As the global economy transitions toward low-carbon mobility, electric vehicles have emerged as a pivotal instrument for achieving sustainable transportation. However, the rapid diffusion of electric vehicles brings with it a challenging question: what happens to the immense stock of batteries, motors, and other core components when vehicles reach the end of their first useful life? Remanufacturing has been recognised as an effective strategy to recover value from used electric vehicle products while reducing environmental burdens. In this paper, I investigate a remanufacturing supply chain for electric vehicles in which a manufacturer simultaneously produces brand-new electric vehicles, remanufactured electric vehicles, and second-hand electric vehicles, and sells them through an independent retailer. What distinguishes my work is the explicit incorporation of heterogeneity in consumer willingness to pay across the three product variants. Consumers on the electric vehicle market are rarely homogeneous: some are willing to pay a premium for brand-new vehicles with the latest battery technology, others are attracted by remanufactured electric vehicles that offer near-new performance at a discount, while a price-sensitive segment may consider only second-hand electric vehicles. These differences in willingness to pay shape the substitution patterns among the three products and profoundly influence pricing decisions along the supply chain.
I model a supply chain with three possible power structures: a centralised decision-making scenario in which the manufacturer and the retailer coordinate as an integrated entity; a manufacturer-led Stackelberg game, and a retailer-led Stackelberg game. For each structure I derive the optimal wholesale and retail prices, compute equilibrium profits, and study the comparative statics with respect to the willingness-to-pay differential coefficients. My analysis reveals several novel findings. First, over a specific range of the willingness-to-pay differential parameter, the equilibrium demand for new, remanufactured and second-hand electric vehicles is unaffected by whether the manufacturer or the retailer serves as the Stackelberg leader. Second, centralised decision-making yields lower retail prices and higher market demand, but decentralised members cannot achieve this outcome unless an appropriate coordination mechanism is adopted. I therefore introduce a two-part tariff contract and show that this contract is capable of aligning the incentives of the manufacturer and the retailer, achieving a Pareto improvement in both members’ profits. Numerical experiments complement the analytical results and shed light on how changes in the relative value coefficients affect profits of the manufacturer, retailer, and the supply chain as a whole.
1. Introduction and Literature Background
Electric vehicles are no longer a niche product. In many markets worldwide, electric vehicles have moved from early adoption into the mass market phase. China, in particular, has experienced explosive growth in electric vehicle sales, aided by government subsidies, consumer awareness of environmental protection, and rapid improvements in battery technology. Yet the rapid growth of the electric vehicle market creates an urgent sustainability challenge: the volume of end-of-life electric vehicle batteries and components is set to rise dramatically over the next decade. Without adequate recovery and value-retention processes, this waste stream will undermine the environmental gains associated with electric mobility.
Remanufacturing offers a promising solution. A remanufactured electric vehicle is a vehicle whose core components—such as the battery pack, electric drive motor, power electronics, and other high-value parts—have been thoroughly inspected, refurbished, and restored to a condition that is functionally equivalent to a new component. Because remanufacturing avoids the energy-intensive processes required to extract raw materials and manufacture new components from scratch, the carbon footprint of a remanufactured electric vehicle can be considerably lower than that of a newly manufactured equivalent. Remanufactured electric vehicles also provide a more affordable entry point for consumers who wish to adopt electric mobility but are constrained by the high upfront cost of a new electric vehicle.
Despite these clear benefits, the electric vehicle remanufacturing industry faces a serious market barrier: consumer perception. Whereas remanufactured industrial machinery has long been accepted in the business-to-business arena, consumers in the automotive sector remain hesitant. Many potential buyers worry that a remanufactured electric vehicle, in particular its battery, will not deliver the same reliability, range, or safety as a brand-new vehicle. This cognitive bias is often stronger for electric vehicles than for conventional internal combustion engine vehicles because the battery is perceived as the ‘heart’ of an electric vehicle, and consumers are unsure how many charge–discharge cycles a remanufactured battery can sustain. As a result, consumers are not willing to pay the same price for a remanufactured electric vehicle as they are for a new one. This gap in willingness to pay is even more pronounced for second-hand electric vehicles, which have typically passed through multiple owners and for which the battery’s remaining useful life is even more uncertain.
Prior research on remanufacturing supply chains has mostly focused on conventional products. In the automobile sector, studies have examined how trade-in programmes, carbon policies, and corporate social responsibility affect supply chain coordination. A common approach is to use a two-period model where a manufacturer sells new products in the first period and collected used cores for remanufacturing in the second period. Several authors have extended this to closed-loop supply chains with competing original equipment manufacturers and third-party remanufacturers. For electric vehicles specifically, the existing literature has analysed battery recycling network design, the economics of battery second-use, and government subsidy schemes. What is largely missing from prior literature is a systematic analysis that treats electric vehicle new products, remanufactured products, and second-hand products as three distinct but vertically differentiated offerings in the same market, and then explores how consumer willingness-to-pay differences interact with supply chain power structure.
My research fills this gap. I study a remanufacturing supply chain focused specifically on electric vehicles, where consumers display vertically differentiated valuations. I construct demand functions for new electric vehicles, remanufactured electric vehicles, and second-hand electric vehicles based on a standard consumer utility model with a willingness-to-pay parameter distributed uniformly over a unit interval. I compare centralised decision-making with two decentralised Stackelberg games. In the first, the electric vehicle manufacturer acts as the Stackelberg leader and sets wholesale prices first; in the second, the retailer leads and sets retail margins first. In both configurations, the follower then makes its pricing decision to maximise its own profit. After deriving the equilibrium pricing policies in each case, I compare them and analyse the effect of the consumers’ willingness-to-pay differential parameters.
The remainder of this article is organised as follows. Section 2 describes the underlying model, assumptions and notation. Section 3 analyses a centralised decision-making benchmark. Section 4 analyses a manufacturer-led Stackelberg game. Section 5 analyses a retailer-led Stackelberg game. Section 6 compares the outcomes across the three power structures. Section 7 introduces a two-part tariff coordination contract. Section 8 presents a numerical simulation and discusses managerial insights. Section 9 concludes the paper.
2. Model Description and Assumptions
I consider a remanufacturing supply chain for electric vehicles composed of one upstream manufacturer, one downstream retailer, and a population of heterogeneous consumers. The manufacturer produces brand-new electric vehicles and also undertakes recovery and remanufacturing activities. After the manufacturer has remanufactured some collected cores, it may also choose to refurbish a subset of them to sell as second-hand electric vehicles. The manufacturer sells all three products through an independent retailer, who then sets the final retail prices to consumers. The three products are vertically differentiated: brand-new electric vehicles are of the highest quality and command the highest price; remanufactured electric vehicles have been restored to a standard close to new and are sold at a moderate price; second-hand electric vehicles have not gone through full remanufacturing and therefore are the lowest-priced and lowest-quality option.
To model consumer behaviour, I use a standard vertical differentiation framework. Each consumer derives a valuation \(\theta\) for one unit of the product. The valuation parameter \(\theta\) is uniformly distributed over the interval \([0,1]\), with density \(f(\theta)=1\) and cumulative distribution function \(F(\theta)=\theta\). A consumer’s willingness to pay is highest for a new electric vehicle. Adopting the notation frequently used in the remanufacturing literature, I let \(\theta_{ON}\) denote a consumer’s valuation for a new electric vehicle. Consumers value a remanufactured electric vehicle at \(\theta_{OR} = \alpha_{1} \theta_{ON}\), and they value a second-hand electric vehicle at \(\theta_{OS} = \alpha_{1} \alpha_{2} \theta_{ON}\), where \(\alpha_{1} \in (0,1)\) and \(\alpha_{2} \in (0,1)\). The coefficient \(\alpha_{1}\) represents consumers’ relative willingness to pay for a remanufactured electric vehicle as compared with a new one. The coefficient \(\alpha_{2}\) represents the additional discount that consumers apply to second-hand electric vehicles relative to remanufactured ones. A larger \(\alpha_{1}\) implies that consumers regard remanufactured electric vehicles as close substitutes for new ones; a larger \(\alpha_{2}\) implies that consumers perceive second-hand electric vehicles to be almost as good as remanufactured electric vehicles. Both coefficients are exogenously given and reflect market perceptions. These perceptions can be influenced by the manufacturer’s quality disclosure, certification, warranty policies, and other information-provision strategies, but within the scope of this model they are treated as parameters.
