Abstract
A monopolist’s ability to conduct non-linear pricing is limited because customers can, at a cost, unbundle bundled output. Three pricing strategies are available to a firm: (1) a separating strategy; (2) a pooling strategy; and (3) an exclusion strategy. Each is optimal for some set of unbundling cost and distribution of customer types. The optimal pricing strategies are contrasted with the well-studied benchmark cases, in which unbundling costs are either zero or arbitrarily high. It is shown that it is not always possible to extrapolate the conclusions from the benchmark cases with respect to pricing, profitability, consumer surplus or efficiency.
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Notes
The reader might be concerned that a unit is endogenous in some of the examples cited above (For example, the size of a can of fruit is determined by the manufacturer). However, irrespective of how a unit is determined, the puzzle identified here will occur if one or more customers are observed buying two single units. There is a profitable opportunity in such cases for virtual bundling (when unbundling is not possible). In addition, a unit is exogenous for many goods that supermarkets could virtually bundle but don't: e.g., mops, buckets, utility knives.
Note that it is not necessary to restrict joint purchases to customers within a type as does Alger.
The label E denotes “exclusion”. It is shown in the next section that, when there are two customer types, these strategies are implemented if the firm does not sell to the low-volume customer type.
This critical value of α is denoted with the superscript MR because the firm bundles output for α ≥ α MR as is assumed by Maskin and Riley.
Maskin and Riley note that their model of bundling is theoretically equivalent to the vertical differentiation that is studied by Mussa and Rosen (1978). Similarly, Deneckere and McAfee (1996) consider how firms may intentionally reduce the quality of their products to conduct vertical price discrimination. The results of this paper are, however, not easily applied to vertical product discrimination as consumers are not normally able to 'unbundle' a high-quality product into two or more low-quality products.
Customers have two actions they can undertake (purchase bundled or unbundled), and firms have one instrument (the bundle). Hence we are considering a multidimensional screening problem. (Rochet and Choné 1998). Consumer preferences satisfies the single crossing property for intermediate L MB.
It is unnecessary to consider the pairwise comparison between strategy P and strategy E 2 (see Fig. 2).
This conclusion could also be obtained by noting that an increase in α relaxes the seller’s problem; thus profit must be non-decreasing.
It is never optimal to sell exclusively to type H customers in this case, as such a strategy would be dominated by a strategy in which a single unit is also sold for the bundle price or \(U^{L}\), whichever is lower.
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Acknowledgments
I would like to thank Bob Hammond, Ann Marsden, David Prentice, two anonymous referees, and the editor, Lawrence White, for useful comments on an earlier draft. All errors remain my responsibility.
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Sibly, H. Pricing Strategies with Costly Customer Arbitrage. Rev Ind Organ 50, 345–366 (2017). https://doi.org/10.1007/s11151-016-9533-0
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DOI: https://doi.org/10.1007/s11151-016-9533-0