subscript

The passage around this formula

and the break-even query volume — the point at which on-device placement stops costing more than cloud placement — is $Q^{*}_{\mathrm{device}} = \frac{C_{\mathrm{dev}} + U}{c_{\mathrm{cloud}} - c_{d}}$. This is the same fixed-cost-against-marginal-cost structure that governs any make-versus-buy or capital-versus-operating-expense decision, and it is the structure Qualcomm’s marginal-cost claim silently assumes has already been paid off. Palkhiwala’s statement that an extra inference event is “effectively free” once the device is purchased is a claim about $c_{d}$ alone; it says nothing about $C_{\mathrm{dev}}$ or U , both of which are paid by the model’s operator, not amortized into the price the customer already paid for the phone. Qualcomm’s own public…

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