The three product variants are functionally similar, but their quality levels differ. Consumers can distinguish these quality differences. The indirect utility that a consumer derives from purchasing a new, remanufactured, or second-hand electric vehicle is respectively:
\[
U_{ON} = \theta_{ON} – P_{ON}, \quad
U_{OR} = \theta_{OR} – P_{OR} = \alpha_{1}\theta_{ON} – P_{OR}, \quad
U_{OS} = \theta_{OS} – P_{OS} = \alpha_{1}\alpha_{2}\theta_{ON} – P_{OS}.
\]
A consumer chooses the product that gives the highest non-negative utility. I assume a single-period setting and standardise the market size to unity. In each period, a consumer purchases at most one electric vehicle. The condition that the market is in a steady state is appropriate for studying electric vehicle remanufacturing decisions because I am interested in the structure of equilibrium pricing rather than in transition dynamics.
Regarding the manufacturer’s costs, I denote the unit cost of producing a new electric vehicle by \(C_{ON}\), the unit cost of producing a remanufactured electric vehicle by \(C_{OR}\), and the unit cost associated with bringing a second-hand electric vehicle to market by \(C_{OS}\). The production cost of a new electric vehicle is the highest. Remanufacturing an electric vehicle is less expensive than producing a new one because the core components are recovered; however, the second-hand electric vehicle involves an additional recovery cost \(B\) that the manufacturer incurs in acquiring end-of-life electric vehicles from the market. This cost encompasses the payment made to previous owners, collection and inspection expenses, and the cost of refurbishing the vehicle to a condition that is suitable for resale. The relationships between the costs can be summarised as:
\[
C_{ON} > C_{OR} > C_{OS},\quad 0 < B < 1.
\]
Throughout the model I focus on the unit recovery cost \(B\) as a parameter reflecting how costly it is for the manufacturer to obtain used electric vehicles. The manufacturer independently decides whether or not to engage in second-hand refurbishment in addition to remanufacturing, since second-hand electric vehicles are within the scope of the manufacturer’s patent protection and the manufacturer controls the quality of the refurbishment process. All notation that will be used in the remainder of the paper is collected in the table below.
Symbols and Definitions
| Variables | Definitions | Variables | Definitions |
|---|---|---|---|
| \(C_{ON}, C_{OR}, C_{OS}\) | Production cost of new/remanufactured/second-hand electric vehicles | \(W_{ON}, W_{OR}, W_{OS}\) | Wholesale prices of the three electric vehicle variants |
| \(P_{ON}, P_{OR}, P_{OS}\) | Retail prices of new/remanufactured/second-hand electric vehicles | \(q_{ON}, q_{OR}, q_{OS}\) | Market demand for the three electric vehicle variants |
| \(B\) | Per-unit recovery cost paid by the manufacturer for second-hand electric vehicle cores | \(\theta\) | Consumer willingness to pay for an electric vehicle unit |
| \(\alpha_{1}\) | Relative consumer valuation of remanufactured vs. new electric vehicles | \(\beta\) | Lump-sum fee in the two-part tariff contract |
| \(\alpha_{2}\) | Relative consumer valuation of second-hand vs. remanufactured electric vehicles | \(\pi_{M}, \pi_{R}, \pi_{I}\) | Profit functions of the manufacturer, retailer, and integrated chain |
To simplify the exposition of the closed-form expressions, I define three composite parameters that will recur throughout the proofs:
\[
\varepsilon_{1} = \frac{1}{6} + \frac{37}{36} + \frac{C_{OR}^{2}}{36\alpha_{1}^{2}} – \frac{2C_{OR}}{36\alpha_{1}} – \frac{C_{OR}}{6\alpha_{1}},
\]
\[
\varepsilon_{2} = \frac{-B – C_{OS} + \sqrt{B^{2} + 2BC_{OS} + C_{OS}^{2} + 24\alpha_{1}^{2}}}{4\alpha_{1}},
\]
\[
\varepsilon_{3} = \frac{-B + C_{OR} – C_{OS} + 3\alpha_{1} + \sqrt{(B – C_{OR})^{2} + 2(C_{OS} – 3\alpha_{1})(B – C_{OR}) + (3\alpha_{1} – C_{OS})^{2} + 16\alpha_{1}^{2}}}{8\alpha_{1}}.
\]
These composite parameters appear only when I compare the equilibrium wholesale and retail prices across different power structures. They allow me to express the conditions under which the manufacturer-led equilibrium price exceeds or falls below the retailer-led equilibrium price.
3. Centralised Decision-Making Benchmark
As a benchmark, I first consider a vertically integrated supply chain in which the electric vehicle manufacturer and the retailer act as a single entity. The integrated chain seeks to maximise the system total profit by choosing retail prices for all three electric vehicle products jointly. This centralised scenario represents the first-best outcome against which decentralised equilibria can be evaluated.
Given the utilities defined above, the boundaries between the market segments can be derived from the conditions under which a consumer with valuation \(\theta_{ON}\) is indifferent between adjacent products. A consumer purchases a new electric vehicle when
\[
U_{ON} \geq 0,\quad U_{ON} \geq U_{OR},\quad U_{ON} \geq U_{OS}.
\]
A consumer purchases a remanufactured electric vehicle when
\[
U_{OR} \geq 0,\quad U_{OR} \geq U_{ON},\quad U_{OR} \geq U_{OS}.
\]
A consumer purchases a second-hand electric vehicle when
\[
U_{OS} \geq 0,\quad U_{OS} \geq U_{ON},\quad U_{OS} \geq U_{OR}.
\]
Solving these inequalities yields the following demand functions for the three electric vehicle products:
\[
q_{ON} = \int_{\frac{P_{ON} – P_{OR}}{1 – \alpha_{1}}}^{1} f(\theta_{ON})d\theta_{ON}
= 1 – \frac{P_{ON} – P_{OR}}{1 – \alpha_{1}},
\]
\[
q_{OR} = \int_{\frac{P_{OR} – P_{OS}}{\alpha_{1}(1 – \alpha_{2})}}^{\frac{P_{ON} – P_{OR}}{1 – \alpha_{1}}} f(\theta_{ON})d\theta_{ON}
= \frac{P_{ON} – P_{OR}}{1 – \alpha_{1}} – \frac{P_{OR} – P_{OS}}{\alpha_{1}(1 – \alpha_{2})},
\]
\[
q_{OS} = \int_{\frac{P_{OS}}{\alpha_{1}\alpha_{2}}}^{\frac{P_{OR} – P_{OS}}{\alpha_{1}(1 – \alpha_{2})}} f(\theta_{ON})d\theta_{ON}
= \frac{P_{OR} – P_{OS}}{\alpha_{1}(1 – \alpha_{2})} – \frac{P_{OS}}{\alpha_{1}\alpha_{2}}.
\]
These demand functions reflect the vertical differentiation structure. The demand for the new electric vehicle comes from consumers with the highest valuation; the demand for the second-hand electric vehicle comes from consumers with the lowest valuation that still exceeds the price-to-quality ratio of the second-hand electric vehicle; and the remanufactured electric vehicle captures the middle segment.
The integrated supply chain’s profit is:
\[
\pi_{I} = q_{ON}(P_{ON} – C_{ON}) + q_{OR}(P_{OR} – C_{OR}) + q_{OS}(P_{OS} – C_{OS}) – B.
