Nonlinear pricing of information goods

This paper analyzes optimal pricing for information goods under incomplete information, when both unlimited-usage (fixed-fee) pricing and usage-based pricing are feasible, and administering usage-based pricing may involve transaction costs. It is shown that offering fixed- fee pricing in addition to a non-linear usage-based pricing scheme is always profit-improving in the presence of any non-zero transaction costs, and there may be markets in which a pure fixed-fee is optimal. This implies that the optimal pricing strategy for information goods is almost never fully revealing. Moreover, it is proved that the optimal usage-based pricing schedule is independent of the value of the fixed- fee, a result that simplifies the simultaneous design of pricing schedules considerably, and provides a simple procedure for determining the optimal combination of fixed-fee and non-linear usage-based pricing. The introduction of fixed-fee pricing is shown to increase both consumer surplus and total surplus. The differential effects of setup costs, fixed transaction costs and variable transaction costs on pricing policy are described. These results suggests a number of managerial guidelines for designing pricing schedules. For instance, in nascent information markets, firms may profit from low fixed-fee penetration pricing, but as these markets mature, the optimal pricing mix should expand to include a wider range of usage-based pricing options. The extent of minimum fees, quantity discounts and adoption levels across the different pricing schemes are characterized, strategic pricing responses to changes in market characteristics are described, and the implications of the paper's results for bundling and vertical differentiation of information goods are discussed.nonlinear pricing, screening, digital goods, information goods, fixed-fee, usage-based pricing, transaction costs

Optimal Income Taxation, Public-Goods Provision and Public-Sector Pricing: A Contribution to the Foundations of Public Economics

The paper develops an integrated model of optimal nonlinear income taxation, public-goods provision and pricing in a large economy. With asymmetric information about labour productivities and publicgoods preferences, the multidimensional mechanism design problem becomes tractable by requiring renegotiation proofness of the final allocation of private goods and admission tickets for excludable public goods. Under an affiliation assumption on the underlying distribution, optimal income taxation, public-goods provision and admission fees have the same qualitative properties as in unidimensional models. These properties are obtained for utilitarian welfare maximization and for a Ramsey-Boiteux formulation with interim participation constraints.Optimal Income Taxation, Public Goods, Public-Sector Pricing, Multidimensional Mechanism Design, Ramsey-Boiteux Pricing

Pricing Digital Goods: Discontinuous Costs and Shared Infrastructure

We develop and analyze a model of pricing for digital products with discontinuous supply functions. This characterizes a number of information technology-based products and services for which variable increases in demand are fulfilled by the addition of 'blocks' of computing or network infrastructure. Examples include internet service, telephony, online trading, on-demand software, digital music, streamed video-on-demand and grid computing. These goods are often modeled as information goods with variable costs of zero, although their actual cost structure features a mixture of positive periodic fixed costs, and zero marginal costs. The pricing of such goods is further complicated by the fact that rapid advances in semiconductor and networking technology lead to sustained rapid declines in the cost of new infrastructure over time. Furthermore, this infrastructure is often shared across multiple goods and services in distinct markets. The main contribution of this paper is a general solution for the optimal nonlinear pricing of such digital goods and services. We show that this can be formulated as a finite series of more conventional constrained pricing problems. We then establish that the optimal nonlinear pricing schedule with discontinuous supply functions coincides with the solution to one specific constrained problem, reduce the former to a problem of identifying the optimal number of 'blocks' of demand that the seller will fulfil under their optimal pricing schedule, and show how to identify this optimal number using a simple and intuitive rule (which is analogous to 'balancing' the marginal revenue with average 'marginal cost'). We discuss the extent to which using 'information-goods' pricing schedules rather than those that are optimal reduce profits for sellers of digital goods. A first extension includes the rapidly declining infrastructure costs associated with Moore's Law to provide insight into the relationship between the magnitude of cost declines, infrastructure planning and pricing strategy. A second extension examines multi-market pricing of a set of digital goods and services whose supply is fulfilled by a shared infrastructure. Our paper provides a new pricing model which is widely applicable to IT, network and electronic commerce products. It also makes an independent contribution to the theory of second-degree price discrimination, by providing the first solution of monopoly screening when costs are discontinuous, and when costs incurred can only be associated with the total demand fulfilled, rather than demand from individual customers.We develop and analyze a model of pricing for digital products with discontinuous supply functions. This characterizes a number of information technology-based products and services for which variable increases in demand are fulfilled by the addition of 'blocks' of computing or network infrastructure. Examples include internet service, telephony, online trading, on-demand software, digital music, streamed video-on-demand and grid computing. These goods are often modeled as information goods with variable costs of zero, although their actual cost structure features a mixture of positive periodic fixed costs, and zero marginal costs. The pricing of such goods is further complicated by the fact that rapid advances in semiconductor and networking technology lead to sustained rapid declines in the cost of new infrastructure over time. Furthermore, this infrastructure is often shared across multiple goods and services in distinct markets. The main contribution of this paper is a general solution for the optimal nonlinear pricing of such digital goods and services. We show that this can be formulated as a finite series of more conventional constrained pricing problems. We then establish that the optimal nonlinear pricing schedule with discontinuous supply functions coincides with the solution to one specific constrained problem, reduce the former to a problem of identifying the optimal number of 'locks' of demand that the seller will fulfil under their optimal pricing schedule, and show how to identify this optimal number using a simple and intuitive rule (which is analogous to 'balancing' the marginal revenue with average 'marginal cost'). We discuss the extent to which using 'information-goods' pricing schedules rather than those that are optimal reduce profits for sellers of digital goods. A first extension includes the rapidly declining infrastructure costs associated with Moore's Law to provide insight into the relationship between the magnitude of cost declines, infrastructure planning and pricing strategy. A second extension examines multi-market pricing of a set of digital goods and services whose supply is fulfilled by a shared infrastructure. Our paper provides a new pricing model which is widely applicable to IT, network and electronic commerce products. It also makes an independent contribution to the theory of second-degree price discrimination, by providing the first solution of monopoly screening when costs are discontinuous, and when costs incurred can only be associated with the total demand fulfilled, rather than demand from individual customers

