Optimal Markup Pricing Strategies in a Green Supply Chain under Different Power Structures

Abstract

Fixed-dollar and flexible markups are two markup pricing strategies commonly adopted in the retail industry, but their impacts on green behaviors of enterprises remain unknown. This paper investigates how the two markup pricing strategies influence firms’ managerial behaviors in a green supply chain, considering three power structures: Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash. We find that the retailer’s pricing strategy choice is jointly affected by power structures and consumer sensitivity to product green levels. Particularly under Manufacturer Stackelberg, the fixed-markup strategy makes the retailer earn a higher profit. However, under Vertical Nash, the retailer’s pricing strategy depends on consumer sensitivity to green levels. When consumers are less sensitive to green levels, a flexible-dollar markup strategy is more profitable for the retailer; otherwise, the fixed-markup strategy is better. Additionally, for the manufacturer, the green levels of the product and the firm profit are always higher when the retailer adopts a fixed-dollar markup strategy under Manufacturer Stackelberg and Vertical Nash. Interestingly, if the retailer adopts a flexible-dollar markup strategy, the manufacturer has the “late-mover advantage” only when consumer sensitivity to the green level is high. Furthermore, the supply chain achieves the highest profit when the manufacturer acts as the leader under the fixed markup strategy.

1. Introduction

In recent years, with increasingly serious global resource and environmental problems, many countries, such as China, the United Kingdom, Denmark, Iceland, and Norway, are investing in the green economy. For example, in order to reduce greenhouse gas emissions, the Netherlands government has made agreements with its transportation department, stating that all Netherlands buses must run on 100% renewable energy or fuel from 2025 and be emission-free by 2030 (https://www.currencytransfer.com/blog/expert-analysis/countries-investing-into-green-economy (accessed on 28 June 2024)). Under the environmental advocacy of governments, a larger number of consumers show a preference for green products that are beneficial or less harmful to the environment [1,2,3]. Meanwhile, the trend of increasing R&D investment in production technologies to improve the green level of products is observed across industries and product categories, ranging from electronics and energy to manufacturing, which can help enterprises gain more competitive advantages [4,5]. For example, automotive giants such as Tesla and Toyota invest in electric vehicle technology to reduce carbon emission. Haier invests in technologies that reduce the energy consumption of refrigerators, air conditioners, and other electrical products.

Improving the green level of products by R&D investment can lead to an increase in consumer demand, thereby affecting pricing decisions of the upstream manufacturer and downstream retailer [6,7]. Generally, retail price consists of two parts: wholesale price and retail markup [8]. The wholesale price is usually determined by the upstream manufacturer, and the retail markup (the retailer’s profit per unit of product) is determined by the downstream retailer. In the face of increased product demand, there is an important choice for downstream retailers who do not bear the cost of green R&D expenditure: whether to raise the retail markup price or keep the retail markup price unchanged compared with that before the manufacturer invested in green R&D.

In practice, some retailers choose to adopt a flexible-dollar markup strategy after upstream manufacturers enable green transformation, i.e., raise retail markup to obtain higher profit per unit of green product. This will lead to higher retail prices of green products and make consumers perceive green products as more expensive than regular products. Differently, some retailers adopt a fixed-dollar markup strategy [9], which means the markup of the retailer is a fixed-dollar amount for whatever upstream manufacturer invests in producing green products. The fixed-dollar markup is commonly used in the agricultural and retail industries [10,11]. For example, Yonghui, no. 1 among China’s top 15 FMCG listed companies of superstores in 2023 (https://mp.weixin.qq.com/s/7qVTsTasFtkW7xsoslBABQ (accessed on 28 June 2024)), does not change retail markup for some brands of garbage bags, paper cups, plastic bins, and some other products, although the suppliers continuously improve the biodegradability and recyclability of these products through green technology R&D over a long period. There are two main reasons for retailers to adopt a fixed-dollar markup strategy. First, green technology R&D investments by suppliers usually increase the wholesale price of these products, and the retailer then increases the markup, which can lead to a higher retail price, thus affecting the demand for the product. Second, managing a large number of categories of retail products requires significant costs (e.g., investments in human and material resources) for enterprises, so maintaining a fixed markup on some products helps to reduce the cost of product management.

In addition, the pricing strategies of manufacturers and retailers generally may be affected by channel power structure. In supply chains, there are three possible channel power structures: the manufacturer is the dominant member, the retailer is the dominant member, and the manufacturer and the retailer have balanced power [12,13]. Traditionally, many large manufacturers enjoy sufficient power to be the channel leaders and have significant influence on the pricing decisions of downstream retailers [14]. However, in the Chinese manufacturing industry, most manufacturers play the role of OEMs supplying the consumer brand owners with the physical products, and they have little pricing power in selling these products [15]. Especially for retailers with greater power such as Walmart, Carrefour, and Tesco, their suppliers are reportedly adopting lower price strategies [16]. Therefore, a more thorough understanding of the effect of power structure on optimal markup pricing decisions is necessary and interesting.

Based on the above discussions, this study aims to address the following questions:

(1)

Which markup pricing strategy is a better choice for the retailer?

(2)

Do the power structures affect the retailers’ markup choices?

(3)

Which markup pricing strategy is more likely to motivate upstream manufacturers to invest more in green R&D?

(4)

How do markup pricing strategies affect the performance of green supply chains?

To address these questions, we study a two-stage supply chain consisting of one manufacturer and one retailer. Taking into account whether manufacturers adopt green R&D investments, two supply chain models—no green transformation (Model N) and green transformation (Model G)—were developed. In Model N, the manufacturer does not implement green R&D investments and the supply chain produces and sells non-green products. In Model G, the manufacturer decides to invest in green R&D to enhance the green level of products and transform to produce and sell green products. Specifically, in Model G, the retailer has two pricing strategies: fixed-dollar markup and flexible-dollar markup. We develop a non-cooperative game and solve the equilibrium results for the retailer and manufacturer under two pricing strategies and three forms of power structures (Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash). Additionally, we discuss the effect of different power structures on the retailers’ markup choices and manufacturer’s green behavior by comparing the equilibrium outcomes across different scenarios.

