Adoption of Buy Now, Pay Later (BNPL): A Time Inconsistency Perspective

Abstract

Buy Now, Pay Later (BNPL) is a rapidly growing fintech tool, which is particularly popular among young consumers, with the potential to support more sustainable retail consumption. While firms increasingly adopt BNPL, its impact on time-inconsistent consumers remains underexplored. We address this gap using two game-theoretic models: one with traditional payment and one with BNPL. In both models, time-inconsistent consumers decide whether to purchase and then whether to return a product after learning about their fitness. In the traditional model, greater time inconsistency reduces optimal price, demand, and profit. In contrast, these outcomes remain unaffected by time inconsistency under BNPL. Comparing the equilibrium results of the two models, we find that the firm always benefits more from offering BNPL than traditional payment when consumers are time-inconsistent. By deferring payment, BNPL increases consumers’ present willingness to buy, enabling firms to charge higher prices without reducing demand, and thereby achieve higher profits. Although BNPL can improve firm revenue and overall welfare, it may reduce consumer surplus by encouraging over-consumption. We also consider the presence of the BNPL provider and default of payments to make our results more robust. These findings highlight the need for caution and potential regulation to protect consumers with self-control problems.

1. Introduction

1.1. Background

‘Buy Now, Pay Later’ (BNPL) is a short-term installment loan allowing consumers to defer payments, often without interest [1]. through providers such as Klarna, Affirm, and AfterPay. BNPL offers a more sustainable and safer method for spreading out payments, which is particularly attractive to consumers who wish to make purchases through 0% card-linked installments [2]. The BNPL market grew significantly in recent years, reaching approximately USD 30.38 billion in 2023, and is expected to grow to USD 37.19 billion in 2024, eventually reaching USD 167.58 by 2032 [3]. Young consumers represent the main audience for BNPL services. Between 2019 and 2021, the use of BNPL among Gen Z increased sixfold, while Millennial usage increased more than double [4]. BNPL has a similar mechanism to credit cards, but with a relatively lower interest rate and greater ease of use, making it popular with young people. Additionally, BNPL has less stringent application requirements than credit cards, making it much more accessible to consumers.

Primarily utilized in e-commerce [5], BNPL is increasingly adopted by retailers and e-commerce platforms, either through partnerships with BNPL providers or by developing their own BNPL options. For example, Amazon and Apple collaborate with Affirm, while Taobao introduces BNPL as the default payment method. The mechanism of BNPL is straightforward: consumers purchase items using their credit, and the payment is deferred. After they receive the product and learn about their fitness, if they are satisfied, they keep the product, and the payment is deducted later. Otherwise, they can return the product, and the payment will be canceled. BNPL has different payment structures, such as an initial payment plus installments over the next few weeks. In this paper, we mainly focus on the form that simply delays a single payment, for example, Klarna’s ‘Pay later in 30 days’ and Taobao’s BNPL option, which allows consumers to buy first and pay for the product without interest within 30 and 7 days of receiving it, respectively.

BNPL is reshaping consumer spending behavior. Consumers who adopt BNPL are more likely to make purchases, with purchase rates rising from 17% to 26% [6]. This shift in behavior has raised concerns about the risk of consumers accumulating unaffordable debt or experiencing financial stress. As the use of BNPL continues to grow, regulators have taken notice. In May 2024, the Consumer Financial Protection Bureau reclassified certain BNPL products as credit cards under Regulation Z and expanded similar protections, such as the right to refunds and dispute resolution [7]. While intended to protect consumers, this regulatory move has also prompted calls for deeper investigation of the impact of BNPL on broader financial health.

1.2. Motivation

Despite the convenience offered by BNPL, it seems to be hurting consumers due to over-consumption [8], which can, in turn, harm financial health [9]. Such over-consumption may result from consumers’ time-inconsistent behavior. This behavior was first observed in experiments that compare individuals’ choices between a smaller, more immediate reward and a larger, later one [10,11]. While people may initially prefer the larger, later reward, they often reverse their choice as the smaller reward becomes more immediate. This shift reflects a strong preference for immediate gratification over future reward and suggests that traditional exponential discounting fails to capture the behavior of individuals with time-inconsistent preferences [12,13,14]. To better capture this tendency, the quasi-hyperbolic discounting model has been proposed [15], in which future value or payment perceived in the current is discounted, while those that occur in the current are not discounted. The detailed definition of this model is in Section 3. The quasi-hyperbolic discounting model is now widely adopted in the literature [16,17,18,19,20,21].

1.3. Research Gap and Research Questions

While prior research has examined whether the firm and the consumers benefit from the adoption of BNPL [22,23], we identify a research gap from the time inconsistency perspective. Consumers’ time-inconsistent behavior can give rise to self-control problems [17,20,24,25,26], which may influence a firm’s choice of payment method and ultimately affect both its profitability and consumer welfare. This study aims to investigate whether BNPL exacerbates these self-control issues among time-inconsistent consumers and whether firms capitalize on such behavior for profit. Additionally, it seeks to evaluate the broader implications of BNPL on consumer surplus and social well-being.

Based on the above discussion, we propose the following research questions: 1. Considering time-inconsistent consumers, which payment method for the firm is more profitable, immediate payment or BNPL? 2. How does consumers’ time inconsistency affect the price and demand under different payment mechanisms? 3. Does BNPL benefit consumers and society?

To address these questions, we study and compare the pricing decisions of a monopoly firm in two game-theoretic models over two periods, the basic model, in which consumers pay immediately, and the BNPL model, in which consumers pay after they receive the product. Consumers are time-inconsistent and we use a quasi-hyperbolic discount function to describe their time inconsistency. For each model, we derive the equilibrium results and then we compare the price, demand, profit, consumer surplus, and social welfare for these two models. We also consider the presence of the BNPL provider in the market and the default of payments to make our results more robust. Our results provide managerial insights for policymakers and firms.

1.4. Findings and Contributions

This paper’s main findings are as follows: First, we demonstrate that when consumers exhibit time inconsistency, it is always more profitable for the firm to adopt BNPL than immediate payment. Due to their time-inconsistent behaviors, consumers underestimate the actual price that they need to pay in the future when using BNPL. The firm could, therefore, increase its price without losing demand and increasing its profit.