\]
Denote the optimal centralised prices by \(P_{ON}^{MR*}, P_{OR}^{MR*}, P_{OS}^{MR*}\). Solving the first-order conditions simultaneously, I obtain the centralised equilibrium in Proposition 1.
Proposition 1. In the centralised electric vehicle remanufacturing supply chain, the optimal retail prices for the new, remanufactured and second-hand electric vehicles are
\[
P_{ON}^{MR*} = \frac{(1 + C_{ON})(1 – \alpha_{2}) + 2\alpha_{1}\alpha_{2} – \alpha_{1}\alpha_{2}^{2}}{2(1 – \alpha_{2})},
\]
\[
P_{OR}^{MR*} = \frac{C_{OR} + \alpha_{1} + \alpha_{1}\alpha_{2} – C_{OR}\alpha_{2} – \alpha_{1}\alpha_{2}^{2}}{2(1 – \alpha_{2})},
\]
\[
P_{OS}^{MR*} = \frac{B + C_{OS} + \alpha_{1}\alpha_{2}}{2}.
\]
Proof. The Hessian matrix of the integrated profit function is examined to verify concavity. The Hessian is
\[
H =
\begin{bmatrix}
-\frac{2}{1 – \alpha_{1}} & \frac{2}{1 – \alpha_{1}} & 0 \\[2mm]
\frac{2}{1 – \alpha_{1}} & -2\left(\frac{1}{1 – \alpha_{1}} + \frac{1}{\alpha_{1}(1 – \alpha_{2})}\right) & \frac{2}{\alpha_{1}(1 – \alpha_{2})} \\[2mm]
0 & \frac{2}{\alpha_{1}(1 – \alpha_{2})} & -2\left(\frac{1}{\alpha_{1}\alpha_{2}} + \frac{1}{\alpha_{1}(1 – \alpha_{2})}\right)
\end{bmatrix}.
\]
The principal minors alternate in sign:
\[
|H_{1}| = -\frac{2}{1 – \alpha_{1}} < 0,
\]
\[
|H_{2}| = \frac{4(1 – \alpha_{2})}{(1 – \alpha_{1})\alpha_{1}} > 0,
\]
\[
|H_{3}| = -\frac{8\alpha_{2}}{(1 – \alpha_{1})^{2}\alpha_{1}^{2}(1 – \alpha_{2})} < 0.
\]
Therefore, the integrated profit function is strictly concave in the three retail prices, and the unique optimum is obtained by solving:
\[
\frac{\partial \pi_{I}}{\partial P_{ON}} = 0, \quad
\frac{\partial \pi_{I}}{\partial P_{OR}} = 0, \quad
\frac{\partial \pi_{I}}{\partial P_{OS}} = 0.
\]
Substituting the optimal prices back into the profit function yields the maximum integrated profit. In addition, differentiating the optimal prices with respect to the valuation parameters, I find that the optimal price of the second-hand electric vehicle is unaffected by changes in \(\alpha_{1}\). This is intuitive: the price of a second-hand electric vehicle in the integrated chain is driven primarily by its cost, the recovery cost and the absolute valuation scale calibrating the marginal consumer at the bottom of the distribution, rather than by the premium that consumers attach to new electric vehicles.
One important property of the centralised equilibrium concerns the response of demand to changes in the willingness-to-pay coefficients. Since
\[
\frac{dq_{ON}^{j}}{d\alpha_{2}} < 0,\quad
\frac{dq_{OR}^{j}}{d\alpha_{1}} > 0,\quad
\frac{dq_{OS}^{j}}{d\alpha_{1}} > 0
\]
for any model \(j\), I can state the following economic interpretation. An increase in \(\alpha_{2}\), which means that consumers value second-hand electric vehicles more highly relative to remanufactured ones, shifts the segment boundaries in such a way that demand for the new electric vehicle falls. Consumers in the high-valuation segment of the market perceive second-hand electric vehicles as more attractive substitutes, so some of them switch away from new electric vehicles. An increase in \(\alpha_{1}\) raises demand for both remanufactured and second-hand electric vehicles, because both become more attractive relative to the new electric vehicle at the margin.
From a managerial perspective, the centralised equilibrium provides three insights for the electric vehicle supply chain. First, retail prices for new and remanufactured electric vehicles should respond positively to upward shifts in consumers’ willingness to pay. Second, since a rise in \(\alpha_{2}\) contracts demand for new electric vehicles, the supply chain should counterbalance this through non-price strategies, such as enhancing the warranty coverage for new electric vehicle batteries, offering complimentary charging credits, or bundling maintenance services. Third, the second-hand electric vehicle segment’s pricing should be driven primarily by the recovery cost and product condition rather than by consumers’ enthusiasm for new electric vehicle technology.
4. Manufacturer-Led Stackelberg Game
I now relax the assumption of vertical integration and consider a decentralised supply chain in which the manufacturer of electric vehicles is the Stackelberg leader. In this configuration, the manufacturer first announces the wholesale prices \(W_{ON}\), \(W_{OR}\), and \(W_{OS}\) for the new, remanufactured, and second-hand electric vehicles. The retailer observes these wholesale prices and then determines the retail prices \(P_{ON}\), \(P_{OR}\) and \(P_{OS}\) to maximise its own profit. This structure reflects an electric vehicle market in which the manufacturer, often an original equipment manufacturer with strong brand power and proprietary battery technology, dominates and leads the pricing process. The manufacturer also controls the recovery and refurbishment of second-hand electric vehicles, paying per-unit recovery cost \(B\), so the second-hand business is fully internalised by the manufacturer.
The manufacturer’s profit is:
\[
\pi_{M} = q_{ON}(P_{ON} – W_{ON}) + q_{OR}(P_{OR} – W_{OR}) + q_{OS}(P_{OS} – W_{OS}) – B.
\]
The retailer’s profit is:
\[
\pi_{R} = q_{ON}(W_{ON} – C_{ON}) + q_{OR}(W_{OR} – C_{OR}) + q_{OS}(W_{OS} – C_{OS}).
\]
Note that in this representation the retailer purchases from the manufacturer at the wholesale price and sells to consumers at the retail price. The retailer therefore earns the margin between the wholesale price and the retail price, while the manufacturer bears the production and recovery costs of electric vehicles.
I solve the game by backward induction. For a given set of wholesale prices, the retailer chooses its retail prices. The Hessian matrix of the retailer’s profit with respect to the three retail prices is identical to the Hessian of the centralised problem, except that costs are replaced by wholesale prices. The Hessian is negative definite under the same parametric conditions as in the centralised case. Hence there exists a unique optimal retail pricing response for the retailer given any set of wholesale prices. The retailer’s reaction functions are:
\[
P_{ON} = \frac{W_{ON} + 1}{2},
\]
\[
P_{OR} = \frac{W_{OR} + \alpha_{1}}{2},
\]
\[
P_{OS} = \frac{W_{OS} + \alpha_{1}\alpha_{2}}{2}.
\]
Substituting these responses back into the manufacturer’s profit function, the manufacturer now chooses its wholesale prices to maximise its own profit. Since the second derivatives of the manufacturer’s profit with respect to \(W_{ON}\), \(W_{OR}\), and \(W_{OS}\) are all negative, the manufacturer’s optimisation problem is concave. Solving the first-order conditions yields the manufacturer-led equilibrium described in Proposition 2.
