′ valuations in high-priced and low-priced markets are uniformly distributed, which can be extended to the situation of general distribution in the future.

Keywords

Gray market; Pricing decision; Consumer heterogeneity; Reference price effect

Issue

Vol. 39, No. 2, 2025

References