Second, we show that in the basic model, the price and demand decrease as consumers become more time-inconsistent, while in the BNPL model, consumers’ time inconsistency does not affect them. Traditionally, consumption is later than payment [27]; hence, time-inconsistent consumers weigh the price more than product valuation. When consumers are more time-inconsistent, they are less willing to pay for the product, and the firm has to lower the price. Despite the decreasing price, the demand decreases. However, when using BNPL, since both payment and consumption are in the future, the negative effects of consumers’ time-inconsistent behaviors are canceled out. So in the BNPL model, the price, the demand, and the firm’s profit are not affected by the time inconsistency parameter.

Third, we examine the broader impacts of BNPL on consumer surplus and social welfare by showing that BNPL can harm consumers by exploiting their time inconsistency and that BNPL benefits society more than immediate payment. When using BNPL, consumers do not know their real preference for the price in the future. Consumers may pay for a product that they could not afford with credit, so consumer surplus could even be negative in the BNPL model. For social welfare, BNPL benefits society more than immediate payment, mainly because the firm’s profit remarkably increases.

Fourth, we find that if the firm cooperates with the BNPL provider to offer BNPL services to consumers, the BNPL provider always sets the commission fee so that the firm’s profit under the BNPL model is the same as under the basic model. When there exists a default of payments, our key findings remain valid when consumers exhibit strong time inconsistency. When consumers pay late, they need to pay extra interests, which decrease consumers’ willingness to pay and hence decreases price and demand when consumers’ time-inconsistency is weak.

Theoretically, we contribute to both the time inconsistency and BNPL literature by examining BNPL through the lens of time-inconsistent consumer behavior, offering a novel perspective on the interplay between payment design and behavioral economics. We also contribute to consumer return literature by exploring refund policies when adopting BNPL. Practically, the findings offer managerial insights for firms, consumers, and policymakers. We suggest that firms adopt BNPL when consumers show time inconsistency. Although BNPL is beneficial for firms, it may come at the expense of consumer surplus, thus, we warn consumers to be cautious while using BNPL. Also, policymakers should set default rules, cooling-off periods, or other types of light-touch regulation to promote more welfare-enhancing consumer decisions.

The rest of the paper is organized as follows: In Section 2, we review the related literature. In Section 3, we introduce the model setup, the game sequence, and the notations used in this paper. In Section 4, we analyze the basic model and the BNPL model, respectively, and then compare the two models. In Section 5, we extend our models to consider the presence of the BNPL provider and default of payments. In Section 6, we discuss our findings, explore the practical implications for policymakers and firms, and consider the limitations and future research directions. In Section 7, we conclude the paper with insights and suggestions. All proofs are provided in Appendices Appendix A and Appendix B.

2. Literature Review

This paper relates to three literature streams: consumers’ time-inconsistent behavior, retailers’ choice of payment mechanisms, and consumer return policies.

We begin by reviewing the literature on time inconsistency, with particular attention to whether time-inconsistent behavior has been examined in the context of BNPL. Time inconsistency has been widely studied in operations and marketing areas, including topics like addiction [28], optimal goals [25], usage of innovative product features [29,30], package size design [19], multi-period payment for employees [26], digital content consumption [31], and contract design [32]. This paper relates to the stream of literature that examines the impact of consumers’ time-inconsistent behavior on pricing strategies. Plambeck and Wang [33] investigate the impact on service pricing brought about by self-control problems caused by consumers’ time-inconsistent behavior, and they found that consumers’ lack of self-control induces firms to lower their usage fees, regardless of whether the firms are trying to maximize profits or social welfare. Jain [30] examines the case of time-inconsistent consumers who need to learn additional features of a product and finds that firms can charge higher prices as the consumer’s self-control problem decreases (reduction in time-inconsistency) and as the proportion of sophisticated consumers increases. Jain and Chen [34] study the effect of sunk cost bias on pricing strategies when consumers are time inconsistent, and they show that firms can increase their prices to increase experienced quality. Li and Jiang [21] study the impact of consumers’ time-inconsistent behavior on pricing strategies in a competitive market with two vertically differentiated firms. They show that firms should adopt dynamic pricing when consumers exhibit strong time inconsistency. Kuang and Jiang [35] examine how a monopoly retailer sets deposits and arrears as well as the return policies. They show that as consumers become less time-inconsistent, the firm arranges the deposit and the arrear to induce no, some, and all deposit payers. Although prior literature has examined the impact of consumers’ time-inconsistent behavior on pricing strategies, it has not been explored in the context of BNPL. However, BNPL fundamentally alters the timing of payments, which interacts directly with time-inconsistent preferences and can lead to distinct pricing dynamics compared to traditional payment settings. To address this gap, we compare two payment methods—immediate payment and BNPL—when consumers exhibit time-inconsistent behavior.

We next review the literature on retailers’ payment method choices, with a focus on BNPL models, and examine whether consumer time inconsistency is considered in this research stream. Previous literature has studied the effect of different payment mechanisms on consumers’ purchasing behaviors and firms’ profitability. Early literature compares cash and credit cards, which is related to our setting. Consumers who use credit cards are more likely to make additional purchases than those who use cash [36,37]. This may be due to credit cards increasing consumers’ willingness to pay [38] by reducing the pain of paying [37] and separating the connection between consumption and payment (decoupling) [39]. The above literature is based on experiments, yet some literature builds theoretical models to compare different payment mechanisms. They discuss this topic from different perspectives, for example, the cost of funds and the merchant’s margin [40], credit card interchange fees [41], and missed sales [42]. Recent literature discusses whether to introduce the BNPL option. Niu et al. [22] examine the choice of an agent selling platform and a reselling platform regarding whether to provide installment services. They find that when the incremental demand is moderate, there exists an asymmetric equilibrium where only the reselling platform offers installment. Duan et al. [23] also considers the decision of an agency platform and a wholesale platform regarding whether to adopt e-commerce consumer credit services (e-CCS), but only with one common supplier. They show that when the demand benefit of e-CCS is high, the wholesale platform always adopts it, but the agency platform only uses it when the risk of bad debt is low. Desai and Jindal [43] study the firms’ decisions about offering BNPL in a vertically differentiated market. They find that one firm may benefit from the other firm, offering BNPL even if it does not provide BNPL itself due to competitive spillovers. Existing literature examines BNPL adoption through perspectives such as incremental demand, the demand benefits of e-CCS, and competitive spillovers. However, it overlooks the role of time-inconsistent consumer behavior. We address this gap by incorporating time inconsistency into consumer decision-making models, highlighting its importance in shaping retailers’ payment mechanism choices.