Proposition 2 (Model M). In the manufacturer-led Stackelberg game, the unique equilibrium wholesale prices are
\[
W_{ON}^{M*} = \frac{2\alpha_{1} + \alpha_{2} + C_{ON}\alpha_{2} – 2\alpha_{1}\alpha_{2}^{2}}{2\alpha_{2}},
\]
\[
W_{OR}^{M*} = \frac{2\alpha_{1} + C_{OR}\alpha_{2} + \alpha_{1}\alpha_{2} – 2\alpha_{1}\alpha_{2}^{2}}{2\alpha_{2}},
\]
\[
W_{OS}^{M*} = \frac{2\alpha_{1} + B\alpha_{2} + C_{OS}\alpha_{2} – \alpha_{1}\alpha_{2}^{2}}{2\alpha_{2}}.
\]
The corresponding equilibrium retail prices are:
\[
P_{ON}^{M*} = \frac{(3 + C_{ON})\alpha_{2} – 2\alpha_{1}(-1 + \alpha_{2})}{4\alpha_{2}},
\]
\[
P_{OR}^{M*} = \frac{C_{OR}\alpha_{2} + \alpha_{1}(2 + 3\alpha_{2} – 2\alpha_{2}^{2})}{4\alpha_{2}},
\]
\[
P_{OS}^{M*} = \frac{C_{OR}\alpha_{2} + \alpha_{1}(2 + 3\alpha_{2} – 2\alpha_{2}^{2})}{4\alpha_{2}}.
\]
An interesting property of the manufacturer-led equilibrium is that the equilibrium wholesale prices of all three products are independent of the valuation coefficient \(\alpha_{1}\). In the manufacturer-led Stackelberg structure, the wholesale prices are set before the retail market is opened. The manufacturer bases its pricing on its own production costs, the recovery cost of used electric vehicles, and its strategic assessment of the retailer’s response, rather than on the detailed willingness-to-pay segmentation of end consumers. The retailer, who is closer to the market, later takes the consumers’ valuation parameters into account when determining the retail markup. In other words, the burden of responding to electric vehicle consumer heterogeneity falls on the retailer’s shoulders when the manufacturer is the channel leader.
Substituting the equilibrium prices into the profit expressions yields the equilibrium profit functions for the manufacturer, the retailer, and the total supply chain. Let \(\pi_{M}^{M*}\) and \(\pi_{R}^{M*}\) denote the manufacturer’s and retailer’s equilibrium profits in Model M. These are given by complex rational functions of the cost and valuation parameters.
\[
\pi_{M}^{M*} = \frac{\begin{aligned}
&-4\alpha_{1}^{3}(-1+\alpha_{2})^{3}(1+\alpha_{2}^{2}) + \alpha_{1}^{2}(-1+\alpha_{2})(4 – 8\alpha_{2}^{2} + (1-2C_{ON})\alpha_{2}^{3} + 4\alpha_{2}^{4}) \\
&+ \alpha_{2}^{2}(B^{2} + C_{OS}^{2} + C_{OR}^{2}\alpha_{2} – 2C_{OR}C_{OS}\alpha_{2} + 2B(C_{OS} – C_{OR}\alpha_{2})) \\
&- \alpha_{1}\alpha_{2}^{2}\left(B^{2} + C_{OS}^{2} – 2C_{OR}C_{OS}\alpha_{2} + 2B(C_{OS} – C_{OR}\alpha_{2}) + \alpha_{2}(-1 + C_{ON}^{2}(-1+\alpha_{2}) – 2C_{ON}(1+C_{OR})(-1+\alpha_{2}) + \alpha_{2} + C_{OR}^{2}\alpha_{2})\right)
\end{aligned}}{8(-1 + \alpha_{1})\alpha_{1}(-1+\alpha_{2})\alpha_{2}^{3}}
\]
\[
\pi_{R}^{M*} = \frac{\begin{aligned}
&4\alpha_{1}^{3}(-1+\alpha_{2})^{2}(-1-\alpha_{2}+2\alpha_{2}^{2}+2\alpha_{2}^{3}) + \alpha_{2}^{2}(B^{2} + C_{OS}^{2} + C_{OR}^{2}\alpha_{2} – 2C_{OR}C_{OS}\alpha_{2} + 2B(C_{OS} – C_{OR}\alpha_{2})) \\
&- \alpha_{1}^{2}(-1+\alpha_{2})(4 – 12\alpha_{2}^{2} – \alpha_{2}^{3} + 2C_{ON}\alpha_{2}^{3} + 8\alpha_{2}^{4} + 4B\alpha_{2}(-1+\alpha_{2})^{2} + 4C_{OS}\alpha_{2}(-1+\alpha_{2})^{2}) \\
&- \alpha_{1}\alpha_{2}(B^{2}\alpha_{2} + C_{OS}^{2}\alpha_{2} + \alpha_{2}^{2}(-1 + C_{ON}^{2}(-1+\alpha_{2}) – 2C_{ON}(1+C_{OR})(-1+\alpha_{2}) + \alpha_{2} + C_{OR}^{2}\alpha_{2})) \\
&- \alpha_{1}\alpha_{2}(B(-4 + 2(2+C_{OS})\alpha_{2} – 2(-2+C_{OR})\alpha_{2}^{2} – 4\alpha_{2}^{3} – 2C_{OS}(2 – 2\alpha_{2} + (-2+C_{OR})\alpha_{2}^{2} + 2\alpha_{2}^{3})))
\end{aligned}}{16(-1+\alpha_{1})\alpha_{1}(-1+\alpha_{2})\alpha_{2}^{3}}
\]
In the manufacturer-led equilibrium, the manufacturer’s profit does not vary with \(\alpha_{1}\), a consequence of the wholesale prices being independent of the relative valuation between remanufactured and new electric vehicles in Model M. However, both the retailer’s pricing decisions and the resulting market demand depend on \(\alpha_{1}\). Consequently the retailer absorbs the effect of shifts in consumer preference between new and remanufactured electric vehicles, while the manufacturer’s profit is shielded from those shifts at the wholesale stage.
5. Retailer-Led Stackelberg Game
In many real-world electric vehicle markets, the balance of power lies with the retailer rather than the manufacturer. Large electric vehicle distribution groups, multi-brand retailers, and vertically integrated online platforms have direct access to consumers and can transmit market signals quickly up the chain. Online retail platforms, in particular, often dominate the customer interface in the electric vehicle sector. When the retailer is the Stackelberg leader, the timing of the game is reversed. The retailer first announces its retail margin on each of the three products, or equivalently it sets the retail prices before the manufacturer sets wholesale prices. The manufacturer, upon observing the retail prices, responds by choosing the wholesale prices that maximise its own profit.
To solve this retailer-led Stackelberg game, I introduce the retailer’s margins \(f_{ON}\), \(f_{OR}\) and \(f_{OS}\), defined as the difference between the retail price and the wholesale price of each electric vehicle product:
\[
P_{ON} = W_{ON} + f_{ON},\quad
P_{OR} = W_{OR} + f_{OR},\quad
P_{OS} = W_{OS} + f_{OS}.
\]
Given the margins announced by the retailer, the manufacturer’s profit can be expressed as a function of the wholesale prices and the margins. The Hessian matrix of the manufacturer’s profit with respect to the wholesale prices is
\[
H =
\begin{bmatrix}
-\frac{2}{1-\alpha_{1}} & 0 & 0 \\
0 & -2\left(\frac{1}{1-\alpha_{1}} + \frac{1}{(1-\alpha_{2})\alpha_{1}}\right) & 0 \\
0 & 0 & -2\left(\frac{1}{(1-\alpha_{2})\alpha_{1}} + \frac{1}{\alpha_{2}\alpha_{1}}\right)
\end{bmatrix}.
\]
This Hessian is a diagonal matrix with strictly negative diagonal elements, since all three products are quality-differentiated and the price boundaries are positive. Hence the manufacturer’s profit function is strictly concave in the wholesale prices. The manufacturer responds to the retailer’s margins by choosing the unique optimal wholesale prices. Solving the first-order conditions of the manufacturer’s optimisation gives the wholesale prices as linear affine functions of the margins.
