Three-part Tariffs Research Articles

Public-Transportation Credits: The potential of three-part tariffs in public transportation

In December 2023, public-transportation providers in Switzerland introduced Public-Transportation Credits (PTCs). PTCs are credits (or “allowances”) that are greater in amount than their price and can be used to purchase any type of public-transportation tickets within a year. With the initial fixed payment, the subsequent use of the allowance and the eventual return to the standard fare, PTCs represent three-part tariff models. We explore the potential of PTCs to target particularly elastic segments of the demand curve, simultaneously allowing for increased consumption and higher revenue. To assess the revenue impact of the PTC empirically, we analyze a pilot study conducted by the Swiss public-transportation providers. In a randomized field experiment with 200,000 PTC invitees and 911 actual PTC buyers, we use the dispach of invitations as an instrumental variable. While observing substantial revenue increases, this result is insignificant due to the weak relationship between invitees and buyers. Therefore, we complement our analysis with a selection-on-observable approach, utilizing machine-learning techniques to match PTC buyers to customers in the control group. This way, we reveal a highly significant treatment effect, indicating a revenue enhancement of CHF179.7 per PTC (approximately USD200). Leveraging our comprehensive dataset and insights from a non-buyer survey, we predict a demand of around 200,000 units for the market-launch version of the PTC.

The Effects of Information Nudges on Consumer Usage of Digital Services under Three-Part Tariffs

ABSTRACT We develop a dynamic model to examine how information nudges influence digital services’ consumer usage behavior and welfare under a three-part tariff structure. We study two types of information nudging: nudging through full and nudging through partial information provision. In the former, information nudges are provided to inform consumers of their usage status at every decision point in a billing cycle. In contrast, in the latter, consumers are nudged at one or more decision points within a billing cycle but not throughout the billing cycle. Our model considers two dimensions of consumer heterogeneity: inattentiveness and preference. Furthermore, our model investigates an important but under-investigated design element of information nudges, namely, the timing of the information nudges. We find that (1) nudging through information provision influences inattentive consumers’ usage decisions and improves consumption efficiency, (2) consumers’ welfare gains from full information nudging depict an inverted-U shape contingent on consumers’ preference heterogeneity, and (3) the timing of nudging matters. Our findings provide managerial implications for the design of information nudging strategies and procedures. Finally, we empirically illustrate the analytical results in the context of consumers’ mobile data usage behavior.

In Pursuit of Sustainable Mobile Policy: A Study of Consumer Tariff Preferences under Uncertainty

Literature suggests that consumers expect disutility not only from payment uncertainties but also from reference uncertainties embedded in mobile plans. This paper develops a model of mobile plan choice incorporating both reference and payment uncertainties and uses this model to derive testable implications. The paper argues that consumer choice reflects those uncertainties more than could be justified by rational choice theory. Such patterns, the paper hypothesizes, would be more salient in the choice of data plan than voice plan because consumers tend to perceive data usage to be less controllable than voice usage, thus preferring the plan that reduces uncertainty. The paper tests the predictions with data from a laboratory study analyzing a series of choices between plans with different tariff structures—flat-rate, two-part, and three-part tariffs. As predicted, the results suggest that payment and reference uncertainties create significant disutility for consumers, especially when they perceive high uncertainty about their usage. Such understanding of consumer preference and underlying psychological biases is important in the sense that it provides an essential basis for the development of sustainable mobile policy.

The Effects of Information Nudges on Consumer Usage of Digital Services under Three-Part Tariffs

The Effects of Information Nudges on Consumer Usage of Digital Services under Three-Part Tariffs

Estimating the Demand for Service Bundles under Three-Part Tariffs

The practice of selling multiple products or services under nonlinear pricing has a long history in the business community. Consumers may face demand uncertainty when choosing a service plan, and preferences for multiple products or services may be inter-dependent. To examine a demand system with these features, we construct a two-stage discrete/continuous choice model for service bundle demand under three-part tariffs, allowing for interactive utility and preference correlations. Implementing a piecewise maximization approach to the consumer utility maximization problem, which is non-differentiable under three-part tariffs, we estimate the model via simulated method of moments. We then apply our model to data from a major wireless service provider in China. Finally, our counterfactual analysis simulates outcomes under three-part tariffs with interchangeable units. Compared to existing tariffs, the proposed ones contain fewer instruments without a significant loss of revenue. We also illustrate the implications of incorporating ex-post usage shocks in model estimates, elasticities and counterfactual outcomes.

On the Optimality of Three-Part Tariff Plans: When Does Free Allowance Matter?