Our contributions are as follows. First, this paper contributes to the literature on pricing decisions in the green supply chain. Specifically, although the existing studies have analyzed wholesale pricing or retail pricing decisions [17,18,19,20,21,22,23], they do not concern the retail markup pricing strategies. This study is among the first to examine how retail markup pricing strategies impact managerial behaviors of players in a green supply chain. Second, our paper also extends the literature on supply chain power structures. Many scholars investigate the effects of power structure on wholesale pricing or retail pricing decisions [14,17,22,24,25,26,27,28,29,30]. However, these studies ignore the influence of power structure on retail markup pricing decisions. As a difference from them, this study focuses on the impact of power structures on retailers’ markup pricing choices. Finally, few studies pay attention to the impact of retailers’ markup pricing choices on green behaviors of participants in supply chains [31,32,33,34,35]. This study demonstrates that downstream retailers’ markup strategies can incentivize upstream manufacturers to increase their green R&D investments, which extends the results of the existing literature on both pricing decisions and green R&D investment in supply chains.

The remainder of this paper is organized as follows. We review the related literature in Section 2. In Section 3, we describe the notations and assumptions of the model. Section 4 analyzes the models under different power structures, respectively. Section 5 compares the equilibrium results under the same markup strategy. Section 6 presents numerical comparisons. Finally, we provide conclusions in Section 7. All proofs are presented in the Appendix B.

2. Literature Review

This paper is closely related to the following three research areas: (i) green R&D investment in supply chains, (ii) markup pricing strategies, and (iii) supply chain power structures. We briefly review the relevant literature in these areas.

2.1. Green R&D Investment in Supply Chains

Along with the increase in public awareness of environmental protection, a lot of upstream manufacturers in supply chains are investing in green R&D to enhance the green level of their products [36,37]. And this has attracted the interest of academics. For example, Song et al. [31] consider a supply chain consisting of a retailer and a manufacturer that invests in green product R&D, and study the impact of the revenue sharing contracts on the membership decision variables and the performance of the supply chain. Dong et al. [32] develop a stylized two-period model, and conclude that supply chain members could earn more when the manufacturer invests in green product development. Zhang et al. [33] investigate whether and when manufacturers should invest in green technology by considering a supply chain with two manufacturers and a common retailer. Li et al. [34] study a green investment problem of a supply chain with a manufacturer deciding whether to implement blockchain and a retailer with emotional fairness concerns. Yi et al. [35] discuss the impact of emissions taxes and green subsidies on the development of green technologies in the supply chain. All of the above scholars focus on manufacturers’ green R&D investments and discuss related management decisions. However, few scholars focused on pricing changes in the supply chain resulting from manufacturers’ R&D investments. In this paper, we study the optimal markup pricing strategy in a supply chain with the manufacturer investing in green R&D.

2.2. Markup Pricing Strategies

Pricing strategy in supply chains is an area that has been extensively studied; however, few studies in the literature have discussed markup pricing strategies. In most of the literature, scholars compare the performance of two widely used markup pricing policies: fixed-dollar markup and percentage markup [38,39,40,41,42]. These studies focus on the traditional supply chain, and do not involve green R&D investments. Some other scholars discuss retail price markup commitment [43,44,45]. In addition, Canyakmaz et al. [46] examine a newsvendor problem with markup pricing in the presence of within-period price fluctuations. These papers also do not focus on green supply chains. In this paper, we explore the retailer’s optimal markup pricing strategy in a green supply chain.

2.3. Supply Chain Power Structure

A stream of literature discusses the effects of power structures on optimal price and members’ performance in different supply chains, including in a supply chain with random and price-dependent demand [24], in an assembly system with one assembler and two suppliers [25], in a closed-loop supply chain with one manufacturer and one retailer [14], in a two-stage green supply chain with one manufacturer and one retailer [17], in a composite green-product supply chain with one supplier and one manufacturer [27], in a green supply chain with one retailer and two competing manufacturers [22], in a two-stage supply chain with one manufacturer that determines whether to introduce a direct sales channel and one retailer that has two capital statuses [29], in a dual-channel supply chain that consists of a manufacturer and a retailer [28], and in a two-level supply chain consisting of one manufacturer and one retailer that needs to make pricing and assortment decisions [30]. In both traditional and green supply chains, the above studies argue that power structures affect the price decisions of upstream and downstream firms. However, none of them has addressed the impact of power structures on markup pricing. In this study, we discuss different markup decisions by retailers under three types of power structures.

Based on the literature above, the research gaps are summarized as follows. First, few scholars focus on markup pricing in a green supply chain. Second, previous research discusses that power structures affect the price decisions of firms. However, none of the previous research has involved studying the impact of power structures on markup pricing. In this paper, we examine the impact of power structures on retailers’ markup pricing choices. Third, few studies in the literature discuss the impact of price decisions on green R&D investments in supply chains. This study examines the role of the markup pricing strategy as an incentive for manufacturers to invest in green R&D.

Table 1. Comparison between this research and the existing literature.

Authors	Green Supply Chain	Markup Pricing	Demand	Green Investment	Power Structure
Dong et al. [32]	Yes	No	Deterministic	Yes	No
Canyakmaz et al. [46]	No	Yes	Stochastic	No	No
Wang et al. [41]	No	Yes	Deterministic	No	Yes
Zhao et al. [2]	Yes	No	Deterministic	No	No
Wang et al. [42]	No	Yes	Deterministic	No	No
Chen et al. [25]	No	No	Deterministic	No	Yes
Liu et al. [45]	No	Yes	Stochastic	No	No
Xiao et al. [28]	No	No	Deterministic	No	Yes
Lu et al. [30]	No	No	Deterministic	No	Yes
Yi et al. [35]	Yes	No	Deterministic	Yes	No
This paper	Yes	Yes	Deterministic	Yes	Yes

lists how this paper is different from closely related papers and the contributions of our proposed study.

