Some economics of providing cloud computing, by Microsoft economists Hummel and Schwarz

 Here's a paper on an aspect of cloud computing by two Microsoft economists. (Microsoft's cloud service is called Microsoft Azure.)  In addition to the capacity question the paper models, it presents a brief, clear overview of the market for cloud computing.

Efficient Capacity Provisioning for Firms with Multiple Locations: The Case of the Public Cloud  by Patrick Hummel∗ and Michael Schwarz*   March 26, 2021

Abstract: This paper presents a model in which a firm with multiple locations strategically chooses capacity and prices in each location to maximize efficiency. We find that the firm provisions capacity in such a way that the probability an individual customer will be unable to purchase the goods the customer desires is lower in locations with greater expected demand. The firm also sets lower prices in larger locations. Finally, we illustrate that if a customer is indifferent between multiple locations, then it is more efficient to place this customer in a location with greater expected demand. These theoretical results are consistent with empirical evidence that we present from a major public cloud provider.

"2.1 Industry Overview

"The cloud computing industry is young, large, and rapidly growing. Although some of the concepts behind the public cloud were developed as early as the 1960s, all modern public clouds first emerged in the 21st century (Foote 2017). Today annual world cloud revenues exceed $250 billion and are expected to grow by another 20% in 2021 (Graham et al. 2020a).

"The public cloud consists of a wide range of services including infrastructure as a service (IaaS), platform as a service (PaaS), and software as a service (SaaS). SaaS involves providing applications such as web-based email and productivity software to a consumer that can be accessed via the Internet. PaaS provides a platform for deploying consumer created applications using the provider’s programming languages, libraries, and tools.

"And IaaS provisions fundamental computing resources such as processing, storage, and network to a consumer that can be used to deploy and run arbitrary software (Mell and Grance 2011)."

...

"2.5 Why Auctions are Not Used

...

"Since cloud providers provision enough capacity to almost always be able to meet demand, if a cloud provider used an auction to sell compute to customers, the final price at the auction would almost always be equal to the reserve price. However, since cloud customers typically have a value per unit of compute that is orders of magnitude higher than the corresponding capacity costs, in the rare event that there was not enough capacity to meet all demand, the final price in an auction would be dramatically higher

than the cloud provider’s costs. Thus, if a cloud provider used an auction to sell compute to customers, there would be a very high probability that all customers could obtain all the compute they wanted at a low price and a low probability that the final price would

be very high.

"There are two problems with this pricing that would make auctions unsuitable in practice. First, using an auction results in a very high amount of uncertainty about the final realized prices. Thus, if either the cloud provider or the cloud customers are at all risk averse, using an auction to set prices will not meet either the cloud provider’s or the cloud customers’ needs.

"Second, under an auction a cloud provider has a far stronger incentive to underinvest in capacity than under a fixed price mechanism. Under a fixed price mechanism, the cloud provider’s revenue can only go down as a result of underinvesting in capacity, as the cloud provider will not be able to service as much demand. But under an auction, underinvesting in capacity will significantly increase a cloud provider’s revenue by increasing the probability that there will not be enough capacity to meet demand, thereby increasing the probability that the final price in the auction will be very high. Thus, using a fixed price mechanism also enables a cloud provider to more credibly commit to provision the efficient amount of capacity. We illustrate these points formally in Appendix A in the

paper."