Two- (2PTs) and three-part tariffs (3PTs) are widely used for selling goods, to compensate workers, and in procurement contracts. They are practical alternatives to complex nonlinear tariffs in on-demand services and technology industries and are more profitable than the restrictive per-unit and unlimited-use pricing. A 2PT imposes both a fixed (access) fee and a per-unit (usage) fee, and a 3PT generalizes it by bundling some free units (an allowance) into the fixed fee. Intuitively, bundling free allowance provides an additional lever to the firm, enabling it to charge differential marginal rates to improve profitability. However, designing a 3PT is a challenging problem, and the optimal solution is known only when the market has homogeneous consumers or two discrete segments. We advance theory about optimal 3PT design by developing a reformulation that simplifies the solution procedure for the general case and generates new theoretical and practical insights. Our analysis reveals, surprisingly, that when the market demand follows an increasing price elasticity (or, approximately, when consumer distribution follows an increasing hazard rate), the optimal 3PT outcomes are identical to optimal 2PT outcomes. This result generalizes to a menu of tariffs. By contrast, the free allowance in a 3PT may be truly impactful when market demand is multimodal or corresponds to distinct segments with sharp across-segment differences, or when consumers have certain tariff biases. Our results help explain how and when 3PT matters, and they can help managers make informed decisions about how to design and employ nonlinear pricing.

A characterization of implementability of decision rules via a menu of three-part tariffs

Posting three-part tariffs is a widespread phenomenon in the telecommunication industry. The paper characterizes the implementability of decision rules involving bunching by using a menu of three-part tariffs. I argue the superiority of three-part tariffs to two-part tariffs.

Three-Part Tariffs with Heterogeneous Users: Monopoly and Duopoly Cases

Although two-part tariffs are widely studied, only three papers consider three-part tariffs, which consist of an access fee in return for an allowance consumption level along with a unit “overage” price for consumption beyond the allowance. Moreover, none of these papers addresses some elementary and fundamental questions concerning the optimal features of the tariff in the presence of heterogeneous users: (1) How does the overage price (and thus marginal benefit for a high-demand user) compare to the marginal cost of the service? (2) How does marginal benefit compare to marginal cost for a low-demand user consuming at the allowance level? (3) How large is the access fee relative to benefits from the service? The purpose of this paper is to answer these questions by using a simple model with two types of consumers and a constant marginal cost. The analysis is carried out for a monopoly provider and then for the duopoly case, with the outcomes under the two market structures compared.

Do three-part tariffs improve efficiency in residential broadband networks?

We analyze subscriber usage data from an Internet Service Provider that sells service using three-part tariff and unlimited plans. Subscribers facing three-part tariffs have lower average usage than subscribers on unlimited plans, and differences among heavy users explain nearly all the overall difference. Hence, the three-part tariff saves network costs and narrows the gap, between light and heavy users, in price per Gigabyte used. However, subscribers facing three-part tariffs cut usage similarly during peak and off-peak hours. Since off-peak usage adds no network costs, these off-peak usage reductions lower welfare. Differentially pricing peak usage could further enhance efficiency.

Usage-Based Pricing of Residential Broadband: Cost Savings and Implications for Subscribers

We analyze subscriber usage data from an Internet Service Provider that sells service using three-part tariff and unlimited plans. Subscribers facing three-part tariffs have lower average usage than subscribers on unlimited plans, and differences among heavy users explain nearly all the overall difference. Hence, the three-part tariff saves network costs and narrows the gap, between light and heavy users, in price per Gigabyte used. However, subscribers facing three-part tariffs cut usage similarly during peak and off-peak hours. Since off-peak usage adds no network costs, these off-peak usage reductions lower welfare. Differentially pricing peak usage could further enhance efficiency.

How to Price Discriminate When Tariff Size Matters

Firms that serve a large market with many diverse consumer types use discriminatory or nonlinear pricing to extract higher revenue, inducing consumers to separate by self-selecting from a large number of tariff options. But the extent of price discrimination must often be tempered by the high costs of devising and managing discriminatory tariffs, including costs of supporting consumers in understanding and making selection from a complex menu of choices. These tariff design trade-offs occur in many industries where firms face many consumer types and each consumer picks the number of units to consume over time. Examples include wireless communication services, other telecom and information technology products, legal plans, fitness clubs, automobile clubs, parking, healthcare plans, and many services and utilities. This paper evaluates alternative ways to price discriminate while accounting for both revenues and tariff management costs. The revenue-maximizing menu of quantity-price bundles can be very (or infinitely) large and hence not practical. Instead, two-part tariffs (2PTs), which charge a fixed entry fee and a per-unit fee, can extract a large fraction of the optimal revenue with a small menu of choices, and they become more attractive once the costs of tariff management are factored in. We show that three-part tariffs (3PTs), which use an additional instrument, the “free allowance,” are an even more efficient way to price discriminate. A relatively small menu of 3PTs can be more profitable than a menu of 2PTs of any size. This 3PT menu can be designed with less information about consumer preferences relative to the menu of two-part tariffs, which, in order to segment customers optimally, needs fine-grained information about preferences. Our analysis reveals a counterintuitive insight that more-complex tariffs need not always be more profitable; it matters whether the complexity is from many choices or more pricing instruments.