Although the above literature studies the adoption of BNPL, the refund policies when using BNPL are seldom considered. We examine the literature stream examining monopoly retailers’ return policies. Full refund for returns can be used as a signal for product quality [44]. Early research identifies when the firm should offer a full refund compared to no refund [45,46]. Then, more research identifies the valuation of partial refund and compares the no, partial, and full refund policies. Xie and Gerstner [47] show that the partial refund is designed to capture the additional surplus generated when a customer discovers a new opportunity and cancels the service. Su [48] compares full refund policies and partial refund policies when consumers’ valuations are uncertain. He points out that the partial refund policy is generally optimal. In contrast with Su [48], Hsiao and Chen [49] show that the use of the no refund policy by retailers can improve supply chain efficiency. Other literature adds other perspectives like purchase deferrals [50], omnichannel [51], product customization [52], consumer search [53], and consumer social learning [54]. Existing literature has not yet addressed how product returns should be modeled in the context of BNPL. This study contributes to that stream by analyzing refund policies when consumers pay using BNPL. Specifically, if the product is returned, the payment is canceled and the credits of consumers are returned. BNPL enables consumers to enjoy the product without immediate payment or waiting for refunds, serving as ‘product inspection’ [55].

3. Model Setup

We consider a single firm selling its product to its consumers in the market. The firm allows consumers to either pay immediately or use BNPL. Here, we assume that the firm provides the BNPL service itself, and in extension, we consider the case where the firm cooperates with a BNPL provider to provide BNPL services. We do not consider the case where the firm allows both payment mechanisms because we show that, in this case, all consumers choose BNPL (see the Appendix A for proof). We first analyze the situation when consumers pay immediately as the basic model and then examine the situation when consumers use BNPL.

We analyze a selling season spanning two periods. Before the selling season begins, the firm chooses between immediate payment and BNPL. The total market size is normalized to one. At the beginning of period one, in both models, the firm sets its price, and then consumers decide whether to pay immediately or use BNPL. Consumers receive the product at the end of period one. Following prior literature [16,21,25,29,30,35,48], we separate the consumption and payment by putting the consumption after the payment. Because Su [27] points out that consumption is always later than the payment, even if consumption and payment happen in the same period, consumers weigh payment more heavily. The production cost of the firm is c, and the salvage value of the returned product is s. We assume that $s<c$ following prior literature [45]. We follow prior literature [21,27,35] to assume the firm applies a discount factor $\alpha =1$, indicating a focus on long-term payoffs.

Consumers are unaware of its fit probability until they receive the product. We assume that the $\rho$ ($0<\rho <1$) proportion of consumers has a good fit and $1-\rho$ has a bad fit. In the case of a good fit, consumers’ valuation is $\theta v$, otherwise, it is 0. Consumers’ taste $\theta$ is heterogeneous and uniformly distributed from 0 to 1, and v is the consumers’ product valuation. Consumers can return the product if it does not fit their needs or if the valuation from returning the product is higher than the product valuation, and we assume that the firm offers a full refund because, in practice, most firms do so.

In the basic model, if a product is returned, consumers receive a refund at the end of period two. In the BNPL model, if consumers are satisfied with the product, a price is deducted at the end of period two. Otherwise, the payment is canceled if the product is returned. Here, we only consider the case where consumers all pay on time. In extension, we relax this assumption to consider default of payments with interests.

We assume that consumers are time-inconsistent in our model. We use a quasi-hyperbolic discount function [15] commonly used in the literature [16,17,18,19,20,21] to describe consumers’ time inconsistency. The time inconsistency of consumers refers to the phenomenon in which future value or price in time t ($t>0$) perceived by consumers at present is discounted by $f\left(t\right)=\beta {\delta }^t$. If $t=0$, the value or price perceived by consumers is not discounted, i.e., $f\left(t\right)=1$. Here, $\beta$ ($0<\beta <1$) is the present-bias parameter, and the smaller $\beta$ is, the more time-inconsistent consumers are; $\delta$ ($0<\delta <1$) is the exponential discount parameter. We assume all consumers are naive, which means currently they do not know their real preferences or valuations in the future. Note that consumers are still rational while naive, i.e., they still intend to maximize their benefits under their perceptions.

Time-inconsistent consumers tend to underestimate the price or valuation that they will receive in the future. For example, when consumers decide whether to pay using BNPL—since the payment is deferred to the end of period two—consumers will underestimate the price, and the firm can take this opportunity to increase its price accordingly. However, in the basic model, if consumers are unsatisfied with the product, the refund is received at the end of period two. When consumers make payment decisions in the basic model, they will underestimate the refund and become less willing to pay. In the BNPL model, since consumers do not need to pay if they are unsatisfied with the product, they do not need to wait for a refund in the future. This may increase the demand for the BNPL model.

The game sequence of the two models is as follows and shown in Figure 1: In the basic model, at the beginning of period one (Time 1), the firm sets the price $p_b$, and consumers decide whether to pay immediately. At the end of period one (Time 2), consumers receive the product and learn about their fitness. Then, they decide whether to return the product. If returned, they will receive a full refund, $p_b$, at the end of period two (Time 3).

In the BNPL model, at Time 1, the firm announces the price p, and consumers then decide whether to purchase. Different from the prior model, here consumers do not need to pay at this moment, instead, they use their line of credit to buy. At Time 2, consumers receive the product and learn about their fitness. Then, they decide whether to return the product. If they choose to keep the product, they will be deducted a price of p at Time 3. Otherwise, the payment is canceled and their credits are returned.

Table 1. Notations.

