Pass-Through with Quantity Discounts:A New Edgeworth-Salinger Paradox

We study cost pass-through under nonlinear pricing when a monopolistic seller offers a single good in two fixed package sizes to heterogeneous consumers. Building on the Edgeworth–Salinger paradox of taxation, we show that Edgeworth-type price responses can arise across package sizes of the same underlying product. A common increase in per-unit marginal cost may induce the seller to lower the per-unit price of the small package while raising that of the large package. Under multinomial logit demand, pass-through to the large package is analytically greater than pass-through to the small package. Numerical analysis shows that this ordering is remarkably robust to random-coefficient demand heterogeneity. Negative pass-through for the small package is quantitatively important and becomes substantially more likely as the difference between package sizes increases. Consumer sorting also matters: a more positive correlation between price sensitivity and preferences for larger packages increases the likelihood of negative pass-through for the small package and widens the pass-through gap across package sizes. Thus, nonlinear pricing can transform a common supply-side cost shock into sharply different price responses across quantities purchased, with potentially important implications for the distributional incidence of cost shocks.