Gray market's product quality in the circular economy era

Abstract

Gray market occurs when a product is diverted from a market to another without the authorisation of the manufacturer. Conventional wisdom believes that (a) the manufacturer should increase product quality as consumer valuation increases, (b) gray market dilutes the manufacturer's incentive to invest in quality, (c) gray products flow from a low-value market to a high-value one, and (d) the manufacturer can decrease product differentiation across regions to curb gray diversion. This paper provides another look by analysing a game-theoretic model wherein one manufacturer sells a product in two markets, a high-value market and a low-value one, each of which contains one single authorised retailer. Using a game-theoretic approach, we find that (a) in the absence of a gray market, the manufacturer may decrease product quality as consumer valuation increases, (b) a unilateral gray market, which diverts products from the low- to the high-value market, can motivate the manufacturer to improve quality, (c) there may exist two gray markets simultaneously: one diverts products from the low- to the high-value market, and the other occurs along the reverse direction, and (d) when quality can be differentiated across markets, the manufacturer might increase quality differentiation in order to manage gray market.

Keywords:

• Gray market
• parallel importation
• product quality
• quality differentiation
• supply chain

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Qingning Cao  http://orcid.org/0000-0003-0094-280X

Jianqiang Zhang  http://orcid.org/0000-0002-8600-0014

Notes

1 In the base model, we assume that the manufacturer sets a uniform quality level. As an extension, we will discuss how the manufacturer can use quality differentiation to manage gray market.

2 Actually, our model can also incorporate the case when the quality of gray products is valued less than white products. We will discuss this case as an extension.

3 The inverse demand functions for $q_1$ and $q_{g2}$ are derived as follows: If t<1, the manufacturer carries lower (higher) quality product in the low (high) market. Consumers for whom ${\theta }_1\ge \frac{p_1-p_{g2}}{u-tu}$ choose quality u and those for whom $\frac{p_{g2}}{tu}\le {\theta }_1<\frac{p_1-p_{g2}}{u-tu}$ choose quality tu. Thus, $q_1=1-\frac{p_1-p_{g2}}{u-tu}$ and $q_{g2}=\frac{p_1-p_{g2}}{u-tu}-\frac{p_{g2}}{tu}$. The inverse demand functions are $p_1=u(1-q_1-t{q}_{g2})$ and $p_{g2}=tu(1-q_1-q_{g2})$. If $t\ge 1$, the manufacturer designs higher (lower) quality product in the low (high) market. Consumers for whom ${\theta }_1\ge \frac{p_{g2}-p_1}{tu-u}$ choose quality tu and those for whom $\frac{p_1}{u}\le {\theta }_1<\frac{p_{g2}-p_1}{tu-u}$ choose quality u. In this way, $q_{g2}=1-\frac{p_{g2}-p_1}{tu-u}$ and $q_1=\frac{p_{g2}-p_1}{tu-u}-\frac{p_1}{u}$, from which we have $p_1=u(1-q_1-q_{g2})$ and $p_{g2}=tu(1-q_1/t-q_{g2})$. We can reexpress the inverse demand functions for $q_1$ and $q_{g2}$ as shown in Equations (36(36) $\begin{array}{rl}{p}_1& =u(1-q_1-min\{t,1\}\cdot q_{g2}),\end{array}$(36) ) and (37(37) $\begin{array}{rl}{p}_{g2}& =tu(1-q_{g2}-min\{1/t,1\}\cdot q_1),\end{array}$(37) ). Equations (38(38) $\begin{array}{rl}{p}_{g1}& =au(1-q_{g1}-min\{t,1\}\cdot q_2),\end{array}$(38) ) and (39(39) $\begin{array}{rl}{p}_2& =atu(1-q_2-min\{1/t,1\}\cdot q_{g1}).\end{array}$(39) ) are obtained using the same method.

4 We also compare the retailers' profits under each case, obtaining similar insights as in the base model. Thus, we do not discuss retailer profit to save space.

5 The assumption that gray products are valued less than authorised products is taken by many researchers, e.g. Xiao, Palekar, and Liu (2011), Iravani, Dasu, and Ahmadi (2016), Zhang (2016), and Ahmadi, Iravani, and Mamani (2017). This assumption also implies that any amount of gray products involves a latent cost. Thus, this extension also covers the case when gray market is not costless. We do not include a separate analysis for the case of positive cost to save pages.

Additional information

Funding

Q. Cao's work is supported by the National Natural Science Foundation of China [grant numbers 71602182, 71520107002], the Natural Science Foundation of Anhui Province [grant number 1708085QG169], and the Fundamental Research Funds for the Central Universities [grant number WK2040160028]. J. Zhang's work is supported by the National Natural Science Foundation of China [grant number 71602078].