Notation	Description
$\alpha$	The firm’s discount factor
$\beta$	The present-bias parameter
$\gamma$	The proportion of the consumers who pay on time
$\delta$	The exponential discount parameter
$\theta$	The consumer’s taste
$\pi$	The firm’s profit
$\rho$	The proportion of the consumers with good fit
b	The subscript denoting the basic model
c	Production cost of the firm
f	Commission fee of the BNPL provider
i	Interest for late payment
p	Retail price
s	The salvage value of the returned product
t	Time
$u_t$	Consumer’s utility at time t
v	Consumer’s valuation
D	The demand
$CS$	Consumer surplus
$SW$	Social welfare

summarizes the notations used in this paper. Throughout this paper, we use subscript b to denote the basic model.

4. Analysis

In this section, we first analyze the basic model, in which consumers pay immediately. Then, we examine the BNPL model. Finally, we compare the two models and generate some interesting insights.

4.1. The Basic Model

We analyze consumers’ utility function and demand by backward induction, which solves problems by reasoning backward from the end of a process to determine optimal actions at each earlier stage. At Time 2, a $\rho$ proportion of consumers has a good fit for the product and decides whether to return it. Their utility functions are $u_{2b}=max\{\theta v,p_b\beta \delta \}$, where $\theta v$ is the utility from keeping the product, and $p_b\beta \delta$ is the utility from returning the product. Since the refund is received at Time 3, the utility from returning the product at Time 2 is discounted by $\beta \delta$. So consumers with a good fit for the product keep the product if their tastes $\theta \ge {\theta }_{2b}={\displaystyle \frac{p_b\beta \delta }{v}}$. A $1-\rho$ proportion of consumers has a bad fit for the product, and their utility functions are $u_{2b}=max\{0,p_b\beta \delta \}=p_b\beta \delta$. Since the utility from keeping the product is now 0, all consumers who find the product a poor fit choose to return it.

The expected utility of consumers at Time 1 is

$$u_{1b}=\rho max\{\theta v\beta \delta ,p_b\beta {\delta }^2\}+(1-\rho )p_b\beta {\delta }^2-p_b$$

(1)

where $\rho max\{\theta v\beta \delta ,p_b\beta {\delta }^2\}$ is the expected utility of consumers with a good fit, and $(1-\rho )p_b\beta {\delta }^2$ is the expected utility of consumers with a bad fit. Note that at Time 1, the utility in Time 2 is discounted by $\beta \delta$ and the refund is discounted by $\beta {\delta }^2$. Consumers purchase the product if $u_{1b}\ge 0$, that is if $\theta \ge {\theta }_{1b}={\displaystyle \frac{\beta {\delta }^2{p}_b\rho -p_b\beta {\delta }^2+p_b}{\beta \delta \rho v}}$, which decreases as $\beta$ increases. When $\beta$ decreases, i.e., when consumers are more time inconsistent, the demand decreases.

It can be verified that ${\theta }_{1b}>{\theta }_{2b}$, so all consumers who already purchase the product and with a good fit will keep the product. The demand is thus $D_b=1-{\theta }_{1b}$. The firm maximizes its profit by setting its price $p_b$:

$$\underset{p_b}{max}{\pi }_b=(p_b-c)D_b+(s-p_b)(1-\rho )D_b$$

(2)

Solving the first-order equation to zero, we derive the optimal price $p_b^{*}$. Substituting $p_b^{*}$ into the functions of demand and profit, we can obtain the equilibrium result, in which the firm obtains the highest profit and hence has no incentive to deviate. The equilibrium result of the two models is provided in

Table 2. The equilibrium results of the two models.

Model	The Basic Model	The BNPL Model
$p_b/p$	${\displaystyle \frac{\beta c{\delta }^2(\rho -1)+c+(\rho -1)s\left(\beta {\delta }^2(\rho -1)+1\right)+\beta \delta {\rho }^{2}v}{2\left(\beta {\delta }^2(\rho -1)\rho +\rho \right)}}$	${\displaystyle \frac{c\delta +\delta \rho s-\delta s+\rho v}{2\delta \rho }}$
$D_b/D$	${\displaystyle \frac{c\left(-\beta {\delta }^2(\rho -1)-1\right)-(\rho -1)s\left(\beta {\delta }^2(\rho -1)+1\right)+\beta \delta {\rho }^{2}v}{2\beta \delta {\rho }^{2}v}}$	${\displaystyle \frac{-c\delta +s(\delta -\delta \rho )+\rho v}{2\rho v}}$
${\pi }_b/\pi$	${\displaystyle \frac{{\left(\beta c{\delta }^2(\rho -1)+c+(\rho -1)s\left(\beta {\delta }^2(\rho -1)+1\right)-\beta \delta {\rho }^{2}v\right)}^2}{4\beta \delta {\rho }^{2}v\left(\beta {\delta }^2(\rho -1)+1\right)}}$	${\displaystyle \frac{{(c\delta +\delta (\rho -1)s-\rho v)}^2}{4\delta \rho v}}$
$C{S}_b/CS$	$\rho v\left({\displaystyle \frac{1}{2}}-{\displaystyle \frac{A_1}{8{\beta }^2{\delta }^2{\rho }^4{v}^2}}\right)+{\displaystyle \frac{A_2}{4\beta \delta {\rho }^{2}v\left(\beta {\delta }^2(\rho -1)+1\right)}}$	${\displaystyle \frac{(\rho v-\delta (c+(\rho -1)s\left)\right)\left(c\right(\delta -2)\delta +(\delta -2\left)\delta \right(\rho -1)s+(3\delta -2\left)\rho v\right)}{8\delta \rho v}}$
$S{W}_b/SW$	${\displaystyle \frac{A_3}{8{\beta }^2{\delta }^2{\rho }^{2}v\left(\beta {\delta }^2(\rho -1)\rho +\rho \right)}}$	${\displaystyle \frac{A_4}{8\rho v}}$

The expressions of $A_1$, $A_2$, $A_3$, and $A_4$ are in Appendix A.

. The detailed analysis is in Appendix A. Consumer surplus is defined as:

$$C{S}_b={\int }_{{\theta }_{1b}}^1(-p_b+\rho \theta v+(1-\rho )p_b)d\theta$$

(3)

Here, we follow the prior literature to assume consumers’ time inconsistency does not work in the long run but affects the price and the demand in the function of consumer surplus [30]. Social welfare is the sum of the firm’s profit and consumer surplus, i.e., $S{W}_b=C{S}_b+{\pi }_b$.

