Demand for Conversational AI: Purpose, Price, and the Social Cost of Wanting a Companion

<jats:p>Relational uses of conversational AI register as barely demanded in stated-preference data, even as the market for AI companions grows quickly. We estimate demand across five purposes — administrative assistance, studying, wellness, friendship, and romance — in a preregistered within-respondent conjoint experiment (N = 1,990) that independently randomizes price, privacy, personalization, modality, and safety policy. Purpose dominates every design attribute: respondents require $7.81 per month to accept a romantic companion in place of an administrative assistant, an order of magnitude more than any feature effect. We show this penalty is not a pure preference parameter. Removing the monetary barrier does not close it, because the zero-price premium is attenuated specifically for relational purposes, which no additive model generates. Second-order beliefs are compressed across purposes relative to own interest, and the ratio of the belief–interest gap to the purpose penalty is statistically constant across relational purposes, as a single social-image cost parameter requires. That ratio is also the welfare statistic, and it is invariant to the price slope: social image accounts for up to 39.6% of the romantic penalty and 46.8% of the friendship penalty. A hierarchical Bayes demand model recovers the taste distribution and shows social-image sensitivity shifting relational purposes while leaving price and attribute sensitivities unchanged.</jats:p>