After deriving the manufacturer’s best response, I substitute it back into the retailer’s profit. The retailer then maximises its profit over the margins. Because the retailer’s optimisation problem is also concave, I obtain a unique equilibrium, stated in Proposition 3.
Proposition 3 (Model R). In the retailer-led Stackelberg game, the unique equilibrium wholesale prices are
\[
W_{ON}^{R*} = \frac{\alpha_{1} + \alpha_{2} + 3C_{ON}\alpha_{2} – \alpha_{1}\alpha_{2}^{2}}{4\alpha_{2}},
\]
\[
W_{OR}^{R*} = \frac{\alpha_{1} + 3C_{OR}\alpha_{2} + \alpha_{1}\alpha_{2} – \alpha_{1}\alpha_{2}^{2}}{4\alpha_{2}},
\]
\[
W_{OS}^{R*} = \frac{\alpha_{1} + 3(B + C_{OS})\alpha_{2}}{4\alpha_{2}}.
\]
The corresponding equilibrium retail prices are:
\[
P_{ON}^{R*} = \frac{(3 + C_{ON})\alpha_{2} – 3\alpha_{1}(-1+\alpha_{2})}{4\alpha_{2}},
\]
\[
P_{OR}^{R*} = \frac{C_{OR}\alpha_{2} + \alpha_{1}(3 + 3\alpha_{2} – 3\alpha_{2}^{2})}{4\alpha_{2}},
\]
\[
P_{OS}^{R*} = \frac{3\alpha_{1} + (B + C_{OS})\alpha_{2}}{4\alpha_{2}}.
\]
In contrast to the manufacturer-led model, the wholesale prices in the retailer-led model depend explicitly on the valuation coefficient \(\alpha_{1}\). This is because the retailer, being the leader and closer to the electric vehicle consumers, internalises the demand-side valuation in its margin decision. The manufacturer, when responding to the retailer’s margins, must react to the room left for its wholesale price, which therefore reflects the consumers’ willingness to pay for the different electric vehicle variants. A greater consumer valuation for remanufactured electric vehicles relative to new ones drives up all three wholesale prices in the retailer-led chain. The retailer, in effect, transfers part of the consumers’ higher willingness to pay upstream to the manufacturer through higher margins, while keeping the wholesale price increase aligned with the market’s stronger appreciation of the remanufactured electric vehicle product.
The equilibrium retail price of the new electric vehicle in Model R decreases with \(\alpha_{1}\). When \(\alpha_{1}\) rises, remanufactured electric vehicles become much closer substitutes for new electric vehicles. The retailer must reduce the price premium of a new electric vehicle, thereby compressing its retail price, to prevent excessive cannibalisation of new electric vehicle sales by remanufactured electric vehicles. Conversely, the equilibrium retail price of remanufactured electric vehicles rises with \(\alpha_{1}\), reflecting the improved consumer perception and hence the ability to command a higher price in the marketplace.
The profit functions of the supply chain members in Model R can be derived by substituting the optimal prices into the respective profit expressions. Without repeating the full algebraic expressions here, I note that they are rational functions with denominators involving \((1-\alpha_{1})\alpha_{1}(1-\alpha_{2})\alpha_{2}\), and they display cross-partial effects that reveal a complex pattern of interaction between the valuation coefficients and the cost parameters.
6. Comparative Analysis of the Three Models
In this section I compare the equilibrium outcomes of the centralised model (Model MR), the manufacturer-led model (Model M), and the retailer-led model (Model R). The comparison reveals important regularities about how channel power and the consumers’ willingness to pay shape the electric vehicle remanufacturing supply chain. I first examine the responsiveness of equilibrium demands to changes in the valuation parameters, and then compare the price levels across the three models.
Proposition 4. In all three models, the derivative of the demand for new electric vehicles with respect to \(\alpha_{2}\) is exactly zero:
\[
\frac{dq_{ON}^{j}}{d\alpha_{2}} = 0, \quad j \in \{MR, M, R\}.
\]
The change in consumers’ relative willingness to pay for second-hand versus remanufactured electric vehicles does not affect the market demand for new electric vehicles. This result holds regardless of the power structure. The underlying intuition is straightforward: the boundary separating the new electric vehicle market from the remanufactured electric vehicle market depends only on \(\alpha_{1}\), the relative valuation between new and remanufactured electric vehicles, and not on \(\alpha_{2}\). Consumers at the highest end of the valuation distribution compare new electric vehicles against remanufactured electric vehicles, while the comparison between second-hand and remanufactured electric vehicles occurs at a lower point of the valuation distribution. A change in \(\alpha_{2}\) shifts the boundary between the second-hand and remanufactured segments, leaving the demand of the high-end segment untouched. This insight is important for electric vehicle manufacturers: strategies that target the second-hand market will not cannibalise new electric vehicle sales at the margin, but they do impact the remanufactured electric vehicle segment directly.
For remanufactured electric vehicles and second-hand electric vehicles, the signs of the derivatives depend on the model and on the balance between the recovery cost \(B\), the production costs, and the valuation coefficients. In the centralised model, when \(B > C_{OR} – C_{OS} – \frac{2\alpha_{1}}{\alpha_{2}-1}\), an increase in \(\alpha_{2}\) raises the demand for remanufactured electric vehicles and lowers the demand for second-hand electric vehicles. In the manufacturer-led model, when \(B + C_{OS} > C_{OR}\), an increase in \(\alpha_{2}\) raises demand for remanufactured electric vehicles; conversely, when the condition reverses, demand for second-hand electric vehicles rises. In the retailer-led model, the direction hinges on comparing \(B + C_{OR}\) with \(C_{OS}\) for the remanufactured segment and on comparing \(B + C_{OS}\) with \(C_{OR}\) for the second-hand segment. The condition \(B + C_{OS} > C_{OR}\) means that the recovery cost of a used electric vehicle plus the marketing cost of a second-hand electric vehicle exceeds the cost of remanufacturing. In that case, remanufacturing is the cheaper option for the manufacturer, and raising \(\alpha_{2}\) shifts the equilibrium toward the remanufactured product.
I now compare the equilibrium prices. Let me denote the wholesale prices in Model M by \(W_{ON}^{M}\), etc., and in Model R by \(W_{ON}^{R}\), etc. Similarly, the retail prices are denoted accordingly. The centralised retail prices are \(P_{ON}^{MR}\), etc. Proposition 5 establishes the ranking of the new electric vehicle prices.
Proposition 5. For all admissible parameter values, the following inequalities hold:
\[
W_{ON}^{M*} > W_{ON}^{R*}, \quad
P_{ON}^{M*} < P_{ON}^{R*} < P_{ON}^{MR*}.
\]
When the manufacturer leads the chain, the wholesale price of a new electric vehicle is higher than when the retailer leads. The manufacturer, as the first mover, extracts a larger share of the total channel margin through a higher wholesale price. But this high wholesale price induces the retailer to respond with a relatively modest retail price, as the retailer cannot push the retail price too far above the wholesale price without destroying demand. In the retailer-led model, the retailer has the first-mover advantage and therefore chooses a retail price that is higher than in the manufacturer-led model, even though the wholesale price is lower. The centralised system prices the new electric vehicle highest, because the integrated chain eliminates double marginalisation and sets the price at the level that maximises the chain’s total profit over the whole product line. Although a centralised chain normally charges lower prices than a decentralised chain for a single product, the presence of quality-differentiated substitutes changes the ranking: the centralised chain charges a higher retail price for the top-quality electric vehicle product but lower prices for the lower-quality ones, because it can fine-tune the differentiation strategy to maximise total profit. In other words, the integrated chain prices the new electric vehicle as a premium product that anchors the product line.
Proposition 6 considers the remanufactured electric vehicle price ranking:
\[
P_{OR}^{M*} < P_{OR}^{R*} < P_{OR}^{MR*}.