We assume that $c<c_b$ and $s<s_b$ (deduced from $s<c<c_b$) to ensure the non-negativity of the demand. The expressions of $c_b$ and $s_b$ are in Appendix A. We analyze the effect of the present bias parameter $\beta$ in the below proposition and illustrate the result in Figure 2.

Proposition 1.

In the basic model, when β increases, the optimal price increases, the demand increases, the profit increases, consumer surplus first increases and then decreases, and social welfare increases.

Proposition 1 and Figure 2 show that when consumers are less time-inconsistent, ($\beta$ increases), and both the price and the demand are higher, making the firm more profitable. This is because at Time 1, if $\beta$ increases, consumers’ perception of future valuation is higher, and they are more willing to pay. Thus, the firm can raise its price. In this case, despite the firm’s price increase, the demand also rises, hence increasing the firm’s profit.

When $\beta$ increases, the growing demand increases consumer surplus, while at the same time, the increasing price decreases consumer surplus. When $\beta$ is small, the effect of growing demand dominates that of price, consumer surplus increases; when $\beta$ is large, the effect of price dominates that of demand and consumer surplus decreases. When $\beta$ increases, social welfare increases because when $\beta$ is small, both consumer surplus and the profit increase; when $\beta$ is large, the increase in the firm’s profit is larger than the decrease in consumer surplus.

4.2. The BNPL Model

In the BNPL model, we also use backward induction to obtain the demand from consumers’ utilities. At Time 2, a $\rho$ proportion of consumers has a good fit for the product and decides whether to return it. Their utility functions are $u_2=max\{\theta v-p\beta \delta ,0\}$, where $\theta v-p\beta \delta$ is the utility of keeping the product and 0 is the utility of returning the product. Therefore, consumers who have a good fit for the product keep the product if their tastes $\theta \ge {\theta }_2={\displaystyle \frac{p\beta \delta }{v}}$. A $1-\rho$ proportion of consumers has a bad fit for the product. Their utility functions are $u_2=max\{-p\beta \delta ,0\}=0$, where $-p\beta \delta$ is the utility of keeping the product and 0 is the utility of returning the product. Thus, all consumers who find the product a poor fit choose to return it.

The expected utility of consumers at Time 1 is

$$u_1=\rho max\{\theta v\beta \delta -p\beta {\delta }^2,0\}$$

(4)

The expected utility of consumers is the expected utility of consumers with a good fit because the expected utility of consumers with a bad fit is zero. Consumers purchase the product if $u_1\ge 0$. That is, if $\theta \ge {\theta }_1={\displaystyle \frac{p\delta }{v}}$.

We can find that ${\theta }_1>{\theta }_2$, so all consumers who already purchase the product and with a good fit keep the product. The demand is thus $D=1-{\theta }_1$. The result also shows that the BNPL model does not induce consumers’ self-control problems, which refers to the behaviors of consumers changing their minds regarding whether to keep the product. Instead, all consumers with a good fit keep the product. The firm maximizes its profit by setting its price p:

$$\underset{p}{max}\pi =(-c)D+p\rho D+s(1-\rho )D$$

(5)

Solving the first-order equation to zero, we derive the optimal price $p^{*}$. Substituting $p^{*}$ into the functions of demand and profit, we can obtain the equilibrium result provided in Table 2. The detailed analysis is in Appendix A. Consumer surplus is defined as:

$$CS={\int }_{{\theta }_1}^1(\rho \theta v-\rho p)d\theta$$

(6)

Social welfare is the sum of the firm’s profit and consumer surplus, i.e., $SW=CS+\pi$. We assume that $c<c_1$ and $s<s_1$ (deduced from $s<c<c_1$) to ensure the non-negativity of the demand. The expressions of $c_1$ and $s_1$ are in Appendix A. We analyze the effect of the present bias parameter $\beta$ in the below proposition.

Proposition 2.

When consumers adopt BNPL, the price, the demand, the profit, consumer surplus, and social welfare are not affected by the present bias parameter β.

Interestingly, the present bias parameter $\beta$ does not work in this model. This is because, at Time 1, both valuations and prices are received or deducted in the future, so $\beta$ is canceled out. This finding suggests that BNPL can eliminate the negative effects of consumers’ time-inconsistent behaviors shown in Proposition 1. Recall that in the basic model, when consumers are more time-inconsistent, consumers weigh future valuations lower, the demand decreases, and the firm has to lower its price to attract consumers, making it less profitable. The firm can adopt the BNPL model to avoid these problems by postponing the payments.

Lemma 1.

When $c<c_1$ and $s<s_1$, consumer surplus can be negative in the BNPL model, specifically, consumer surplus in the BNPL is positive only when $\delta >{\displaystyle \frac{2}{3}}$, $c<c_2$, and $\rho >{\rho }_1$, where the expressions of $c_2$ and ${\rho }_1$ are in Appendix A.

Consumer surplus in the BNPL model is positive only when the exponential discount parameter $\delta$ is large, the proportion of the consumers with a good fit $\rho$ is large, and the production cost c is small. The optimal price $p^{*}$ decreases when $\delta$ increases and c decreases. This is because when $\delta$ increases, consumers’ perception of the price increases in Time 1, so the firm has to lower its price. Moreover, with a lower production cost, the firm could lower its price while remaining profitable. Thus, when $\delta$ is large and c is small, consumer surplus increases due to the decreasing price. Also, it is intuitive that consumer surplus increases as the proportion of consumers with a good fit grows.

Lemma 1 shows that consumer surplus in the BNPL model can be negative, while consumer surplus in the basic model is always positive. This is because when consumers use BNPL, in Time 1, they underestimate the price they need to pay in the future ($p\beta {\delta }^2$), while in Time 3, the actual price they need to pay is p. Some consumers with low valuations purchase the product due to their time inconsistency. In other words, BNPL may induce consumers’ overconsumption problems. From this perspective, BNPL may hurt consumers. Therefore, consumers should be wary when using BNPL.

