| 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. |