What is in a Price? Estimating Willingness-to-Pay with Bayesian Hierarchical Models
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arXiv
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| Natura: | Preprint |
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2025
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| author | Pillai, Srijesh Chandrawat, Rajesh Kumar |
| author_facet | Pillai, Srijesh Chandrawat, Rajesh Kumar |
| contents | For premium consumer products, pricing strategy is not about a single number, but about understanding the perceived monetary value of the features that justify a higher cost. This paper proposes a robust methodology to deconstruct a product's price into the tangible value of its constituent parts. We employ Bayesian Hierarchical Conjoint Analysis, a sophisticated statistical technique, to solve this high-stakes business problem using the Apple iPhone as a universally recognizable case study. We first simulate a realistic choice based conjoint survey where consumers choose between different hypothetical iPhone configurations. We then develop a Bayesian Hierarchical Logit Model to infer consumer preferences from this choice data. The core innovation of our model is its ability to directly estimate the Willingness-to-Pay (WTP) in dollars for specific feature upgrades, such as a "Pro" camera system or increased storage. Our results demonstrate that the model successfully recovers the true, underlying feature valuations from noisy data, providing not just a point estimate but a full posterior probability distribution for the dollar value of each feature. This work provides a powerful, practical framework for data-driven product design and pricing strategy, enabling businesses to make more intelligent decisions about which features to build and how to price them. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_11089 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | What is in a Price? Estimating Willingness-to-Pay with Bayesian Hierarchical Models Pillai, Srijesh Chandrawat, Rajesh Kumar Applications Machine Learning Econometrics For premium consumer products, pricing strategy is not about a single number, but about understanding the perceived monetary value of the features that justify a higher cost. This paper proposes a robust methodology to deconstruct a product's price into the tangible value of its constituent parts. We employ Bayesian Hierarchical Conjoint Analysis, a sophisticated statistical technique, to solve this high-stakes business problem using the Apple iPhone as a universally recognizable case study. We first simulate a realistic choice based conjoint survey where consumers choose between different hypothetical iPhone configurations. We then develop a Bayesian Hierarchical Logit Model to infer consumer preferences from this choice data. The core innovation of our model is its ability to directly estimate the Willingness-to-Pay (WTP) in dollars for specific feature upgrades, such as a "Pro" camera system or increased storage. Our results demonstrate that the model successfully recovers the true, underlying feature valuations from noisy data, providing not just a point estimate but a full posterior probability distribution for the dollar value of each feature. This work provides a powerful, practical framework for data-driven product design and pricing strategy, enabling businesses to make more intelligent decisions about which features to build and how to price them. |
| title | What is in a Price? Estimating Willingness-to-Pay with Bayesian Hierarchical Models |
| topic | Applications Machine Learning Econometrics |
| url | https://arxiv.org/abs/2509.11089 |