3. The Model

Our model is built upon a supply chain that consists of one manufacturer (he, indexed by “M”) and one retailer (she, indexed by “R”). The manufacturer M sells products to the retailer R at the wholesale price of $w$, then the retailer R sells products to the end consumers at market price $p$. As in previous studies, the retail price is considered to be the sum of the wholesale price and retail margin decisions [8]; thus, we consider $p=w+k$, where $k$ is the retail markup. Meanwhile, manufacturer M may increase the green level of products by investing in R&D expenditure, and we assume the green level of products is $e$. The cost of improving the product green level is assumed to be quadratic in nature, and it is given by $\frac{1}{2}\eta e^2$, where $\eta$ is an investment parameter. This assumption is widely used in the relevant literature [18,20,26,31,47,48].

The market demand relies on the pricing decisions of both manufacturer and retailer and the product green level in the following ways: the market demand decreases with wholesale price and retail markup, but increases with the product green level. A similar demand model is common in the supply chain and operations literature [17]. The market demand is as follows:

$$d=a-b\left(w+k\right)+\gamma e$$

(1)

In this equation, $a$ represents the market potential, $b$ denotes the sensitivity of demand to price changes, and $\gamma$ indicates the sensitivity of demand to the product green level.

Before pursuing green transformation of products, manufacturer M chooses not to invest in developing and producing green products ($e=0$), and the supply chain adopts no green model (Model N); we denote the retail markup of retailer R in this (benchmark) case as $k^{\mathrm{N}}$. Note that we use a superscript ($i$) to indicate the game player; hence, $i=M$ indicates the manufacturer and $i=R$ indicates the retailer.

In Model N, the profits for manufacturer M, retailer R, and the supply chain are as follows:

$${\pi }_M^N=\left(w-c\right)\left[a-b\left(w+k\right)\right]$$

(2)

$${\pi }_R^N=k\left[a-b\left(w+k\right)\right]$$

(3)

$${\pi }_{SC}^N={\pi }_M^N+{\pi }_R^N=\left(w+k-c\right)\left[a-b\left(w+k\right)\right]$$

(4)

In practice, after enabling the green transformation of products, manufacturer M chooses to invest in producing green products ($e\ne 0$), and the supply chain adopts a green model (Model G). In Model G, the profits for manufacturer M, retailer R, and the supply chain are as follows:

$${\pi }_M^G=\left(w-c\right)\left[a-b\left(w+k\right)+\gamma e\right]-\frac{1}{2}\eta e^2$$

(5)

$${\pi }_R^G=k\left[a-b\left(w+k\right)+\gamma e\right]$$

(6)

$${\pi }_{SC}^G={\pi }_M^G+{\pi }_R^G=\left(w+k-c\right)\left[a-b\left(w+k\right)+\gamma e\right]-\frac{1}{2}\eta e^2$$

(7)

In Model G, retailer R has two pricing strategies:

(1)

Fixed-dollar markup strategy (Strategy F): the markup of retailer R is a fixed-dollar amount; that is, the retailer chooses to adopt a fixed-dollar amount markup no matter whether manufacturer M invests in producing green products [9]. In this case, retailer R’s markup is denoted as $k^F$. Obviously, we have $k^F=k^N$.

(2)

Flexible-dollar markup strategy (Strategy L): the markup of retailer R is not a fixed-dollar amount; that is, the retailer chooses to adjust markup to manufacturer M and consumers’ green behavior. In this case, retailer R’s markup is denoted as $k^L$.

Next, we consider and compare the equilibrium decisions of manufacturer M and retailer R under two pricing strategies of the retailer—Strategy F and Strategy L—and three types of power structures—Manufacturer Stackelberg (M), Retailer Stackelberg (R), and Vertical Nash (V). We use “${\pi }_i^{QH}$” to denote the game player $i$’s firm profit under the pricing strategy $H$ and the type of power structure $Q$, where $H\in \{F,L\}$; specifically, superscript F represents the fixed-dollar markup strategy, and superscript L represents the flexible-dollar markup strategy. Additionally, in $Q\in \{M,R,V\}$, superscript M denotes Manufacturer Stackelberg, superscript R denotes Retailer Stackelberg, and superscript V denotes Vertical Nash. In addition, we use “$e^{QH}$”, “$k^{QH}$”, “$w^{QH}$”, “$q^{QH}$”, and “${\pi }_{SC}^{QH}$” to denote manufacturer M’s product green level, retailer R’s retail markup, manufacturer M’s wholesale price, and the market demand and profit of the supply chain under the pricing strategy $H$ and the type of power structure $Q$, respectively. All of the parameters and variables are listed in

Table 2. Notations.

Notation	Definition
$i$	Game players, $i\in [M,R]$. M represents the manufacturer, R represents the retailer.
$H$	Pricing strategies of retailer, $H\in [F,L]$. F represents fixed-dollar markup strategy, L represents flexible-dollar markup strategy.
$Q$	Three types of power structure, $Q\in \{M,R,V\}$. M represents Manufacturer Stackelberg, R represents Retailer Stackelberg, V represents Vertical Nash.
$c$	The cost of producing green products.
$w$	The wholesale price of products.
$p$	The retail price of products.
$k$	The markup of the retailer.
$a$	The total market potential.
$b$	Consumer sensitivity to product price.
$d$	The market demand for products.
$\gamma$	The consumer sensitivity to product green level.
$e$	The green level of products.
$\eta$	The investment efficiency of the manufacturer in improving the green level of products.
${\pi }_M$	The profit of the manufacturer.
${\pi }_R$	The profit of the retailer.
${\pi }_{SC}$	The total profit of the supply chain.

.

4. Retail Markup Strategy Analysis

This section provides and compares equilibrium decisions of both manufacturers and retailers between two pricing strategies under three types of power structures. In order to ensure that all players in the supply chain make a profit in the business and ensure the convexity of the objective functions, we assume that $w>c$, $p>w$, $a-bc>0$, and $0<\gamma <\sqrt{2\eta b}$.

