Intertemporal Content Variation with Customer Learning

Forthcoming in Manufacturing & Service Operations Management

45 Pages Posted: 12 Dec 2019 Last revised: 8 Jul 2021

See all articles by Fernando Bernstein

Fernando Bernstein

Duke University

Soudipta Chakraborty

University of Kansas, School of Business

Robert Swinney

Duke University - Fuqua School of Business

Date Written: August 27, 2020


Problem Definition: We analyze a firm that sells repeatedly to a customer population over multiple periods. While this setting has been studied extensively in the context of dynamic pricing—selling the same product in each period at a varying price—we consider intertemporal content variation, wherein the price is the same in every period, but the firm varies the content available over time. Customers learn their utility on purchasing and decide whether to purchase again in subsequent periods. The firm faces a budget for the total amount of content available during a finite planning horizon, and allocates content to maximize revenue.

Academic/Practical Relevance: A number of new business models, including video stream- ing services and curated subscription boxes, face the situation we model. Our results show how such firms can use content variation to increase their revenues.

Methodology: We employ an analytical model in which customers decide to purchase in multiple successive periods, and a firm determines a content allocation policy to maximize revenue.

Results: Using a lower bound approximation to the problem for a horizon of general length T, we show that while the optimal allocation policy is not, in general, constant over time, it is monotone: content value increases over time if customer heterogeneity is low and decrease otherwise. We demonstrate that the optimal policy for this lower bound problem is either optimal or very close to optimal for the general T period problem. Furthermore, for the case of T = 2 periods, we show how two critical factors—the fraction of "new" versus "repeat" customers in the population, and the size of the content budget—affect the optimal allocation policy and the importance of varying content value over time.

Managerial Implications: We show how firms that sell at a fixed price over multiple periods can vary content value over time to increase revenues.

Keywords: intertemporal content variation, revenue management, customer learning

JEL Classification: M11, M13

Suggested Citation

Bernstein, Fernando and Chakraborty, Soudipta and Swinney, Robert, Intertemporal Content Variation with Customer Learning (August 27, 2020). Forthcoming in Manufacturing & Service Operations Management, Available at SSRN: or

Fernando Bernstein

Duke University ( email )

100 Fuqua Drive
Durham, NC 27708-0204
United States

Soudipta Chakraborty

University of Kansas, School of Business ( email )

1654 Naismith Drive
Lawrence, KS 66045-0001
United States


Robert Swinney (Contact Author)

Duke University - Fuqua School of Business ( email )

Box 90120
Durham, NC 27708-0120
United States


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