Essays in nonlinear pricing




Hagemann, Garrett Patrick

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This dissertation addresses several open issues in the economics surrounding the use of nonlinear pricing. The first chapter empirically examines the impact of the use of nonlinear pricing by wholesalers. The second chapter evaluates how firm profit depends on the number of prices offered in a nonlinear price schedule. Finally, the third chapter investigates the use of all-unit discounts as a price discrimination instrument.

The first chapter exploits a unique data set of price schedules to provide the first empirical estimate of the welfare impact of second degree price discrimination in a market with double marginalization. Theoretical predictions in such a context are ambiguous. Quantity discounts at the wholesale level reduce costs for larger retailers, increasing efficiency. However, quantity discounts raise input costs for smaller retailers, increasing prices consumers may pay. The combined welfare effects on consumers depends on how much of input cost discounts are passed through to consumers and the distribution of retailer size. I develop and estimate a model of the New York State retail liquor market where wholesalers offer a multi-part nonlinear tariff for each product. The structural model is then used to estimate the welfare impact of restricting wholesale pricing to be linear. I find that banning quantity discounts reduces total welfare by approximately 14% on average. Consumer surplus and wholesaler profit decline by approximately 26% on average. Average retailer profit increases by a similar magnitude, though effects for a particular retailer are heterogeneous across retailer size.

The second chapter examines the shape of observed price schedules more directly. Sellers often offer price schedules with relatively few segments rather than completely nonlinear price schedules which offer a unique price for each unit sold. By not offering a completely nonlinear, sellers are foregoing some additional profit in favor of a simpler pricing strategy. I find that the scale of these foregone profits is relatively small and only loosely related to product characteristics. When considered in percentage terms, foregone profits are very similar across a large number of products. This suggests that simple pricing strategies obtain almost all the profits available and this is a common property of nonlinear pricing strategies.

The final chapter compares price discrimination through two different quantity discount mechanisms: all-unit discounts and incremental discounts. All-unit-discounts give consumers a lower marginal price on all units purchased once total purchase size crosses a threshold. Incremental discounts only provide discounts on units above the threshold. Relative to incremental discounts, all-unit-discounts imply higher marginal prices and bunching of purchase sizes in equilibrium. The equilibrium bunching may present a challenge for estimating the model empirically.



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