When Talk is “Free”: The Effect of Tariff Structure on Usage under Two- and Three-Part Tariffs

In many service industries, firms introduce three-part tariffs to replace or complement existing two-part tariffs. In contrast with two-part tariffs, three-part tariffs offer allowances, or “free” units of the service. Behavioral research suggests that the attributes of a pricing plan may affect behavior beyond their direct cost implications. Evidence suggests that customers value free units above and beyond what might be expected from the change in their budget constraint. Nonlinear pricing research, however, has not considered such an effect. The authors examine a market in which three-part tariffs were introduced for the first time. They analyze tariff choice and usage behavior for customers who switch from two-part to three-part tariffs. The findings show that switchers significantly “overuse” in comparison with their prior two-part tariff usage. That is, they attain a level of consumption that cannot be explained by a shift in the budget constraint. The authors estimate a discrete/continuous model of tariff choice and usage that accounts for the valuation of free units. The results show that the majority of three-part-tariff users value minutes under a three-part tariff more than they do under a two-part tariff. The authors derive recommendations for how the provider can exploit these insights to further increase revenues.

Strategic Effects of Three-Part Tariffs Under Oligopoly

A three-part tariff refers to a pricing scheme consisting of a fixed fee, a free allowance of units up to which the marginal price is zero, and a positive per-unit price for additional demand beyond that allowance. The three-part tariff and its variations are commonly used in both final-goods and intermediate-goods markets. Recently, the offering of three-part tariffs and the like by dominant firms has become a prominent antitrust issue. Existing studies have focused on monopoly models, interpreting the three-part tariff as a price discrimination device. In this paper, I investigate the strategic effects of three-part tariffs in a sequential-move game and offer an equilibrium theory of three-part tariffs in a competitive context. I show that, compared with linear pricing equilibrium and two-part tariff equilibrium, a three-part tariff always strictly increases the dominant firm's (the leader's) profit when competing against a rival (the follower) with substitute products, in the absence of usual price discrimination motive. To explore the effects of a three-part tariff on welfare, I further perform comparative statics analysis using general differentiated linear demand system. I show that the competitive effect of a three-part tariff in contrast to linear pricing depends on the degree of substitutability between products: Competition is intensified when two products are more differentiated, yet softened when two products are more substitutable. This is in stark contrast with the competitive scenario posed by a two-part tariff: A two-part tariff always enhances competition and gives the highest total surplus of these three pricing schemes. Moreover, the rival firm always gets hurt in both profit and quantity sale when the dominant firm switches from linear pricing to a two-part tariff, yet it enjoys higher profit when the dominant firm moves from a two-part tariff to the more ornate three-part tariff, despite the fact that its quantity and market share are decreased even further. My findings offer a new perspective on three-part tariffs, a perspective which could help antitrust enforcement agencies distinguish the exclusionary three-part tariff from the procompetitive one.

Dynamic nonlinear pricing: Biased expectations, inattention, and bill shock

Recent research highlights the importance of biased expectations and inattention for nonlinear pricing in dynamic environments. Findings are: (1) Three-part tariffs, such as cellular service contracts, exploit consumer overconfidence. (2) Surprise penalty fees may be used to further exploit biased beliefs or alternatively to price discriminate more efficiently whenever consumers are inattentive. (3) Implementing the recent bill-shock agreement between cellular carriers and the FCC is predicted to harm rather than help consumers when endogenous price changes are taken into account.

Contracts, Biases, and Consumption of Access Services

We study theoretically and empirically the consumption of access services. We demonstrate that consumption is affected by contract structure (pay-per-use versus three-part tariffs) even if the optimal consumption plans are identical. We find that, although there is extensive individual heterogeneity, on average, consumers' choices follow a structure that is similar to a nearly optimal heuristic and correctly react to imbalances between the number of free calls and call opportunities remaining. However, consumers use the free units too quickly, leading to overconsumption and lost surplus. These errors are partially driven by mistaken beliefs about the value distribution. We also measure subjects' willingness to pay for a contract with free access units, and we find that nearly half of subjects are willing to pay at least the full per-unit price, with a substantial fraction willing to overpay. In response, the optimal firm strategy offers a three-part tariff at a very small discount, which increases revenue by 8%–14% compared to only offering a pay-per-use contract.Data, as supplemental material, are available at http://dx.doi.org/10.1287/mnsc.2013.1889 .This paper was accepted by Teck-Hua Ho, behavioral economics.