Customized Bundle Pricing for Information Goods: A Nonlinear Mixed-Integer Programming Approach

This paper proposes using nonlinear mixed-integer programming to solve the customized bundle-pricing problem in which consumers are allowed to choose up to N goods out of a larger pool of J goods. Prior work has suggested that this mechanism has attractive features for the pricing of information and other low-marginal cost goods. Although closed-form solutions exist for this problem for certain cases of consumer preferences, many interesting scenarios cannot be easily handled without a numerical solution procedure. In this paper, we investigate the efficiency gains created by customized bundling over the alternatives of pure bundling or individual sale under different assumptions about customer preferences and firm cost structure, as well as the potential loss of efficiency caused by pricing with incomplete information about consumer reservation values. Our analysis suggests that customized bundling enhances sellers’ profits and enhances welfare when consumers do not place positive values on all goods, and that this consumer characteristic is much more important than the shape of the valuation distribution in determining the optimal pricing scheme. We also find that customized bundling outperforms both pure bundling and individual sale in the presence of incomplete information, and that customized bundling still outperforms other simpler pricing schemes even when exact consumer valuations are not known ex ante

Managing Digital Piracy: Pricing, Protection and Welfare

This paper analyzes the optimal choice of pricing schedules and technological deterrence levels in a market with digital piracy, when legal sellers can sometimes control the extent of piracy by implementing digital rights management (DRM) systems. It is shown that the seller's optimal pricing schedule can be characterized as a simple combination of the zero-piracy pricing schedule, and a piracy-indifferent pricing schedule which makes all customers indifferent between legal consumption and piracy. An increase in the level of piracy is shown to lower prices and profits, but may improve welfare by expanding the fraction of legal users and the volume of legal usage. In the absence of price- discrimination, the optimal level of technology-based protection against piracy is shown to be the technologically-maximal level, which maximizes the difference between the quality of the legal and pirated goods. However, when a seller can price-discriminate, it is always optimal for them to choose a strictly lower level of technology-based protection. Moreover, if a DRM system weakens over time, due to its technology being progressively hacked, the optimal strategic response may involve either increasing or decreasing the level of technology-based protection and the corresponding prices. This direction of change is related to whether the technology implementing each marginal reduction in piracy is increasingly less or more vulnerable to hacking. Pricing and technology choice guidelines based on these results are presented, some social welfare issues are discussed, and ongoing work on the role of usage externalities in pricing and protection is outlineddigital piracy, digital rights management, DRM, information goods, nonlinear pricing, screening, type-dependent participation constraints, copyright, IP, intellectual property

Optimal Income Taxation, Public-Goods Provision

The paper develops an integrated model of optimal nonlinear income taxation, public-goods provision and pricing in a large economy. With asymmetric information about labour productivities and publicgoods preferences, the multidimensional mechanism design problem becomes tractable by requiring renegotiation proofness of the final allocation of private goods and admission tickets for excludable public goods. Under an affiliation assumption on the underlying distribution, optimal income taxation, public-goods provision and admission fees have the same qualitative properties as in unidimensional models. These properties are obtained for utilitarian welfare maximization and for a Ramsey-Boiteux formulation with interim participation constraints.

