We study the problem of weak instruments in a demand estimation of spatial price competition models by Pinkse, Slade, and Brett (2002) (hereafter, PSB). Product characteristics are included in price instruments and have correlation with prices through the markup. We check whether product characteristics hold their identification power as the number of product grows in analogy with random coefficient discrete choice approach investigated by Armstrong (2016). The conventional weak instruments asymptotics do not work in PSB's model because a series estimation is nested in their two-stage least square estimator, and the number of endogenous regressors (and instruments) also grows as the number of products grows. We provide two asymptotic results that indicate the lack of inconsistency of PSB's estimator.