Consumers with time-inconsistent preferences often struggle to make optimal consumption decisions over time. Sophisticated consumers (aware of their time- inconsistent preferences) may try to limit their consumption of certain goods by strategically rationing the quantities they purchase, taking advantage of the time delay between purchase and consumption. In this paper, we show that a monopolist selling a storable good of repeated consumption does not make quantity discounts when faced with time-consistent consumers. In contrast, when consumers are time- inconsistent, the optimal strategy includes quantity discounts both when consumers are sophisticated and naive (unaware of the time inconsistent preferences). When consumers are time-inconsistent, quantity discounts increase consumption of the good (for a given average price of the good): Naive consumers take advantage of a small quantity discount with the intention of saving on future purchases, not anticipating that the higher availability of the good after the purchase leads to higher consumption of the good. Instead, sophisticated consumers realize that taking advantage of the quantity discount leads them to consume more that they would like. Because of that, they require a signi…cant quantity discount to increase the quantity purchased. These results are consistent with the empirical evidence that quantity discounts are deeper and more prevalent for vice goods than for virtue goods.

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Keywords: Hyperbolic Discounting, Monopoly Pricing, Quantity Discounts, Self Control, Time-Inconsistent Preferences.