4.1. Manufacturer Stackelberg

In this case, manufacturer M is the Stackelberg leader and retailer R is the follower. We provide the game sequence of the two models as follows: In Model N, manufacturer M first determines product wholesale price $w^{MN}$. Then, retailer R decides retail markup $k^{MN}$ based on the manufacturer’s wholesale price. In Model G, retailer R first chooses pricing strategies because the fixed-dollar markup strategy is an ex ante commitment. If retailer R chooses Strategy F, she keeps the retail markup $k^{MF}$ ($k^{MF}=k^{MN}$) in Model G as she adopts in Model N. Then, manufacturer M determines product wholesale price $w^{MF}$ and green level $e^{MF}$ based on the fixed retail markup $k^{MF}$. If retailer R chooses Strategy L, manufacturer M first determines product wholesale price $w^{ML}$ and green level $e^{ML}$, then retailer R decides the retail markup $k^{ML}$ based on the manufacturer’s decisions. The equilibrium results under Manufacturer Stackelberg are shown in

Table 3. Equilibrium values under Manufacturer Stackelberg.

	No Green Transformation (Model N)	Green Transformation (Model G)
		Strategy F	Strategy L
$e^{\mathrm{*}}$	0	$\frac{3\gamma \left(a-bc\right)}{4\left(2\eta b-{\gamma }^2\right)}$	$\frac{\gamma \left(a-bc\right)}{4\eta b-{\gamma }^2}$
$w^{\mathrm{*}}$	$c+\frac{a-bc}{2b}$	$c+\frac{3\eta \left(a-bc\right)}{4\left(2\eta b-{\gamma }^2\right)}$	$c+\frac{2\eta \left(a-bc\right)}{4\eta b-{\gamma }^2}$
$k^{\mathrm{*}}$	$\frac{a-bc}{4b}$	$\frac{\left(a-bc\right)}{4b}$	$\frac{\eta \left(a-bc\right)}{4\eta b-{\gamma }^2}$
$p^{\mathrm{*}}$	$c+\frac{3\left(a-bc\right)}{4b}$	$c+\frac{\left(5\eta b-{\gamma }^2\right)\left(a-bc\right)}{4b\left(2\eta b-{\gamma }^2\right)}$	$c+\frac{3\eta \left(a-bc\right)}{4\eta b-{\gamma }^2}$
${\pi }_M^{\mathrm{*}}$	$\frac{{\left(a-bc\right)}^2}{8b}$	$\frac{9\eta {\left(a-bc\right)}^2}{32\left(2\eta b-{\gamma }^2\right)}$	$\frac{\eta {\left(a-bc\right)}^2}{2\left(4\eta b-{\gamma }^2\right)}$
${\pi }_R^{\mathrm{*}}$	$\frac{{\left(a-bc\right)}^2}{16b}$	$\frac{3\eta {\left(a-bc\right)}^2}{16\left(2\eta b-{\gamma }^2\right)}$	$\frac{{\eta }^{2}b{\left(a-bc\right)}^2}{{\left(4\eta b-{\gamma }^2\right)}^2}$
${\pi }_{SC}^{\mathrm{*}}$	$\frac{{3\left(a-bc\right)}^2}{16b}$	$\frac{15\eta {\left(a-bc\right)}^2}{32\left(2\eta b-{\gamma }^2\right)}$	$\frac{\eta \left(6\eta b-{\gamma }^2\right){\left(a-bc\right)}^2}{2{\left(4\eta b-{\gamma }^2\right)}^2}$

.

First, we compare the optimal values of the decision variables, i.e., green level, wholesale price, retail markup, and retail price, under the two markup pricing strategies.

Proposition 1. 

The comparisons of green level, wholesale prices, retail markups, and retail prices respectively satisfy the following orders: $e^{MF}>e^{ML}$; $\left\{\begin{array}{cc}{w}^{MF}<w^{ML},& if 0<\gamma <\frac{2\sqrt{5\eta b}}{5}\\ w^{MF}=w^{ML},& if \gamma =\frac{2\sqrt{5\eta b}}{5}\\ w^{MF}>w^{ML},& if \frac{2\sqrt{5tb}}{5}<\gamma <\sqrt{2\eta b}\end{array}\right.$; $k^{MF}<k^{ML}$; $\left\{\begin{array}{cc}{p}^{MF}<p^{ML},& if 0<\gamma <\sqrt{\eta b}\\ p^{MF}=p^{ML},& if \gamma =\sqrt{\eta b}\\ p^{MF}>p^{ML},& if \sqrt{tb}<\gamma <\sqrt{2\eta b}\end{array}\right.$.

Proposition 1 presents the comparative results of two markup pricing strategies under Manufacturer Stackelberg. Firstly, we find that the optimal green level of products under the fixed-dollar markup strategy is higher than that under the flexible-dollar markup strategy, which implies that adopting the fixed markup provides an incentive for the upstream manufacturer to increase green R&D investments (since $e^{ML}<e^{MF}$, we have $\frac{1}{2}\eta {\left(e^{ML}\right)}^2<\frac{1}{2}\eta {\left(e^{MF}\right)}^2$). Secondly, consumer sensitivity to the green level has an impact on wholesale price comparisons. When consumer sensitivity to the green level is lower, the optimal wholesale price under the flexible-dollar markup strategy is higher than that under the fixed-dollar markup strategy. However, when consumer sensitivity to the green level is lower, the optimal wholesale price of products under the fixed-dollar markup strategy is higher. Thirdly, we find that the optimal markup of the retailer under the flexible-dollar markup strategy is higher than that under the fixed-dollar markup strategy, which means that the manufacturer gains higher margins under the flexible-dollar markup strategy. Fourthly, similar to the wholesale price, consumer sensitivity to the green level also affects the comparison of the retail price.

Then, we compare the profits of the manufacturer, retailer, and supply chain under these two markup pricing strategies.

Proposition 2. 

The comparisons of profits of the manufacturer, retailer, and supply chain, respectively, satisfy the following orders: ${\pi }_M^{MF}>{\pi }_M^{ML}$; ${\pi }_R^{MF}>{\pi }_R^{ML}$; ${\pi }_{SC}^{MF}>{\pi }_{SC}^{ML}$.