4.3. Comparison

In this subsection, we compare the prices, demands, profits, consumer surplus, and social welfare of the two models. Before comparison, we assume that $c<min\{c_b,c_1\}=c_b$ and $s<min\{s_b,s_1\}=s_b$ to ensure the non-negativity of the demands in both models.

Proposition 3.

Comparing the prices and demands, we have the following results:

(i) 

The price is larger in the BNPL model than in the basic model, i.e., $p>p_b$.

(ii) 

The demand is larger in the BNPL model than in the basic model, i.e., $D>D_b$.

From Proposition 3, we observe that although prices are higher in the BNPL model compared to the basic model, consumer demand is also greater. This phenomenon arises because BNPL delays payment, leading consumers to underestimate their future financial obligations. As a result, firms can strategically raise prices without significantly reducing demand. Moreover, due to consumers’ time-inconsistent preferences, they place greater weight on immediate benefits—such as acquiring a product without upfront payment—while discounting the financial burden of future payments. This behavioral bias further amplifies demand under BNPL. Consequently, firms that adopt BNPL can not only set higher prices but also attract more consumers.

Proposition 4.

When consumers exhibit time inconsistency, the firm can earn more profit by asking the consumers to use BNPL instead of paying immediately, i.e., $\pi >{\pi }_b$.

When consumers exhibit time-inconsistent behavior, characterized by a present-bias parameter $0<\beta <1$, the BNPL model consistently generates higher profits compared to the basic model. This is because time-inconsistent consumers tend to prioritize immediate gratification while underestimating future financial obligations. By delaying payment, BNPL exploits this cognitive bias, making purchases feel more affordable in the present, thereby increasing demand. As a result, firms can charge higher prices while still attracting more consumers, ultimately increasing overall revenue.

A real-world example of this strategy is Taobao, which has integrated BNPL as the default payment option. By making BNPL the standard choice at checkout, Taobao effectively nudges consumers toward deferred payment, increasing their likelihood of completing purchases and driving higher overall sales.

Corollary 1.

When $\beta =\delta =1$, the firm’s profit is the same in the basic model and the BNPL model.

When $\beta =\delta =1$, consumers exhibit neither time-inconsistent preferences nor impatience. In this case, they fully account for future costs and valuations without discounting them. As a result, the timing of payment—whether at Time 1 in the basic model or at Time 3 in the BNPL model—becomes irrelevant to their purchasing decisions. Consumers perceive both models as equivalent, treating payments made at different times as having the same value in their decision-making process.

For the firm, this implies that BNPL does not provide any strategic advantage when consumers are fully patient and time-consistent. Since demand remains unchanged regardless of payment timing, BNPL does not lead to higher prices or increased consumer willingness to buy. Therefore, the profitability of BNPL hinges entirely on the presence of time-inconsistent consumers who tend to underestimate future costs and prioritize immediate consumption. In other words, BNPL is only advantageous when firms can leverage consumers’ behavioral biases to drive higher demand and revenue.

Proposition 5.

Comparing consumer surplus and social welfare under these two models, we have the following:

(i) 

Consumer surplus is higher in the BNPL model than in the basic model ($C{S}_b<CS$) when $\beta <{\beta }_1$.

(ii) 

Social welfare is higher in the BNPL model than in the basic model, i.e., $SW>S{W}_b$.

The expression of ${\beta }_1$ is in Appendix A. Consumer surplus in the basic model ($C{S}_b$) first increases and then decreases when $\beta$ increases (Proposition 1), and consumer surplus in the BNPL model is unaffected by $\beta$ (Proposition 2). When $\beta$ is small ($\beta <{\beta }_1$), consumers exhibit strong time inconsistency, leading to lower willingness to pay, reduced demand, and consequently lower consumer surplus in the basic model. In this case, the BNPL model provides greater consumer surplus since it allows deferred payment, mitigating the effects of time inconsistency. However, as $\beta$ increases—indicating weaker present bias—consumer surplus in the basic model rises, eventually surpassing that of the BNPL model. This suggests that BNPL is particularly beneficial for consumers with high time inconsistency but offers less advantage as consumers become more time-consistent.

From a social welfare perspective, the BNPL model consistently yields higher overall welfare than the basic model, regardless of the value of $\beta$. When $\beta <{\beta }_1$, both consumer surplus and firm profit are higher under the BNPL model, leading to greater overall social welfare. This occurs because BNPL mitigates the impact of strong present bias, increasing both consumer participation and firm revenue. When $\beta >{\beta }_1$, the firm extracts more profit under BNPL at the expense of consumer surplus. However, the gain in firm profit outweighs the reduction in consumer surplus, resulting in a net increase in social welfare. Therefore, from a welfare perspective, adopting the BNPL payment method is beneficial, as it enhances total economic efficiency by generating a higher combined value for both consumers and firms.

5. Extension

In this section, we consider several extensions to include more practical assumptions and to make our results more robust.

5.1. Cooperation Between Retailer and BNPL Provider

In Section 3, we assume that the retailer can choose whether to offer the BNPL option by itself. However, in reality, retailers often cooperate with BNPL providers to offer BNPL service by paying heavy commission fees. These fees are generally in the range of 1% to 5% of the value of transactions [23], which is far greater than typical payment processing charges (typically 1–3%).

To take the commission fee paid by the retailer to the BNPL provider into consideration, we build a game-theoretic model based on the BNPL model. We consider a market with one retailer and one BNPL provider. The BNPL first announces f as the proportion of sales that it charges from the retailer, and the retailer decides whether to accept it to use the BNPL service. The other settings are the same as the BNPL model. We normalize the traditional payment processing fees in the basic model to zero, so the basic model remains the same. We compare the equilibrium result of the new model with the basic model and summarize the result in the following proposition.

Proposition 6.

When the retailer cooperates with the BNPL provider to offer the BNPL option, comparing with the equilibrium result in the basic model, we have the following results:

(i) 

The price is larger in this model than in the basic model, i.e., $p^{\prime }>p_b$.

(ii) 

The demand, the profit, and social welfare are the same in this model as in the basic model, i.e., $D^{\prime }=D_b$, ${\pi }^{\prime }={\pi }_b$, $S{W}^{\prime }=S{W}_b$.

