Pricing Digital Goods: Discontinuous Costs and Shared Infrastructure

We develop and analyze a model of pricing for digital products withdiscontinuous supply functions. This characterizes a number ofinformation technology-based products and services for which variableincreases in demand are fulfilled by the addition of 'blocks' ofcomputing or network infrastructure. Examples include internet service,telephony, online trading, on-demand software, digital music, streamedvideo-on-demand and grid computing. These goods are often modeled asinformation goods with variable costs of zero, although their actualcost structure features a mixture of positive periodic fixed costs, andzero marginal costs. The pricing of such goods is further complicated bythe fact that rapid advances in semiconductor and networking technologylead to sustained rapid declines in the cost of new infrastructure overtime. Furthermore, this infrastructure is often shared across multiplegoods and services in distinct markets. The main contribution of thispaper is a general solution for the optimal nonlinear pricing of suchdigital goods and services. We show that this can be formulated as afinite series of more conventional constrained pricing problems. We thenestablish that the optimal nonlinear pricing schedule with discontinuoussupply functions coincides with the solution to one specific constrainedproblem, reduce the former to a problem of identifying the optimalnumber of 'blocks' of demand that the seller will fulfil under theiroptimal pricing schedule, and show how to identify this optimal numberusing a simple and intuitive rule (which is analogous to 'balancing' themarginal revenue with average 'marginal cost'). We discuss the extent towhich using 'information-goods' pricing schedules rather than those thatare optimal reduce profits for sellers of digital goods. A firstextension includes the rapidly declining infrastructure costs associatedwith Moore's Law to provide insight into the relationship between themagnitude of cost declines, infrastructure planning and pricingstrategy. A second extension examines multi-market pricing of a set ofdigital goods and services whose supply is fulfilled by a sharedinfrastructure. Our paper provides a new pricing model which is widelyapplicable to IT, network and electronic commerce products. It alsomakes an independent contribution to the theory of second-degree pricediscrimination, by providing the first solution of monopoly screeningwhen costs are discontinuous, and when costs incurred can only beassociated with the total demand fulfilled, rather than demand fromindividual customers.