Network Effects, Nonlinear Pricing and Entry Deterrence

A number of products that display positive network effects are used in variable quantities by heterogeneous customers. Examples include corporate operating systems, infrastructure software, web services and networking equipment. In many of these contexts, the magnitude of network effects are influenced by gross consumption, rather than simply by user base. Moreover, the value an individual customer derives on account of these network effects may be related to the extent of their individual consumption, and therefore, the network effects may be heterogeneous across customers. This paper presents a model of nonlinear pricing in the presence of such network effects, under incomplete information, and with the threat of competitive entry. Both homogeneous and heterogeneous network effects are modeled. Conditions under which a fulfilled-expectations contract exists and is unique are established. While network effects generally raise prices, it is shown that accompanying changes in consumption depend on the nature of the network effects -- in some cases, it is optimal for the monopolist to induce no changes in usage across customers, while in others cases, network effects raise the usage of all market participants. Optimal pricing is shown to include quantity discounts that increase with usage, and may also involve a nonlinear two-part tariff. These results highlight the impact of network effects on the standard trade-off between price discrimination and value creation, and have important implications for pricing policy. The threat of entry generally lowers profits for the monopolist, and increases customer surplus. When network effects are homogeneous across customers, the resulting entry-deterring monopoly contract is a fixed fee and results in the socially optimal outcome. However, when the magnitude of heterogeneous network effects is relatively high, there are no changes in total surplus induced by the entry threat, and the price changes merely cause a transfer of value from the seller to its customers. The presence of network effects, and of a credible entry threat, are also shown to increase distributional efficiency by reducing the disparity in relative value captured by different customer types. Regulatory and policy implications of these results are discussed.network externalities, network externality, non-linear pricing, screening, adverse selection, price discrimination, information goods, software pricing, Microsoft

Nonlinear Pricing of Shareable Products

We consider a durable-goods monopolist who is able to control the collaborative consumption of its goods on an aftermarket by a sharing tariff. Consumers are heterogeneous with respect to their respective need propensities in each period. We show that the firm may be able to extract this private information by offering a nonlinear pricing scheme, which amounts to a menu of options that distinguish themselves by different combinations of retail price and sharing tariff, whereby the latter is charged to owners at the point of sharing their item with a nonowner on the sharing market. The solution, which is obtained using optimal control theory, critically depends on the product\u27s durability

Monopoly quality degradation and regulation in cable television

Using an empirical framework based on the Mussa-Rosen model of monopoly quality choice, we calculate the degree of quality degradation in cable television markets and the impact of regulation on those choices. We find lower bounds of quality degradation ranging from 11 to 45 percent of offered service qualities. Furthermore, cable operators in markets with local regulatory oversight offer significantly higher quality, less degradation, and greater quality per dollar, despite higher prices

Model Selection in an Information Economy : Choosing what to Learn

As online markets for the exchange of goods and services become more common, the study of markets composed at least in part of autonomous agents has taken on increasing importance. In contrast to traditional completeinformation economic scenarios, agents that are operating in an electronic marketplace often do so under considerable uncertainty. In order to reduce their uncertainty, these agents must learn about the world around them. When an agent producer is engaged in a learning task in which data collection is costly, such as learning the preferences of a consumer population, it is faced with a classic decision problem: when to explore and when to exploit. If the agent has a limited number of chances to experiment, it must explicitly consider the cost of learning (in terms of foregone profit) against the value of the information acquired. Information goods add an additional dimension to this problem; due to their flexibility, they can be bundled and priced according to a number of different price schedules. An optimizing producer should consider the profit each price schedule can extract, as well as the difficulty of learning of this schedule. In this paper, we demonstrate the tradeoff between complexity and profitability for a number of common price schedules. We begin with a one-shot decision as to which schedule to learn. Schedules with moderate complexity are preferred in the short and medium term, as they are learned quickly, yet extract a significant fraction of the available profit. We then turn to the repeated version of this one-shot decision and show that moderate complexity schedules, in particular two-part tariff, perform well when the producer must adapt to nonstationarity in the consumer population. When a producer can dynamically change schedules as it learns, it can use an explicit decision-theoretic formulation to greedily select the schedule which appears to yield the greatest profit in the next period. By explicitly considering the both the learnability and the profit extracted by different price schedules, a producer can extract more profit as it learns than if it naively chose models that are accurate once learned.Online learning; information economics; model selection; direct search