Trial Length, Pricing, and Rationally Inattentive Customers

F. Nguyen

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arXiv · 2507.06422

Trial Length, Pricing, and Rationally Inattentive Customers

F. Nguyen

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Abstract

The "free trial" followed by automatic renewal is a dominant business model in the digital economy. Standard models explain trials as a mechanism for consumers to learn their valuation for a product. We propose a complementary theory based on the rational inattention framework. Consumers know their valuation but face a cognitive cost to remember to cancel an unwanted subscription. We model this using a Shannon entropy-based cost of information processing, where a consumer's baseline attention level decays with the length of the trial period. This creates a novel trade-off for a monopolist firm: a longer trial increases "inattentive revenue" from consumers who fail to cancel, but it also lowers ex-ante consumer utility, making the initial offer less attractive. We show that this trade-off leads to an interior optimal trial length, even for products where value-learning is instantaneous. Our model, under standard assumptions about demand elasticity and the distribution of consumer valuations, generates sharp, testable predictions about the relationship between contract terms. We find that the optimal renewal price and trial length are complements: firms offering longer trials will also set higher post-trial prices. We analyze the impact of policies aimed at curbing consumer exploitation, such as "click-to-cancel" regulations. We show that such policies, by making attention effectively cheaper, lead firms to reduce trial lengths. The effect on price depends directly on the elasticity of demand from loyal subscribers. We also extend the model to include paid trials, showing that introductory prices and trial lengths act as strategic substitutes. Our framework provides a micro-founded explanation for common features of subscription contracts and offers a new lens through which to evaluate consumer protection policies in digital markets.

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F. Nguyen. 2025-07-08. Trial Length, Pricing, and Rationally Inattentive Customers. https://arxiv.org/abs/2507.06422

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