(iii) 

Consumer surplus is smaller in this model than in the basic model, i.e., $C{S}^{\prime }<C{S}_b$.

When the BNPL provider sets the commission fee, it wants the commission fee to be as large as possible. However, the larger the commission fee, the smaller the retailer’s profit. The bottom line for the retailer to cooperate with the BNPL provider is that the profit with cooperation is at least greater than or equal to the profit without cooperation; otherwise, the retailer rejects the contract, and the BNPL receives zero profit. So, in equilibrium, the BNPL provider sets the commission fee so that the retailer is indifferent between accepting and rejecting the contract, i.e., ${\pi }^{\prime }={\pi }_b$. In this condition, the demand and social welfare are also the same as in the basic model. The price in this model is still larger than that in the basic model, so with the same demand, the consumer surplus in this model is smaller than that in the basic model.

From the above analysis, we can conclude that to ensure the retailer accepts the contract, the commission fee set by the BNPL provider should not be too high. The retailer needs to compare its profit with that in the basic model to clarify its bottom line. Consumers may consider not using the BNPL service if it is provided by the BNPL provider rather than by the retailer itself due to the decrease in consumer surplus.

5.2. Default of Payments

In Section 3, we assume that all consumers pay on time. However, there may exist consumers who are in default of payment. The default rate of BNPL services is around 2% [56]. To capture these consumer segments, we assume that only $\gamma$ proportion of consumers pay on time, while $1-\gamma$ proportion of consumers pay at the end of period three and need to pay $p(1+i)$, where $0<i<1$ is the interest for late payment. The other settings are the same as the BNPL model. We compare the equilibrium results of this model to the basic model and obtain the result in the below proposition.

Proposition 7.

When there is a default of payments, our key findings remain valid when β is small, i.e., the price, the demand, the profit, consumer surplus, and social welfare under this new model are higher than those under the basic model when consumers exhibit strong time inconsistency.

It is interesting to find that with default on payments, the benefits of the BNPL model remain only when consumers exhibit strong time inconsistency. Recall that without defaults, as long as consumers exhibit time-inconsistent preferences, it is always more profitable for the firm to adopt BNPL. This is because the possibility of paying interest reduces the perceived attractiveness of BNPL from the consumer’s perspective. As a result, consumers are less likely to buy under BNPL unless the price is reduced to offset the expected interest burden. Only if time inconsistency is strong will consumers still heavily discount future payments, and even with the possibility of charging interest, the behavioral bias will continue to drive high demand and keep firms profitable under the BNPL.

We can conclude that for the firm if there exists a default of payment, it is always beneficial to adopt BNPL when consumers exhibit strong time inconsistency; however, when consumers’ time inconsistency becomes weak, it is better to use traditional payment. The profitability of BNPL depends not only on whether consumers are time-inconsistent but also on the strength of that inconsistency and how it interacts with perceived future payment burdens.

6. Discussion

In this section, we discuss our findings in more detail, explore the practical implications for policymakers and firms, consider the limitations of the study, and suggest directions for future research.

6.1. Managerial Implications and Policy Recommendations

Our key finding is that BNPL enables firms to charge higher prices without reducing demand when serving time-inconsistent consumers, resulting in increased profitability. This effect is grounded in behavioral economics: present-biased consumers tend to underestimate future costs, making them more willing to commit to purchases when payment is delayed. Empirical evidence supports this theoretical insight: Kumar et al. [57] use a hyperbolic discounting framework to show that BNPL users spend 6.42% more than non-users. They also estimate that brands could recover approximately USD 290,000 in lost revenue annually through BNPL adoption. Our paper complements this empirical work by offering a theoretical foundation that explains why such profit gains occur. Based on our findings, we recommend that monopoly firms adopt BNPL when facing time-inconsistent consumers.

At the same time, firms must be mindful of potential risks. While BNPL may boost demand and revenue, it can also encourage over-consumption, especially among consumers with limited self-control. The Consumer Financial Protection Bureau (CFPB) has raised concerns about credit overextension, such as loan stacking and sustained use of deferred payment options [7]. Therefore, consumers should be encouraged to better understand their own behavioral tendencies, especially their susceptibility to time-inconsistent decision-making, and to use BNPL with caution.

To promote more welfare-enhancing consumer decisions in the use of BNPL services, policymakers should consider setting policies and regulations. These may include the introduction of default rules that do not present BNPL as the default payment option at checkout, thereby requiring consumers to make a more deliberate choice before opting into deferred payment. In addition, cooling-off periods could allow consumers to cancel purchases made using BNPL within a short window, giving them time to reflect on the financial commitment and potentially avoid impulsive or regrettable spending. Other forms of light-touch regulation, such as clear and concise disclosures of repayment terms, automated reminders about upcoming payments, and improved digital choice architecture, can further support consumers by increasing transparency and reducing decision-making errors. Collectively, these interventions aim to mitigate risks associated with over-borrowing or misinformed choices, while preserving consumer autonomy and access to credit.

6.2. Limitations and Future Directions

Several behavioral concepts—such as the pain of paying [39], mental accounting [58], and the distinction between acquisition utility and transaction utility [58]—may also influence consumer behavior in the context of BNPL. For instance, deferring payment can reduce the immediate psychological discomfort of spending, shift perceived budget constraints to the future, and enhance the perceived attractiveness of a purchase. These effects may further amplify consumers’ tendency to over-consume under BNPL. In this paper, we focus primarily on time-inconsistent preferences, modeled through quasi-hyperbolic discounting, to capture intertemporal self-control issues. Future research could extend our framework by integrating these additional behavioral factors to offer a more comprehensive understanding of consumer decision-making under BNPL.

In this paper, we assume that all consumers are naive. However, consumers may differ in their awareness of their time-inconsistent preferences—that is, they can be either naive or sophisticated. Sophisticated consumers anticipate future self-control problems and may select payment methods accordingly. Gao and Guo [32] examine how the firm can design contracts to screen consumers based on their belief heterogeneity. Building on this, future research could investigate how firms might screen consumers using different payment mechanisms.