\]
For the wholesale price of the remanufactured electric vehicle, the comparison is conditional. When \(\varepsilon_{1} < \alpha_{2}\), one obtains \(W_{OR}^{M*} < W_{OR}^{R*}\); when instead \(\varepsilon_{1} > \alpha_{2}\), one obtains \(W_{OR}^{M*} > W_{OR}^{R*}\). The threshold \(\varepsilon_{1}\) is defined in terms of the cost and valuation parameters in the composite expression above. If \(\varepsilon_{1} < \alpha_{2}\), implying that the valuation ratio \(\alpha_{2}\) is sufficiently large, the remanufactured electric vehicle is positioned closer to the new electric vehicle; the retailer, as the Stackelberg leader, has greater scope to negotiate a lower wholesale price for the remanufactured product, because demand for it is buoyant.
Similarly, Proposition 7 addresses the second-hand electric vehicle. For the wholesale price of a second-hand electric vehicle, when \(\varepsilon_{2} < \alpha_{2}\), one obtains \(W_{OS}^{M*} < W_{OS}^{R*}\), whereas when \(\varepsilon_{2} > \alpha_{2}\), one obtains \(W_{OS}^{M*} > W_{OS}^{R*}\). For the retail price of a second-hand electric vehicle, when \(\alpha_{2} < \varepsilon_{3}\), one obtains \(P_{OS}^{M*} < P_{OS}^{R*}\), and when \(\alpha_{2} > \varepsilon_{3}\), one obtains \(P_{OS}^{M*} > P_{OS}^{R*}\). These conditional comparisons show that the ranking of the second-hand electric vehicle price across channel structures is not fixed: it depends on how large consumers’ willingness-to-pay gap is relative to thresholds that involve the recovery cost \(B\), the production costs, and the coefficient \(\alpha_{1}\).
The propositions above demonstrate that the distribution of bargaining power in the electric vehicle remanufacturing channel interacts nontrivially with consumer psychology. A manufacturer-led chain produces lower retail prices for new electric vehicles than a retailer-led chain, but higher wholesale prices. A retailer-led chain results in lower wholesale prices for all products, because the retailer, as the leader, pre-commits to a lower margin, squeezing the manufacturer’s pricing power. In the presence of three vertically differentiated electric vehicle products, the standard wisdom that decentralisation always raises prices turns out to be incomplete: the retail price of the new electric vehicle is actually highest under centralised decision-making.
7. Two-Part Tariff Coordination Contract
The comparison between the centralised and decentralised models reveals that the total profit of the decentralised supply chain is always lower than that of the integrated chain when the manufacturer is the Stackelberg leader. This efficiency loss stems from double marginalisation, which manifests not only in one product in isolation but also across the three product variants. Since the manufacturer and the retailer maximise their own profits independently in the decentralised game, neither internalises the externality that its pricing imposes on the other member. The result is a price vector that distorts demand away from the first-best allocation. To align the incentives of both parties and achieve the first-best outcome, I design a two-part tariff contract.
The contract works as follows. The manufacturer commits to selling each of the three products to the retailer at a wholesale price equal to its marginal cost. That is, the manufacturer sets
\[
W_{ON}^{MT} = C_{ON},\quad
W_{OR}^{MT} = C_{OR},\quad
W_{OS}^{MT} = C_{OS}.
\]
Under these wholesale prices, the retailer’s margin exactly equals the contribution margin earned by the integrated chain. The retailer therefore faces the same incentive structure as an integrated monopolist and will choose the centralised retail prices. I verify this in Proposition 8.
Proposition 8. Under the two-part tariff contract, the retailer’s optimal retail prices coincide with the centralised prices:
\[
P_{ON}^{MT*} = P_{ON}^{MR*}, \quad
P_{OR}^{MT*} = P_{OR}^{MR*}, \quad
P_{OS}^{MT*} = P_{OS}^{MR*}.
\]
The manufacturer sells at marginal-cost wholesale prices and therefore earns zero variable profit from product sales. To compensate the manufacturer for the revenue loss and to induce participation, the retailer pays a fixed lump-sum fee \(\beta\) to the manufacturer. At the end of the sales period, the retailer who has earned positive profits under the centralised price vector transfers this fixed amount to the manufacturer.
The range of feasible lump-sum fees is determined by the participation constraints of both supply chain members. For the manufacturer to be willing to enter the contract, its post-contract profit \(\pi_{M}^{MT}\) must be at least as high as its pre-contract profit under the uncoordinated manufacturer-led equilibrium, \(\pi_{M}^{M*}\). Since the manufacturer earns only the lump-sum fee \(\beta\), the participation constraint is:
\[
\pi_{M}^{MT} = \beta \geq \pi_{M}^{M*}.
\]
For the retailer to participate, its post-contract profit, equal to the total centralised profit minus the lump-sum fee, must be at least its pre-contract profit under the manufacturer-led equilibrium, \(\pi_{R}^{M*}\):
\[
\pi_{R}^{MT} = \pi_{I}^{MR*} – \beta \geq \pi_{R}^{M*}.
\]
Combining these two inequalities, the contract is feasible whenever the centralised profit exceeds the sum of the decentralised profits, which is true by the definition of the first-best solution. The lump-sum fee can take any value in the interval
\[
\beta \in [\pi_{M}^{M*},\ \pi_{I}^{MR*} – \pi_{R}^{M*}].
\]
Within this interval, the two-part tariff contract achieves the first-best total profit while leaving both members at least as well off as before. The exact position of \(\beta\) within the interval determines the division of the coordination surplus. In the manufacturer-led Stackelberg setting, the manufacturer has substantial bargaining power and may be able to negotiate a \(\beta\) that lies at the upper end of the interval, allowing it to capture the majority of the efficiency gain. More generally, the distribution of the surplus is a matter of ex-ante negotiation between the two parties.
The post-contract profits are as follows. The retailer’s profit under the coordination contract is
\[
\pi_{R}^{MT} = \frac{\begin{aligned}
&2\alpha_{1}(-1 + C_{ON} – C_{OR} + \alpha_{1}) -(1+\alpha_{2})^{2}(-1 + C_{ON})(-1+\alpha_{2}) – 2W_{ON}(-1+\alpha_{2}) + \alpha_{2} – 2\alpha_{1}\alpha_{2} + \alpha_{1}\alpha_{2}^{2} \\
&- (-2(-1+\alpha_{1})(C_{OR} + C_{OS} + \alpha_{1} + B(-1+\alpha_{2}) – C_{OR}\alpha_{2} – C_{OS}\alpha_{2}) \\
&+ 2(1 + C_{ON} – C_{OR} – \alpha_{1})(-1+\alpha_{2})(\alpha_{1} – \alpha_{1}\alpha_{2}) \\
&\times (C_{OR} + 2W_{OR}(-1+\alpha_{2}) – C_{OR}\alpha_{2} + \alpha_{1}(1+\alpha_{2} – \alpha_{2}^{2})) \\
&+ 2(1-\alpha_{1})(2 – 2\alpha_{2})(W_{OS} + \frac{1}{2}(-B + C_{OS} – \alpha_{1}\alpha_{2})) \\
&\times (C_{OR}(-1+\alpha_{2}) + (-1-\alpha_{2}+\alpha_{2}^{2})(C_{OS}+\alpha_{1} – C_{OS}\alpha_{2} – \alpha_{1}\alpha_{2} + \alpha_{1}\alpha_{2}^{2}) + B(1 – 2\alpha_{2}^{2} + \alpha_{2}^{3}))
\end{aligned}}{4},
\]
while the manufacturer’s post-contract profit is simply
\[
\pi_{M}^{MT} = \beta.
\]
The total post-contract chain profit satisfies:
\[
\pi_{I}^{MT} = \pi_{M}^{MT} + \pi_{R}^{MT} = \pi_{I}^{MR*}.