Proposition 2 suggests that the manufacturer, retailer, and supply chain all obtain higher profits under the fixed-dollar markup strategy than under the flexible-dollar markup strategy. This is because a higher green level under the fixed-dollar markup strategy leads to more demand for the product, which ultimately makes the strategy more profitable for the supply chain members. As a consequence, both the manufacturer and the retailer prefer fixed-dollar markup compared to flexible markups under Manufacturer Stackelberg.

4.2. Retailer Stackelberg

In this case, retailer R is the Stackelberg leader and manufacturer M is the follower. We provide the game sequence of the two models as follows: In Model N, retailer R first decides retail markup $k^{RN}$. Then, manufacturer M determines product wholesale price $w^{RN}$ based on the retail’s markup. In Model G, the same as with Manufacturer Stackelberg, the retailer first commits to whether to set a fixed markup. If retailer R chooses Strategy F, she keeps the retail markup $k^{RF}$ ($k^{RF}=k^{RN}$) in Model G as she adopts in Model N. Then, manufacturer M determines product wholesale price $w^{RF}$ and green level $e^{RF}$ based on the fixed retail markup $k^{RF}$. If retailer R chooses Strategy L, retailer R first decides the retail markup $k^{RL}$ flexibly, then manufacturer M determines product wholesale price $w^{RL}$ and green level $e^{RL}$ based on retail’s decisions. The equilibrium results under Retailer Stackelberg are shown in

Table 4. Equilibrium values under Retailer Stackelberg.

	No Green Transformation (Model N)	Green Transformation (Model G)
		Strategy F	Strategy L
$e^{\mathrm{*}}$	0	$\frac{\gamma \left(a-bc\right)}{2\left(2\eta b-{\gamma }^2\right)}$	$\frac{\gamma \left(a-bc\right)}{2\left(2\eta b-{\gamma }^2\right)}$
$w^{\mathrm{*}}$	$c+\frac{a-bc}{4b}$	$c+\frac{\eta \left(a-bc\right)}{2\left(2\eta b-{\gamma }^2\right)}$	$c+\frac{\eta \left(a-bc\right)}{2\left(2\eta b-{\gamma }^2\right)}$
$k^{\mathrm{*}}$	$\frac{a-bc}{2b}$	$\frac{a-bc}{2b}$	$\frac{a-bc}{2b}$
$p^{\mathrm{*}}$	$c+\frac{3\left(a-bc\right)}{4b}$	$c+\frac{\left(3\eta b-{\gamma }^2\right)\left(a-bc\right)}{2b\left(2\eta b-{\gamma }^2\right)}$	$c+\frac{\left(3\eta b-{\gamma }^2\right)\left(a-bc\right)}{2b\left(2\eta b-{\gamma }^2\right)}$
${\pi }_M^{\mathrm{*}}$	$\frac{{\left(a-bc\right)}^2}{16b}$	$\frac{\eta {\left(a-bc\right)}^2}{8\left(2\eta b-{\gamma }^2\right)}$	$\frac{\eta {\left(a-bc\right)}^2}{8\left(2\eta b-{\gamma }^2\right)}$
${\pi }_R^{\mathrm{*}}$	$\frac{{\left(a-bc\right)}^2}{8b}$	$\frac{\eta {\left(a-bc\right)}^2}{4\left(2\eta b-{\gamma }^2\right)}$	$\frac{\eta {\left(a-bc\right)}^2}{4\left(2\eta b-{\gamma }^2\right)}$
${\pi }_{SC}^{\mathrm{*}}$	$\frac{{3\left(a-bc\right)}^2}{16b}$	$\frac{3\eta {\left(a-bc\right)}^2}{8\left(2\eta b-{\gamma }^2\right)}$	$\frac{3\eta {\left(a-bc\right)}^2}{8\left(2\eta b-{\gamma }^2\right)}$

.

Proposition 3. 

The comparisons of the green level, wholesale prices, retail markups, and retail prices respectively satisfy the following equalities: $e^{RF}=e^{RL}$; $w^{RF}=w^{RL}$; $k^{RF}=k^{RL}$; $p^{RF}=p^{RL}$.

Proposition 4. 

The comparisons of profits of the manufacturer, retailer, and supply chain respectively satisfy the following equalities: ${\pi }_M^{RF}={\pi }_M^{RL}$; ${\pi }_R^{RF}={\pi }_R^{RL}$; ${\pi }_{SC}^{RF}={\pi }_{SC}^{RL}$.

Propositions 3 and 4 show that the optimal green level, wholesale prices, retail markups, and retail prices, as well as the profits of the manufacturer, retailer, and supply chain, are all equal under the flexible-dollar markup strategy and fixed-dollar markup strategy under Retailer Stackelberg. This is because, when the retailer is in a dominant position, the downstream retailer is always the first to make the markup decision regardless of whether the upstream manufacturer invests in green R&D. Realistically speaking, for the retailer, keeping the same markups with no green transformation as with green transformation can encourage the manufacturer to invest more in green R&D.

4.3. Vertical Nash

Different from Manufacturer Stackelberg and Retailer Stackelberg, this case assumes that neither the manufacturer nor the retailer dominates the channel. It is a balanced power structure between manufacturer M and retailer R. We provide the game sequence of the two models as follows: In Model N, manufacturer M determines product wholesale price $w^{VN}$ and retailer R determines retail markup $k^{VN}$ simultaneously. In Model G, the same as with Manufacturer Stackelberg and Retailer Stackelberg, if retailer R chooses Strategy F, she keeps the same retail markup $k^{VF}$ ($k^{VF}=k^{VN}$) in Model G that she adopts in Model N. Then, manufacturer M determines product wholesale price $w^{VF}$ and green level $e^{VF}$ based on the fixed retail markup $k^{VF}$. If retailer R chooses Strategy L, manufacturer M decides product wholesale price $w^V$ and green level $e^{ML}$ and retailer R decides retail markup $k^{\mathrm{V}}$ simultaneously. The equilibrium results under Vertical Nash are shown in

Table 5. Equilibrium values under Vertical Nash.

