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

Sharing delay information in service systems: a literature survey

Service providers routinely share information about upcoming waiting times with their customers, through delay announcements. The need to effectively manage the provision of these announcements has led to a substantial growth in the body of literature which is devoted to that topic. In this survey paper, we systematically review the relevant literature, summarize some of its key ideas and findings, describe the main challenges that the different approaches to the problem entail, and formulate research directions that would be interesting to consider in future work

Self-Selecting Priority Queues with Burr Distributed Waiting Costs

Service providers, in the presence of congestion and heterogeneity of customer waiting costs, often introduce a fee-based premier option using which the customers self-segment themselves. Examples of this practice are found in health care, amusement parks, government (consular services), and transportation. Using a single-server queuing system with customer waiting costs modeled as a Burr Distribution, we perform a detailed analysis to (i) determine the conditions (fees, cost structure, etc.) under which this strategy is profitable for the service provider, (ii) quantify the benefits accrued by the premier customers; and (iii) evaluate the resulting impact on the other customers. We show that such self-selecting priority systems can be pareto-improving in the sense that they are beneficial to everyone. These benefits are larger when the variance in the customer waiting costs is high and the system utilization is high. We use income data from the poorest and richest areas (identified by zipcode) in the United States along with the countrywide income distribution to illustrate our results. Numerical results indicate that planning for a 20–40% enrollment in the high-priority option is robust in ensuring that all the stakeholders benefit from the proposed strategy

Why Imposing New Tolls on Third-Party Content and Applications Threatens Innovation and Will Not Improve Broadband Providers’ Investment

While some broadband providers have called Internet content and application providers free riders on their infrastructure, this is incorrect and misguided. End-users pay for their residential broadband providers for access to the Internet, and content providers pay their own ISPs for connectivity as well. However, content providers need not pay residential broadband providers’ ISPs in order to reach their customers. This feature of the Internet has been one key factor that has allowed innovation to prosper and kept barriers to entry low, as the network transport market for content and application providers functions relatively efficiently. In this paper, I consider the impact of a departure from this current system. I examine the possible impact of last-mile broadband providers’ imposing “termination fees” on third-party content providers or application providers to reach end-users. Broadband providers would engage in paid prioritization arrangements – that is, application and content providers could pay the broadband provider to have their traffic prioritized over competitors’ services. I argue that these arrangements would create inefficiency in the market and harm innovation. Because the last mile access broadband market is concentrated and consumers face switching costs, these concerns are particularly significant. Broadband providers insist that imposing these new charges will greatly improve network investment, and thus these charges are beneficial. I argue that this is not the case. Possible higher revenues from discrimination may simply be returned to shareholders and not invested. Additionally, evidence suggests networks invest more under non-discrimination requirements, and paid prioritization schemes would divert money towards managing scarcity instead of expanding capacity. Paid prioritization could even create an incentive for broadband providers to create congestion to increase the price of prioritized service.

Proactive Customer Service: Operational Benefits and Economic Frictions

Problem Definition: We study a service setting where the provider has information about some customers' future service needs and may initiate service for such customers proactively, if they agree to be flexible with respect to the timing of service delivery. Academic / Practical Relevance: Information about future customer service needs is becoming increasingly available through remote monitoring systems and data analytics. However, the literature has not systematically examined proactive service as a tool that can be used to better match demand to service supply when customers are strategic. Methodology: We combine i) queueing theory, and in particular a diffusion approximation developed specifically for this problem that allows us to derive analytic approximations for customer waiting times, with ii) game theory, which captures customer incentives to adopt proactive service. Results: We show that proactive service can reduce customer waiting times, even if only a relatively small proportion of customers agree to be flexible, the information lead time is limited, and the system makes occasional errors in providing proactive service - in fact we show that the system's ability to tolerate errors increases with (nominal) utilization. Nevertheless, we show that these benefits may fail to materialize in equilibrium because of economic frictions: customers will under-adopt proactive service (due to free-riding) and over-join the system (due to negative congestion-based externalities). We also show that the service provider can incentivize optimal customer behavior through appropriate pricing. Managerial Implications: Our results suggest that proactive service may offer substantial operational benefits, but caution that it may fail to fulfill its potential due to customer self-interested behavior

Priority Service Pricing with Heterogeneous Customers: Impact of Delay Cost Distribution

This is the peer reviewed version of the following article: Cao, P., Wang, Y. and Xie, J. (2019), Priority Service Pricing with Heterogeneous Customers: Impact of Delay Cost Distribution. Prod Oper Manag, 28: 2854-2876., which has been published in final form at https://doi.org/10.1111/poms.13086. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Use of Self-Archived Versions.National Natural Science Foundation of Chin