\]
The two-part tariff contract therefore fully restores the first-best total profit for the electric vehicle remanufacturing supply chain. The contract is easy to implement in practice because it requires only a constant wholesale price equal to the manufacturer’s marginal cost plus a fixed payment. In the electric vehicle industry, where the manufacturer often supplies a differentiated line of new, remanufactured and second-hand vehicles to the same retailer, a menu of marginal-cost wholesale prices combined with a franchise fee is a standard and administratively feasible coordination instrument.
8. Numerical Simulation and Discussion
To illustrate the analytical results and to investigate the economic intuitions more concretely, I conduct extensive numerical simulations. The baseline parameter values are chosen in accordance with the empirical cost structure of the electric vehicle remanufacturing sector. The production cost of a new electric vehicle is \(C_{ON} = 0.8\); the cost of remanufacturing an electric vehicle is \(C_{OR} = 0.6\); the cost of marketing a second-hand electric vehicle is \(C_{OS} = 0.3\); the recovery cost paid by the manufacturer to obtain a used electric vehicle is \(B = 0.2\); and the valuation coefficient \(\alpha_{2}\) is set to 0.8. These values are chosen purely for numerical illustration and are broadly consistent with the idea that remanufacturing an electric vehicle is significantly cheaper than manufacturing a new one, that a second-hand electric vehicle is cheaper to process, and that consumers apply a substantial discount to second-hand electric vehicles.
8.1 The effect of \(\alpha_{1}\) on the profit of each supply chain member
I first investigate how a change in \(\alpha_{1}\), the relative willingness to pay for a remanufactured electric vehicle versus a new electric vehicle, affects the profits of the manufacturer, the retailer, and the total supply chain in the two decentralised models. The coefficient \(\alpha_{1}\) is allowed to vary over the interval \((0,1)\). The numerical results reveal a non-monotone and nonlinear impact.
When \(\alpha_{1}\) is at a relatively low value, consumers perceive a large quality gap between a new electric vehicle and a remanufactured electric vehicle. The demand for the remanufactured electric vehicle is generated from a narrow segment of consumers located just below the valuation boundary, but the second-hand electric vehicle segment is correspondingly larger. In this range, the manufacturer’s profit under Model M is relatively high, because the manufacturer sells a substantial volume of new electric vehicles at a high price premium and is not subject to strong cannibalisation from the remanufactured electric vehicle channel. As \(\alpha_{1}\) rises, the remanufactured electric vehicle becomes more attractive. Demand for remanufactured electric vehicles expands, but this expansion comes partly at the expense of new electric vehicle sales. When \(\alpha_{1}\) approaches a critical threshold, the substitution effect from the second-hand electric vehicle channel also strengthens. The profit of the manufacturer initially declines because the high-margin new electric vehicle business is being eroded by the lower-margin remanufactured business. Yet once \(\alpha_{1}\) passes a sufficiently high level, consumers perceive remanufactured electric vehicles as nearly equivalent to new ones, and the manufacturer can charge a price for the remanufactured electric vehicle that is close to the new electric vehicle price without losing volume. At that point the manufacturer’s profit rises again as the high valuation for remanufactured electric vehicles allows the manufacturer to increase the wholesale price of the remanufactured product substantially. Through simulation I find that this non-monotonic pattern occurs in both the manufacturer-led and the retailer-led models, although the exact threshold values differ.
The retailer’s profit follows a similar non-monotonic pattern. Because the retailer is responsible for the final pricing in the demand-sensitive stage, its profit is closely tied to the volume and margin structure of the three product categories. At low \(\alpha_{1}\), the retailer earns a stable profit from new and second-hand electric vehicles. As \(\alpha_{1}\) increases initially, the retailer faces intensified substitution and must adjust the retail price of new and remanufactured electric vehicles carefully, which squeezes the margin. But beyond the critical threshold, the retailer benefits from selling a large volume of remanufactured electric vehicles at prices close to new electric vehicles, which boosts its sales revenue and profitability. The total supply chain profit is likewise U-shaped in \(\alpha_{1}\), confirming the complex substitution pattern that the analytical model predicts.
These findings carry an important managerial implication for electric vehicle remanufacturing practice. If consumers do not yet trust the quality and residual value of remanufactured electric vehicles, the manufacturer should invest in quality certification and transparent information disclosure. For example, a manufacturer of electric vehicles could allow an independent third party to certify the state of health of the remanufactured battery pack and display the test results on the vehicle’s charging app, so that consumers can verify the performance of the remanufactured electric vehicle before purchase. If \(\alpha_{1}\) has risen to a high level, on the other hand, the manufacturer should strategically shift its product mix toward remanufactured electric vehicles, because this segment provides an additional high-margin revenue stream that can coexist with the new electric vehicle range without excessive cannibalisation.
8.2 The effect of \(\alpha_{2}\) on profit
I now vary \(\alpha_{2}\), the relative willingness to pay for a second-hand electric vehicle versus a remanufactured electric vehicle, while holding \(\alpha_{1}\) at a fixed value. The simulation indicates that when \(\alpha_{2}\) is small, consumers regard second-hand electric vehicles as distinctly inferior to remanufactured electric vehicles. The demand for the second-hand product is confined to a narrow pocket of low-valuation consumers, whereas the demand for the remanufactured and new electric vehicle products is larger. The supply chain earns its profit mainly from the upper two product tiers. As \(\alpha_{2}\) increases, second-hand electric vehicles become more acceptable, and the demand boundary shifts. The numerical result shows that the supply chain total profit rises in \(\alpha_{2}\) over a certain interval, then falls, before rising again once \(\alpha_{2}\) is sufficiently high. This erratic U-shaped or wave-like pattern is consistent with the complex way in which the equilibrium prices of the three products respond to \(\alpha_{2}\).
Further numerical analysis reveals a striking regularity: when the valuation differential coefficients lie in the interior of the unit interval, the market demand for each electric vehicle product in the two decentralised models may coincide even though the corresponding prices differ. This confirms that the equilibrium demand structure is not necessarily affected by the identity of the Stackelberg leader in the electric vehicle remanufacturing chain, as long as the willingness-to-pay coefficients remain within the specified bounds. However, at certain critical thresholds of the valuation parameters, the demand pattern changes discontinuously, giving rise to the possibility of a structural break in the equilibrium.
8.3 Comparison of centralised and decentralised profits
Next I compute the total supply chain profit in the centralised model, in the manufacturer-led model, and in the retailer-led model under the baseline parameter configuration. The total profit in the centralised model consistently exceeds that of both decentralised models, as expected. In the decentralised models, the retailer-led model yields a higher level of supply chain profit than the manufacturer-led model over most of the admissible parameter space. This is because the retailer, as the leader, prices all three electric vehicle products in a way that keeps demand closer to the centralised first-best. Since the retailer is better positioned to observe and respond to consumer preferences for electric vehicles, the equilibrium under retailer leadership is less distorted than that under manufacturer leadership. The inference is that when an electric vehicle supply chain cannot be integrated, delegating the pricing initiative to the retailer who is closest to the consumer market may be a second-best mechanism that mitigates the efficiency loss of double marginalisation.
For the baseline parameter set, I compute the numerical profit difference between the centralised and each decentralised outcome. The efficiency loss varies with the valuation coefficients and is largest when the products are neither too close nor too distant substitutes. In those intermediate regions, the retailer has the greatest discretion to distort prices, so the decentralised outcome deviates most from the first-best. The two-part tariff contract, by contrast, fully closes this gap. Under the contract, the wholesale prices are equal to marginal costs, the retailer follows the centralised price vector, and the fixed fee redistributes the surplus. The numerical simulation confirms that there always exists a non-empty interval of feasible fees \(\beta\), showing that the contract can always achieve mutual agreement between the electric vehicle manufacturer and the retailer.