An Empirical Analysis of Mobile Voice Service and SMS: A Structural Model

In addition to the wireless telephony boom, a similar exponentially increasing trend in wireless data service—for example, short message service (SMS)—is visible as technology advances. We develop a structural model to examine user demand for voice service and SMS. Specifically, we measure the own- and cross-price elasticities of these services. The cross-price elasticity is of significant importance because marketing activities are critically influenced by whether the goods are substitutes or complements. The research context poses significant econometric challenges due to three-part tariffs and sequential discrete plan choice and continuous quantity choice decisions. Using detailed individual consumption data of more than 6,000 customers, we find that SMS and voice service are small substitutes. A 10% increase in the price of voice minutes will induce about a 0.8% increase in the demand for SMS. The own-price elasticity of voice is also low, to the order of approximately −0.1. Younger users' demand is far more inelastic than that of older users. We then conduct counterfactual policy experiments that fully capture the effects of changes in key parameters on the firm's revenues. Finally, we discuss the generalizability of our framework.

Three-Part Tariffs and Short-Run Rationality in the Local Fixed Telephone Consumption: Empirical Evidence from Medellín

In this paper we are interested in investigating the effects of the threepart tariffs system on consumers’ behavior in the local fixed telephone service provided by the incumbent Telecommunications Company UNE in Medellín, which was authorized by the Telecommunications Regulatory Commission (CRT, for its Spanish name). In order to study consumer behavior and the effect of this tariff system we specify a sort of Engel Curve, which relates expenditure in fixed telephone service and expenditure in public utilities. Endogeneity problems could well arise from this specification, so the empirical strategy for studying households’ consumption is based on a panel data analysis by performing instrumental variables and GMM procedures. Our results supports the hypothesis that consumers surpass expected consumption levels and therefore the total payment for the service is greater than planned, showing a sort of short-run irrationality in consumption.

When Talk is 'Free': The Effect of Tariff Structure on Usage under Two- and Three-Part Tariffs

In many service industries, firms introduce three-part tariffs to replace or complement existing two-part tariffs. As opposed to two-part tariffs, three-part tariffs offer allowances, or “free” units of the service. Behavioral research suggests that the attributes of a pricing plan may affect behavior beyond their direct cost implications. There is evidence that customers value “free” units above and beyond what would be expected based on the change to their budget constraint. Nonlinear pricing research, however, has not considered such an effect.We consider a market where three-part tariffs were introduced for the first time. We analyze tariff choice and usage behavior for customers who switch from two-part to three-part tariffs. We find that switchers significantly “over-use” compared to their prior two-part tariff usage. They attain a level of consumption that cannot be explained by a shift in the budget constraint. We estimate a discrete-continuous model of tariff choice and usage that accounts for the valuation of “free” units. Our results show that 83.9% of three-part tariff users value minutes on a three-part tariff more than they would on a two-part tariff. We derive recommendations for how the provider can exploit these insights to further increase revenues.

Doing More with Less: Price Discrimination with Three-Part vs. Two-Part Tariffs

Multi-part tariffs, such as menus of two-part tariffs and three-part tariffs, are widely used in industry, especially for pricing of information goods, online services, telecommunications products, etc. This paper examines the effectiveness of these price structures for price discriminating between heterogeneous customers. We show that a relatively small menu of three-part tariffs (3PTs) can be more profitable and, sometimes, socially more desirable than a larger menu (more items) of two-part tariffs (2PTs). Often, a single three-part tariff can beat a menu of multiple two-part tariffs. Moreover, this 3PT menu has lower hidden costs - it can be designed with less information about consumer preferences, relative to the menu of two-part tariffs. The 3PT structure not only produces higher profit, but has lower managerial and decision complexity.

Does Uncertainty Matter? Consumer Behavior Under Three-Part Tariffs

In communication, information, and other industries, three-part tariffs are increasingly popular. A three-part tariff is defined by an access price, an allowance, and a marginal price for any usage in excess of the allowance. Empirical nonlinear pricing studies have focused on consumer choice under two-part tariffs. We show that consumer behavior differs under three-part tariffs and assess how consumer demand uncertainty impacts tariff choice. We develop a discrete/continuous model of choice among three-part tariffs and estimate it using consumer-level data on Internet usage. Our model extends prior work in accommodating consumer switching to competitors, thereby capturing behavior in competitive industries more accurately. Our empirical work shows that demand uncertainty is a key driver of choice among three-part tariffs. Consumers' expected bill increases with the variation in their usage, steering them toward tariffs with high allowances. Consequently, demand uncertainty decreases consumer surplus and increases provider revenue. A further analysis of consumers' responsiveness to the different elements of a three-part tariff under the provider's current pricing structure reveals that prices affect a consumer's tariff choice more than her usage quantity and that the allowance plays a strong role in consumer tariff choice. Based on our results, we derive implications for pricing with three-part tariffs.