The equivalence of bundling and advance sales
We show that a monopolist's problem of optimal advance selling strategy can be mathematically transformed into a problem of optimal bundling strategy if four conditions hold: i. consumers and the firm agree on the probability of the states occurring, ii. the firm pre-commits to the spot prices to be charged in the advance selling stage, iii. consumers are risk-neutral, and iv. consumers and the firm do not have time preferences or when they do have time preferences, they discount future at the same rate. The result allows both researchers and practitioners to apply the insights from the well-developed vast literature on bundling to advance selling problems. In particular, we show that advance selling is more profitable than spot selling when consumer valuations across the states are independent or negatively dependent or positively dependent up to a point. We furthermore illustrate the effect of advance selling on the spot prices and consumer welfare: When the firm offers advance selling discounts, it sets higher spot prices, so consumers who do not buy in advance are worse off due to the firm offering advance selling discounts. We extend our analysis to the cases of more than two states and competition only in one of the states. We also show how advance selling can be used as an entry deterrence strategy.
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