Time-inconsistent Consumers Research Articles

Optimal Contracts for Time-Inconsistent Consumers with Heterogeneous Beliefs

In many markets (e.g., cell phones, video games), firms offer menus of contracts that include some tariffs charging per-use prices above marginal cost and others below marginal cost. We term this puzzling phenomenon as two-sided deviations from marginal cost pricing and present a potential explanation based on two well-recognized consumer characteristics. The first one is that consumers’ actual consumptions may depart systematically from their initial plans (i.e., time-inconsistent preferences). In addition, consumers can be either sophisticated or naive in their beliefs about their time inconsistency (i.e., heterogenous beliefs). We characterize properties of the optimal contracts for a firm to screen the time-inconsistent consumers with heterogeneous beliefs. We articulate the conditions under which the optimal menu may account for two-sided deviations from marginal cost pricing. We also show that, contrary to intuition, a higher degree of time inconsistency may reduce firm profit and increase social welfare. Meanwhile, reducing consumer naivete may harm the society. Moreover, we confirm that our main results are robust to the presence of time-consistent consumers. This paper was accepted by Dmitri Kuksov, marketing. Funding: This work was supported by the Hunan Provincial Natural Science Foundation of China [Grant 2022JJ40102]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.02653 .

Intertemporal price discrimination with time-inconsistent consumers

We consider the intertemporal price discrimination problem of a durable good monopolist facing a population of consumers who are time inconsistent. We show that price trajectories, profits and welfare are sensitive to consumers’ first- and second-order beliefs regarding their time preferences. Surprisingly, we find that sales and profits are largest when consumers are sophisticated, i.e., when consumers hold correct expectations on their own future choices. The monopolist is thus unable to take advantage of consumers’ naiveté, and could instead benefit from informing consumers about their true preferences and commitment problems, or otherwise communicate its beliefs about them.

A government policy with time-inconsistent consumers

This paper examines monetary and fiscal policies to prevent consumers' present bias by implementing a benchmark exponential discounting allocation in a hyperbolic discounting economy. We analyze classical money-in-the-utility-function models and establish that a monetary policy alone cannot curb behavioral mistakes. Instead, it needs to be combined with either a consumption tax or capital tax. If the government uses consumption (capital) tax, the monetary policy should be more expansionary (contractionary) compared to the benchmark exponential discounting economy. In the calibration, we confirm that a paternalistic policy intervention generates significant welfare gains based on both true (long-run) and choice (short-run) utility.

Buy-One-Get-One Promotions in a Two-Echelon Supply Chain

Buy-one-get-one (BOGO) promotions have become popular. With BOGO, the first unit is sold for the regular price, and the second unit is discounted. We analyze BOGO in manufacturer–retailer supply chains. We identify conditions under which BOGO outperforms price reduction (PR) and everyday low price (EDLP) policies. We find that, for some products, whether consumers stockpile or not, if BOGO and PR have the same market size, BOGO has a larger retailer profit and the same or larger manufacturer profit because BOGO induces more consumers to buy and consume two units. When consumers stockpile, the retailer sets prices to prevent such behavior, and the retailer’s share of supply chain profits is largest under BOGO, whereas consumer surplus with BOGO is smaller than PR. We also find that BOGO reduces double marginalization. When PR expands market size more than BOGO, BOGO’s effectiveness diminishes. When consumers stockpile without increasing consumption and/or production cost is high, EDLP is best. Our results are robust to multiperiod with single-promotion-period settings. A large number of regular-price periods following a promotion period increases stockpiling, which erodes the retailer’s profit and favors EDLP. If promotions are offered for consecutive periods, a larger number of promotion periods increases PR’s efficacy relative to BOGO. Time-inconsistent consumers increase stockpiling and make PR outperform BOGO. Heterogeneous consumers’ holding cost and marginal utility prevent retailers from perfectly discriminating among consumers who make profit-reducing choices. Compared with retailers’ BOGO, manufacturers’ BOGO increases double marginalization and decreases retailers’ and manufacturers’ profits and consumer surplus. This paper was accepted by Jayashankar Swaminathan, operations management. Funding: This work was partially supported by the National Science Foundation of China [Grants 71972026, 72101102]. Y. Li’s work was supported by the China Scholarship Council [Grant 201806070094]. Supplemental Material: The online companion and data are available at https://doi.org/10.1287/mnsc.2022.4638 .

Time Inconsistency and Product Design: A Strategic Analysis of Feature Creep

This paper examines how time-inconsistent consumers affect firms’ product design and pricing decisions.

Incentivizing self-control effort

We analyze the determinants of the incentives that a paternalistic social planner should provide to improve the behavior of time-inconsistent consumers. We focus on the specific case in which consumers can reduce their future consumption by exerting self-control effort in non-observable and non-contractible activities. For example, they can reduce their future healthcare costs by practicing physical exercise. Differently from the results obtained by the sin taxes theory, we find that incentives that address the under-exertion of effort by present-biased consumers are always socially costly even when consumers are homogeneous. Moreover, we show that incentives are first increasing and then decreasing in the level of time-inconsistency, due to the ineffectiveness of incentive policies. Incentives are also affected by the degree of naivety in a non-monotonic way.

