Estimating demand for spatially differentiated firms with unobserved quantities and limited price data

•I introduce a model to estimate demand with only one firm's prices.•Consumers first choose from symmetric retailers and then choose quantity.•Demand yields cubic pricing equation that identifies key structural parameters.•Demand parameters are estimated precisely, but cost terms are not.•Most plausible disturbance misspecification conservatively biases estimates.

Extending the circular-city model, I derive a pricing equation that identifies key structural parameters from one firm's data. Simulations indicate demand shifters and rotators can be distinguished, cost parameters are imprecise, and the likeliest specification error biases estimates toward zero.