We assume the firm implements a full-refund policy; however, in reality, a firm might also adopt a no-refund or partial-refund policy. From prior literature, we know that when consumers’ degree of time inconsistency decreases, a firm might transfer its refund policy from a full-refund policy to a partial-refund policy [35]. Therefore, when consumers are less time-inconsistent, further research may need to compare the profit under the partial-refund policy with the profit under the BNPL model.

While our analysis is based on a monopoly setting to isolate the effects of time-inconsistent consumer behavior on BNPL adoption, this abstraction may limit the generality of our findings to a competitive market. In practice, many BNPL decisions occur in competitive marketplaces—such as Amazon or Taobao—where firms face price-sensitive consumers and low switching costs. In such contexts, the strategic advantage of offering BNPL may be diminished if all firms adopt it, potentially resulting in a prisoner’s dilemma where no firm gains additional profit despite incurring adoption costs. Moreover, competition may lead to more complex equilibria, including payment mechanism differentiation, where firms target heterogeneous consumer segments with distinct payment methods. Future research could extend this work by modeling competitive environments and examining how competition affects BNPL pricing strategies, consumer surplus, and welfare outcomes. Exploring these competitive dynamics would provide a more comprehensive understanding of BNPL adoption in real-world markets.

7. Conclusions

This study examines how a monopoly firm should design payment mechanisms when facing time-inconsistent consumers, focusing on the strategic implications of adopting BNPL. We compare immediate payment and BNPL in terms of profitability, pricing, demand, and their impacts on consumer and social welfare. We build two game-theoretic models in which the firm, before a two-period selling season, chooses between immediate payment and BNPL. Consumers then decide whether to purchase the product based on the firm’s announced price and whether to return it after learning about their fitness. Time-inconsistent consumers, like procrastinators who change plans when faced with immediate costs, tend to favor short-term gratification, affecting their purchase decisions. We derive equilibrium outcomes under both payment mechanisms and highlight how BNPL can influence firm strategy, consumer surplus, and overall welfare.

First, by adopting BNPL, the firm can avoid the negative effects of consumers’ time-inconsistent behaviors. Traditionally, the firm requires the consumers to pay immediately, while the product is consumed later. Time-inconsistent consumers, who tend to underestimate their future valuation of the product, are less willing to purchase, forcing the firm to lower its price to stimulate demand. However, with BNPL, both payment and consumption occur in the future, effectively neutralizing the impact of time inconsistency. Since consumers no longer discount the product’s value relative to its cost, the firm can maintain higher prices without reducing demand. This strategic shift enables the firm to avoid revenue loss due to present bias and the tendency to focus too much on immediate costs and benefits. These findings suggest that firms can strategically use BNPL to boost demand and sustain higher prices, effectively leveraging consumer present bias. Firms should balance the profitability gains with long-term customer well-being when designing payment mechanisms.

Second, the firm should adopt BNPL when consumers exhibit time inconsistency. Time-inconsistent consumers tend to underestimate future costs, making them less sensitive to price increases when payment is deferred. By leveraging this behavioral bias, firms can raise prices without significantly reducing demand, ultimately boosting profitability. This strategy has been applied in practice. For example, online platforms like Taobao have made BNPL the default payment method to boost sales and increase transaction conversion rate and turnover through deferred payment. However, if consumers are fully time-consistent and patient, or if the firm cooperates with a BNPL provider to offer BNPL services, BNPL provides no advantage over immediate payment, making its adoption unnecessary. Also, if there exist consumers who do not pay on time, it is only beneficial for the firm to adopt BNPL when consumers exhibit strong time inconsistency.

Third, despite all these benefits, BNPL may reduce consumer surplus. When consumers exhibit strong time inconsistency, their surplus under immediate payment remains low, making BNPL a beneficial option. However, as consumers become less time-inconsistent, their surplus under immediate payment increases and eventually surpasses that of BNPL. In this case, BNPL primarily benefits the firm, as it allows for higher pricing at the expense of consumer surplus. Therefore, consumers should be wary when using BNPL, as it may not always benefit them.

Still, from a social welfare perspective, BNPL remains advantageous. When consumers are highly time-inconsistent, both consumer surplus and firm profit increase under BNPL. When consumers become more time-consistent, firms extract greater profits while consumer surplus declines. However, the overall gain in firm profit exceeds the reduction in consumer surplus, leading to a net increase in total social welfare.

This study highlights that BNPL can bring significant benefits to firms, including higher prices, increased demand, and greater profitability, particularly when serving time-inconsistent consumers. The substantial gains in the firm’s profit can also enhance social welfare. However, BNPL also carries risks: by deferring payment, it may encourage over-consumption and lead some consumers to make purchases they later regret, potentially harming their financial well-being. While firms can profit from this behavioral tendency, doing so irresponsibly may erode consumer trust, requiring regulatory interventions. As such, BNPL should be adopted with a balance of strategic benefit and consumer responsibility in mind.

This paper offers several key contributions:

• It studies the adoption of BNPL from the perspective of time inconsistency, contributing to the literature by studying the interplay between payment design and behavioral economics.
• It extends consumer return literature by modeling the refund policies when adopting BNPL.
• It shows that BNPL can raise firm profitability by reducing the negative effects of time inconsistency, while also identifying potential risks to consumer surplus through over-consumption.
• It provides guidance for firms, suggesting BNPL adoption when consumers exhibit time inconsistency, and for policymakers, recommending light-touch interventions to promote more balanced outcomes.

This study focuses on time-inconsistent preferences modeled through quasi-hyperbolic discounting. Future research could enrich this framework by incorporating other behavioral concepts, such as the pain of paying, mental accounting, and the distinction between acquisition and transaction utility, which may further shape consumer decisions under BNPL. Additionally, we assume that all consumers are naive, but in reality, consumers vary in their awareness of future self-control problems. Future studies could explore how firms screen between naive and sophisticated consumers using differentiated payment mechanisms. We also assume a full-refund policy under BNPL. Future work could examine the profitability of partial- or no-refund policies, especially when consumers are less time-inconsistent. Finally, our model assumes a monopoly setting. Extending the analysis to competitive markets could reveal new strategic dynamics, including payment mechanism differentiation and asymmetric equilibria.