	No Green Transformation (Model N)	Green Transformation (Model G)
		Strategy F	Strategy L
$e^{\mathrm{*}}$	0	$\frac{2\gamma \left(a-bc\right)}{3\left(2\eta b-{\gamma }^2\right)}$	$\frac{\gamma \left(a-bc\right)}{3tb-{\gamma }^2}$
$w^{\mathrm{*}}$	$c+\frac{a-bc}{3b}$	$c+\frac{2\eta \left(a-bc\right)}{3\left(2\eta b-{\gamma }^2\right)}$	$c+\frac{\eta \left(a-bc\right)}{3\eta b-{\gamma }^2}$
$k^{\mathrm{*}}$	$\frac{a-bc}{3b}$	$\frac{a-bc}{3b}$	$\frac{\eta \left(a-bc\right)}{3\eta b-{\gamma }^2}$
$p^{\mathrm{*}}$	$c+\frac{2\left(a-bc\right)}{3b}$	$c+\frac{\left(4\eta b-{\gamma }^2\right)\left(a-bc\right)}{3b\left(2\eta b-{\gamma }^2\right)}$	$c+\frac{2\eta \left(a-bc\right)}{3\eta b-{\gamma }^2}$
${\pi }_M^{\mathrm{*}}$	$\frac{{\left(a-bc\right)}^2}{9b}$	$\frac{2\eta {\left(a-bc\right)}^2}{9\left(2\eta b-{\gamma }^2\right)}$	$\frac{\eta \left(2\eta b-{\gamma }^2\right){\left(a-bc\right)}^2}{2{\left(3\eta b-{\gamma }^2\right)}^2}$
${\pi }_R^{\mathrm{*}}$	$\frac{{\left(a-bc\right)}^2}{9b}$	$\frac{2\eta {\left(a-bc\right)}^2}{9\left(2\eta b-{\gamma }^2\right)}$	$\frac{{\eta }^{2}b{\left(a-bc\right)}^2}{{\left(3tb-{\gamma }^2\right)}^2}$
${\pi }_{SC}^{\mathrm{*}}$	$\frac{{2\left(a-bc\right)}^2}{9b}$	$\frac{4\eta {\left(a-bc\right)}^2}{9\left(2\eta b-{\gamma }^2\right)}$	$\frac{\eta \left(4\eta b-{\gamma }^2\right){\left(a-bc\right)}^2}{2{\left(3\eta b-{\gamma }^2\right)}^2}$

.

Proposition 5. 

The comparisons of the green level, wholesale prices, retail markups, and retail prices respectively satisfy the following orders: $e^{VF}>e^{VL}$; $w^{VF}>w^{VL}$; $k^{VF}<k^{VL}$; $\left\{\begin{array}{cc}{p}^{VF}<p^{VL},& if 0<\gamma <\sqrt{\eta b}\\ p^{VF}=p^{VL},& if \gamma =\sqrt{\eta b}\\ p^{VF}>p^{VL},& if \sqrt{tb}<\gamma <\sqrt{2\eta b}\end{array}\right.$.

Proposition 5 presents the comparative results of the optimal green level, wholesale price, retail markup, and retail price under the two markup strategies in the scenario Vertical Nash. Firstly, we find that the optimal green level and wholesale price under the fixed-dollar markup strategy are also higher than those under the flexible-dollar markup strategy. This implies that the fixed-dollar markup strategy leads to more investments in green R&D by the manufacturer and the manufacturer charges a higher wholesale price. Secondly, the optimal markup of the retailer under the flexible-dollar markup strategy is also higher than that under the fixed-dollar markup strategy. Thirdly, consumer sensitivity to the green level also has an impact on the comparison of retail prices. When consumer sensitivity to the green level is lower, the optimal retail price of products under the flexible-dollar markup strategy is higher than that under the fixed-dollar markup strategy. When consumer sensitivity to the green level is higher, the optimal retail price of products under the fixed-dollar markup strategy is higher.

Proposition 6. 

The comparisons of profits of the manufacturer, retailer, and supply chain respectively satisfy the following orders:  ${\pi }_M^{VF}>{\pi }_M^{VL}$; $\left\{\begin{array}{cc}{\pi }_R^{VF}<{\pi }_R^{VL},& if 0<\gamma <\frac{\sqrt{6\eta b}}{2}\\ {\pi }_R^{VF}={\pi }_R^{VL},& if \gamma =\frac{\sqrt{6\eta b}}{2}\\ {\pi }_R^{VF}>{\pi }_R^{VL},& if \frac{\sqrt{6\eta b}}{2}<\gamma <\sqrt{2\eta b}\end{array}\right.$; ${\pi }_{SC}^{VF}>{\pi }_{SC}^{VL}$.

Proposition 6 demonstrates the comparative results for the profits of the manufacturer, retailer, and supply chain. Firstly, the manufacturer and the supply chain gain higher profits under the fixed-dollar markup strategy than under the flexible-dollar markup strategy. However, the comparative results for the retailer’s profits are affected by consumer sensitivity to the green level, which is different. When consumer sensitivity to the green level is lower, choosing the flexible-dollar markup strategy can lead to higher profit than choosing the fixed-dollar markup strategy for the retailer. This is because the demand for products under the fixed-dollar markup strategy is more than that under the flexible-dollar markup strategy. However, the optimal markup of the retailer under the fixed-dollar markup strategy is lower. When consumer sensitivity to the green level is relatively low, the profit from increased product demand is less than the profit reduction from the lower marginal products for the retailer. On the contrary, when consumer sensitivity to the green level is higher, the profit is greater for the retailer. Therefore, under Vertical Nash, the retailer should consider the impact of consumer sensitivity to the green level on the profit when making markup decisions.

5. Discussion

In this section, we compare the profits of the manufacturer, retailer, and supply chain under the three different power structures to study the effects of power structures under the two markup pricing strategies, respectively.

5.1. Fixed-Dollar Markup Strategy

Proposition 7. 

The comparisons of profits of the manufacturer, retailer, and supply chain respectively satisfy the following orders: ${\pi }_M^{MF}>{\pi }_M^{VF}>{\pi }_M^{RF}$; ${\pi }_R^{MF}<{\pi }_R^{VF}<{\pi }_R^{RF}; {\pi }_{SC}^{MF}>{\pi }_{sc}^{VF}>{\pi }_{sc}^{RF}$.

