Pricing Digital Goods: Discontinuous Costs and Shared Infrastructure

Abstract

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.