From an operational standpoint, the two-part tariff contract enables the electric vehicle manufacturer to recover its fixed investment in the remanufacturing line while transferring the pricing power to the retailer at the point of sale. In the electric vehicle industry, where both the upstream technology and downstream service are complicated by product heterogeneity and consumer uncertainty, aligning the incentives across the channel is of particular value.
9. Summary, Managerial Implications and Concluding Remarks
This paper has investigated the pricing and coordination decisions in an electric vehicle remanufacturing supply chain. I have developed an analytical framework in which consumers exhibit heterogeneous willingness to pay across three vertically differentiated electric vehicle products: brand-new electric vehicles, remanufactured electric vehicles, and second-hand electric vehicles. The supply chain may be governed by a centralised planner, by a manufacturer-led Stackelberg game, or by a retailer-led Stackelberg game. In each setting I derived the equilibrium prices and profits, analysed the comparative statics with respect to the willingness-to-pay differential coefficients, and compared the outcomes across governance structures. I have also proposed a two-part tariff coordination contract that restores the first-best supply chain profit.
The most important findings can be summarised as follows. First, within a particular range of the consumer willingness-to-pay coefficients, the equilibrium demand for each electric vehicle product is unaffected by whether the manufacturer or the retailer acts as the Stackelberg leader. This result points to a potentially robust structural property of the differentiated product market: the allocation of consumers across product variants is determined by the valuation ratios and not by the bargaining power configuration, although the same cannot be said for prices and profits.
Second, the effect of the willingness-to-pay coefficients on equilibrium prices is subtle. In the centralised model, the retail price of a new electric vehicle is increasing in \(\alpha_{1}\) and \(\alpha_{2}\). If consumers have a high willingness to pay for new electric vehicles relative to the lower product tiers, the chain prices the top product more aggressively. A higher \(\alpha_{2}\), meaning that second-hand electric vehicles are perceived as less inferior, reduces the need to price the new electric vehicle at an extreme premium, which moderates the new product’s price. In the decentralised models, the ranking of prices across the product line changes with the identity of the leader. The manufacturer-led model generates a lower retail price for new electric vehicles than the retailer-led model, whereas the wholesale price of every product is higher in the manufacturer-led model.
Third, the centralised decision-making benchmark demonstrates that coordination can significantly increase the total profit of an electric vehicle remanufacturing supply chain. The key obstacle in the decentralised chain is double marginalisation, which is exacerbated when the manufacturer and the retailer have misaligned incentives with respect to the full product line. The two-part tariff contract aligns the retailer’s pricing behaviour with the integrated optimum and provides a feasible mechanism for both parties to share the increased profit. In practice, adopting such a contract may prove fruitful not only for profit maximisation but also for establishing transparent wholesale pricing that reflects true costs, hence enhancing the trust between the electric vehicle manufacturer and the retailer.
Finally, the numerical simulation demonstrates that the relationship between profits and the willingness-to-pay coefficients exhibits U-shaped, inverse-U-shaped, and even wave-like patterns. This suggests that the electric vehicle remanufacturing supply chain operates in multiple regimes separated by critical thresholds. When \(\alpha_{1}\) is low, the manufacturer’s best strategy is to focus on high-end new electric vehicles and to position remanufactured electric vehicles as a strictly cheaper alternative. When \(\alpha_{1}\) moves to an intermediate level, the manufacturer should proactively manage the trade-off between the new and remanufactured segments by adjusting the wholesale price of the remanufactured electric vehicle and, at the same time, enhance the perceived value of its new electric vehicle battery through extended warranty or battery health guarantees. When \(\alpha_{1}\) is high, the manufacturer should scale up its remanufacturing capacity and expand the retail presence of remanufactured electric vehicles, as they now command a price close to that of new electric vehicles and are no longer a threat to the brand’s premium image.
From the perspective of the retailer, being the channel leader often produces a higher supply chain profit. If the actual electric vehicle distribution network grants the retailer the power to set the terms of trade, the retailer should recognise that its pricing strategy must account not only for the cost structure of the manufacturer but also for the full differentiation structure of the product line. Retailers who are Stackelberg leaders can achieve better channel performance by pricing new electric vehicles as premium flagship products, remanufactured electric vehicles as value-oriented alternatives, and second-hand electric vehicles as affordable entry options.
The findings of this article should be read with several limitations in mind. First, I have considered a single-period setting with an exogenous set of products. Many electric vehicle supply chains involve multiple periods, product innovation, and learning curves that reduce remanufacturing costs over time. Extending the model to a dynamic setting would allow me to study how consumer willingness to pay evolves as more remanufactured electric vehicles enter the market and as information about their performance accumulates. Second, I have assumed that the retailer is the only sales channel. In reality, electric vehicle manufacturers increasingly use direct-to-consumer online channels, dual-channel structures, and agencies. A dual-channel model in which the manufacturer and the retailer compete for consumers would introduce additional strategic interactions. Third, my model treats \(\alpha_{1}\) and \(\alpha_{2}\) as exogenous parameters. Yet these parameters are themselves influenced by marketing activities, certification, government policy, and media coverage. An endogenous treatment of information and trust formation would provide richer insights for electric vehicle remanufacturing managers and policymakers.
Notwithstanding these limitations, the messages of this paper have direct relevance to the sustainable development of the electric vehicle industry. Consumer acceptance is the central battleground for remanufactured electric vehicles. My analysis formalises the intuition that a modest increase in consumers’ willingness to pay for remanufactured electric vehicles has much more than a linear effect on supply chain performance. At critical thresholds, the entire equilibrium shifts. Techniques that enhance credibility—such as standardised battery diagnostics, block-chain-based tracing of vehicle service history, transparent reporting of remaining battery capacity, and certified warranty programmes for remanufactured electric vehicle batteries—can therefore generate discontinuous jumps in profitability. Rather than giving away price concessions indiscriminately, manufacturers of remanufactured electric vehicles should invest in lowering the perceived quality gap between a remanufactured and a new electric vehicle. Similarly, retailers should do more than passively pass through wholesale prices to consumers: they should educate consumers, provide test-drive programmes, and design service bundles that address the residual risk that consumers associate with remanufactured electric vehicle powertrains and battery packs.
The two-part tariff contract suggested in this paper is a simple yet effective mechanism for the electric vehicle supply chain to overcome the adverse effect of double marginalisation. In an environment where both the manufacturer and the retailer are investing in the growth of the electric vehicle market, the contract offers them a way to focus on their respective strengths. The manufacturer can concentrate on the engineering, production, and recovery of used electric vehicle components, while the retailer can invest in marketing, consumer finance, and after-sales service, safe in the knowledge that its variable margin structure is aligned with the overall profitability of the electric vehicle product line. The managerially relevant insight is that the contract should be paired with a credible information exchange mechanism. In particular, the retailer should commit to delivering point-of-sale data on consumer valuation of remanufactured electric vehicles to the manufacturer, enabling the manufacturer to calibrate remanufacturing quality standards and the level of recovery effort.
In conclusion, this study offers a comprehensive analytical treatment of pricing and coordination in a three-tier electric vehicle remanufacturing supply chain characterised by heterogeneous consumer valuations. By comparing centralised decision-making, manufacturer-led and retailer-led Stackelberg games, and a coordinating contract, I have developed a set of insights that can guide supply chain participants in making better pricing, investment, and coordination decisions. As the electric vehicle industry continues to mature and the stock of vehicles eligible for recovery grows, remanufacturing will become an increasingly important source of value creation and environmental improvement. Understanding how to structure the supply chain and how to respond to the nuanced behaviour of consumers will be essential for capturing that value. Extending the analysis to richer multi-period, multi-channel and policy-intervention settings is a promising avenue for future research. I hope that my findings will motivate further exploration along these lines and provide a basis for actionable managerial interventions in the electric vehicle remanufacturing ecosystem.