Proposition 7 illustrates the profit comparison results of the manufacturer, retailer, and supply chain under the fixed-dollar markup strategy. Firstly, as the power shifts from the retailer to the manufacturer, the optimal profits for the manufacturer and supply chain increase. This means that the manufacturer’s profit is the highest when the manufacturer is in a dominant position. Interestingly, the supply chain also makes the most profit at this point. Secondly, as the power shifts from the manufacturer to the retailer, the optimal profit for the retailer increases, which is the same as for the manufacturer.

5.2. Flexible-Dollar Markup Strategy

Proposition 8. 

The comparisons of profits of the manufacturer, retailer, and supply chain respectively satisfy the following orders: $\left\{\begin{array}{cc} {\pi }_M^{ML}>{\pi }_M^{NL}\ge {\pi }_M^{RL},& if 0<\gamma \le \sqrt{\eta b}\\ {\pi }_M^{ML}\ge {\pi }_M^{RL}>{\pi }_M^{VL},& if \sqrt{\eta b}<\gamma \le \frac{2\sqrt{3\eta b}}{3}\\ {\pi }_M^{RL}>{\pi }_M^{ML}>{\pi }_M^{VL},& if \frac{2\sqrt{3\eta b}}{3}<\gamma <\sqrt{2\eta b}\end{array}\right.$; ${\pi }_R^{ML}<{\pi }_R^{VL}\le {\pi }_R^{RL}$; ${\pi }_{SC}^{ML}<\left\{{\pi }_{sc}^{RL}, {\pi }_{sc}^{VL}\right\}$, and $\left\{\begin{array}{cc} {\pi }_{sc}^{RL}<{\pi }_{sc}^{VL},& if 0<\gamma <\sqrt{\eta b}\\ {\pi }_{sc}^{RL}={\pi }_{sc}^{VL},& if \gamma =\sqrt{\eta b}\\ {\pi }_{sc}^{RL}>{\pi }_{sc}^{VL},& if \sqrt{tb}<\gamma <\sqrt{2\eta b}\end{array}\right.$.

Proposition 8 shows the comparative results for the profits for the manufacturer, retailer, and supply chain under the flexible-dollar markup strategy. Firstly, the impact of power structures on the manufacturer’s profit depends on consumer sensitivity to the green level, which is different from that under the fixed-dollar markup strategy. The profit of the manufacturer under Manufacturer Stackelberg is the highest when consumer sensitivity to the green level is lower, while under Retailer Stackelberg, it is the highest when consumer sensitivity to the green level is higher. Secondly, as the power shifts from the manufacturer to the retailer, the optimal profit of the retailer increases, which is the same as in the fixed-dollar markup strategy. Thirdly, the profits of the supply chain under Retailer Stackelberg and Vertical Nash are higher than those under Manufacturer Stackelberg. And consumer sensitivity to the green level also affects the comparative results for the supply chain profit under Retailer Stackelberg and Vertical Nash. The profit of the supply chain under Vertical Nash is higher than that under Retailer Stackelberg when consumer sensitivity to the green level is lower, while under Retailer Stackelberg it is higher than that under Vertical Nash when consumer sensitivity to the green level is higher.

6. Numerical Analysis

In this section, we study the impact of consumer sensitivity to green level parameters on the optimal green level, wholesale prices, retail markups, and retail prices, and the profits of the manufacturer, the retailer, and the supply chain under different models. Following Ghosh and Shah [17], in the numerical study, we assume that $a=1000$, $b=45$, $c=10$, $\eta =50$, and the value of $\gamma$ varies from 25 to 60. Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6, Figure 7, Figure 8, Figure 9 and Figure 10 show the analysis results of the numerical studies. Note that even when adjusting the parameters, our main conclusions remain the same.

As we can observe in Figure 1, Figure 2, Figure 3, Figure 4, Figure 5, Figure 6 and Figure 7, firstly, consumer sensitivity to the green level has a positive effect on the optimal green level, wholesale prices, retail prices of the product, and the profits of both the retailer and supply chain under Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash ($\frac{d{e}^{QH}}{d\gamma }>0$, $\frac{d{w}^{QH}}{d\gamma }>0$, $\frac{d{p}^{QH}}{d\gamma }>0$, $\frac{d{\pi }_R^{QH}}{d\gamma }>0$, $\frac{d{\pi }_{sc}^{QH}}{d\gamma }>0$). Secondly, the optimal retail markups also increase with consumer sensitivity to the green level under Manufacturer Stackelberg and Vertical Nash under the flexible-dollar markup strategy ($\frac{d{k}^{ML}}{d\gamma }>0$, $\frac{d{k}^{VL}}{d\gamma }>0$). However, in the other four scenarios, the optimal retail markups remain the same. Thirdly, the profits of the manufacturer also increase with consumer sensitivity to the green level in five scenarios ($\frac{d{\pi }_M^{QH}}{d\gamma }>0$, $QH\ne VL$). However, under the flexible-dollar markup strategy, the profits of the manufacturer tend to increase first and then decrease with consumer sensitivity to the green level under Vertical Nash ($\frac{d{\pi }_M^{VL}}{d\gamma }>0$, $\mathrm{i}\mathrm{f}$ $\gamma \in \left(0,\sqrt{\eta b}\right)$; $\frac{d{\pi }_M^{VL}}{d\gamma }<0$, $\mathrm{i}\mathrm{f}$ $\gamma \in \left(\sqrt{\eta b }, \sqrt{2\eta b}\right)$). This is because both the optimal green level and the demand for products increase with consumer sensitivity to the green level. When consumer sensitivity to the green level is lower, the manufacturer’s benefits from increased product demand are higher than the cost of increased green R&D investment. On the contrary, they are lower when consumer sensitivity to the green level is higher. So, under Vertical Nash, the manufacturer should consider the impact of consumer sensitivity to the green level on profits when making decisions.