Credit Card Competition and Naive Hyperbolic Consumers

I explain the credit card market’s observed systematic pricing patterns by examining time-inconsistent consumers. I find that time inconsistency steers the competition from long-term borrowing contingent prices to short-term noncontingent ones. This pattern occurs because the consumer in the contracting period underestimates the future charges, and therefore pays attention only to short-term price elements, such as annual fees. The consumer’s risk of default also plays a role in determining who gets which contract.

Smoking Cessation: A Model of Planned vs. Actual Behavior for Time-Inconsistent Consumers

We offer a simple model of intertemporal choice to characterize how planned versus actual behaviors evolve for time-inconsistent smokers. Our results suggest that smokers' participation and cessation decisions are governed by the interplay between three effects. The cessation effect leads smokers to advance their plans to quit smoking, whereas the procrastination effect leads them to consecutively revise their planned quitting age upwards. Consequently, the duration of smoking is effectively governed by which one of these two effects is dominant. Finally, for certain consumer segments, a threshold effect causes an “all or nothing” type of extreme smoking behavior based on certain critical values of present-biased preferences. Our results provide some preliminary evidence that both marketing efforts by tobacco firms and public policy initiatives can have a significant influence on smoking behavior. In particular, we find that reductions in the age at which individuals start smoking may not only vastly extend their duration of smoking, but also convert potential “never smokers” into lifetime smokers. Finally, we estimate a hazard model using survey data from over 800 smokers to provide evidence in support of our theoretical model.

Inter-temporal Price Discrimination with Time-inconsistent Consumers

This paper analyzes the inter-temporal price discrimination problem of a durable good monopolist facing time-inconsistent consumers. We look at both cases of sophisticated and naive time-inconsistent consumers, but the emphasis is on the naive case. When consumers are naive, we first need to confront the following question: how does the consumers' naivete about their preferences interact with their ability to predict future prices? We solve the game under two solution concepts. Under the first solution concept, which is similar in spirit to the SPNE, consumers have correct expectations about future prices. Under the second one, which relies on backwards induction, consumers' naive expectations concerning their future preferences lead them to have incorrect expectations about future prices. We show that under both solution concepts, as the degree of naivete rises, monopoly profits fall. The monopolist does not benefit from consumers' naivete and should instead educate naive consumers into sophisticated ones. Moreover, as the degree of naivete rises, both solution concepts predict that welfare falls for all consumers, except for the highest valuation ones, and prices approach marginal cost at a lower rate.

Credit Card Competition and Naive Hyperbolic Consumers

We show that naive hyperbolic consumers might be unresponsive to interest rates and credit limits of credit card offers by companies because the offers have a grace period and there is a one-period lag in using a new card. Consequently, we demonstrate that there might be no competition on the interest rate and credit limit, even if more than one firm is in the market and even if the consumer accepts only one card. We determine whether the credit card companies can exploit time-inconsistent consumers and gain positive expected profits. We show that in fact there are circumstances in which both zero and positive expected profits could be possible.

Efficiency and equilibrium when preferences are time-inconsistent

We consider an exchange economy with time-inconsistent consumers whose preferences are additively separable. If consumers have identical discount factors, then allocations that are Pareto efficient at the initial date are also renegotiation-proof. In an economy with a sequence of markets, competitive equilibria are Pareto efficient in this sense, and for generic endowments, only if preferences are locally homothetic.

Contract Design and Self-Control: Theory and Evidence

How do rational firms respond to consumer biases? In this paper we analyze the profit-maximizing contract design of firms if consumers have time-inconsistent preferences and are partially naive about it. We consider markets for two types of goods: goods with immediate costs and delayed benefits (investment goods) such as health club attendance, and goods with immediate benefits and delayed costs (leisure goods) such as credit card-financed consumption. We establish three features of the profit-maximizing contract design with partially naive time-inconsistent consumers. First, firms price investment goods below marginal cost. Second, firms price leisure goods above marginal cost. Third, for all types of goods firms introduce switching costs and charge back-loaded fees. The contractual design targets consumer misperception of future consumption and underestimation of the renewal probability. The predictions of the theory match the empirical contract design in the credit card, gambling, health club, life insurance, mail order, mobile phone, and vacation time-sharing industries. We also show that time inconsistency has adverse effects on consumer welfare only if consumers are naive.

Behavioral Decision-Making: An Application to the Setting of Magazine Subscription Prices

Using data from American magazines, we explore the relationship between subscription discounts and magazine characteristics. We focus in particular on those magazine features that might lead time-inconsistent consumers to wish to engage in commitment behavior. We find that for magazines whose payoff is in the future and/or that are meritorious for other reasons, subscription discounts are lower all else equal. This finding suggests that publishers may be able to set subscription prices in order to extract rents from consumers' willingness to tie their own hands in terms of their future reading.