As shown in Figure 8, Figure 9 and Figure 10, we can also observe some results in the analytical and numerical comparisons of profits of the manufacturer, the retailer, and the supply chain between the fixed-dollar markup strategy and flexible-dollar markup strategy under Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash. Firstly, under Manufacturer Stackelberg and Retailer Stackelberg, the profits the manufacturer, the retailer, and the supply chain gain under the fixed-dollar markup strategy are not less than those under the flexible-dollar markup strategy. Secondly, under Vertical Nash, the results show that the manufacturer and the supply chain gain higher profits under the fixed-dollar markup strategy than under the flexible-dollar markup strategy. However, the retailer’s profits under the fixed-dollar markup strategy are higher than those under the flexible-dollar markup strategy when parameter $\gamma$ is in a certain range. When the value of $\gamma$ is in the range of [25.00, 58.09), the retailer’s profits under the flexible-dollar markup strategy are higher than those under the fixed-dollar markup strategy. On the contrary, when the value of $\gamma$ is in the range of (58.09, 60.00], the retailer’s profits under the fixed-dollar markup strategy are higher than those under the flexible-dollar markup strategy. In summary, the results of the comparison of profits under Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash are as shown in

Table 6. Comparisons of profits under Manufacturer Stackelberg.

	Strategy F	Strategy L
Manufacturer	Higher	—
Retailer	Higher	—
Supply chain	Higher	—

,

Table 7. Comparisons of profits under Retailer Stackelberg.

	Strategy F	Strategy L
Manufacturer	Equal	Equal
Retailer	Equal	Equal
Supply chain	Equal	Equal

and

Table 8. Comparisons of profits under Vertical Nash.

	Strategy F	Strategy L
Manufacturer	Higher	—
Retailer	$\mathrm{Higher} (\gamma >58.09$)	$\mathrm{Higher} (\gamma <58.09)$
Supply chain	Higher	—

.

7. Discussion and Conclusions

In practice, fixed- and flexible-dollar markups are important markup pricing strategies. However, few studies investigate the implication of the two markup pricing strategies for the green behavior of enterprises. Motivated by this research gap, we investigated the impact of the two markup pricing strategies on firms’ management decisions in a green supply chain with one manufacturer and one retailer. Further, we discussed the effects of three types of power structures (Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash) on optimal markup pricing decisions. Some interesting and valuable results and managerial insights are summarized as follows:

Firstly, under Manufacturer Stackelberg, the retailer prefers the fixed-dollar markup strategy to achieve higher profits, and the manufacturer and supply chain can also gain higher benefits. In addition, this strategy can motivate the manufacturer to invest more in green R&D. This phenomenon implies that fixed-dollar markups can achieve a Pareto improvement in profits for both the manufacturer and the retailer compared to flexible-dollar markup. Thus, when the manufacturer acts as the leader of the supply chain, retailers should keep their markups unchanged after manufacturers invest in green technology, which could also provide an incentive for the upstream manufacturer to increase green R&D investments.

Secondly, under Retailer Stackelberg, all the equilibrium results under fixed-dollar markup and flexible-dollar markup strategies are the same. Therefore, when the retailer is the leader of the supply chain, retailers should maintain the same markup with no green transformation as with green transformation.

Thirdly, under Vertical Nash, the manufacturer prefers a fixed-dollar markup strategy. However, the retailer prefers a fixed-dollar markup strategy only when consumer sensitivity to the green level is higher, while when consumer sensitivity to the green level is lower, a flexible-dollar markup strategy is more preferable for the retailer. At this point, unlike the cases of the other two power structures, consumer sensitivity to the green level affects the retailer’s markup choices in this case. Thus, when the manufacturer and the retailer have balanced power, the retailer should consider the impact of consumer sensitivity to the green level of products. When consumer sensitivity to the green level is high, choosing a fixed-dollar markup strategy is more appropriate for both of them. When consumer sensitivity to the green level is low, this may require resolving conflict between manufacturers and retailers regarding markup choices.

Fourthly, under Manufacturer Stackelberg, Retailer Stackelberg, and Vertical Nash (when consumer sensitivity to the green level is higher), the profits the manufacturer, the retailer, and the supply chain gain under the fixed-dollar markup strategy are not less than those under the flexible-dollar markup strategy. Thus, both manufacturers and retailers would agree to a fixed-dollar markup. Under Vertical Nash, the manufacturer and the supply chain also gain more profits under the fixed-dollar markup strategy than under the flexible-dollar markup strategy. However, the retailer’s profits under the flexible-dollar markup strategy are more than those under the fixed-dollar markup strategy when consumer sensitivity to the green level is lower. At this point, manufacturers and retailers may choose different markup strategies, requiring further coordination in the future.

Finally, under both the flexible-dollar and fixed-dollar markup strategies, for the retailer, being the leader always leads to the highest profit. However, it is different for the manufacturer. Under the fixed-dollar markup strategy, for the manufacturer, being a leader can also be the most profitable. Interestingly, under the flexible-dollar markup strategy, the manufacturer acting as a follower can obtain the highest profit when consumer sensitivity to the green level is relatively high. In other words, it has a “late-mover advantage” for the manufacturer. Thus, at this point, allowing retailers to prioritize decision making is better for both manufacturers and retailers. For the supply chain, under the fixed-dollar markup strategy, it obtains the highest profit when the manufacturer becomes the leader. Under the flexible-dollar markup strategy, the retailer acting as the leader leads to the highest profit for the supply chain when consumer sensitivity to the green level is high. Therefore, the performance of the supply chain can be improved by implementing either different markup strategies or different sequences of decision making by supply chain members or both.

This paper has limitations that can be improved through future research. The supply chain in this study involves only one retailer and one manufacturer, which is a basic scenario. Therefore, examining multiple participants can enhance the scope of the research. Percentage markup pricing policy is also widely used, and further research can be performed by exploring different percentage markup strategies in this area. In addition, in order to simplify the model, we adopted a linear demand model based on some existing literature, but the randomness of demand may affect our results, and incorporating demand uncertainty and examining its effects on markup choice can be a potential direction for future research.