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Selling a product before a consumer will actually use it can benefit both sellers and consumers. It helps sellers to plan ahead and reduce demand variability. And for consumers, they can ensure they will get the product, possibly at a lower price.

Selling in advance also gives sellers an opportunity to exploit consumer uncertainties about their valuations of their purchase, which cannot be realised until the “spot” period when they have it in their hands. That leads to some questions: when should sellers adopt advance selling? What quantity should they sell in advance? And what kinds of products are best to sell in advance?

Man Yu, Roman Kapuscinski and Hyun-Soo Ahn argue that sellers should consider the correlation among consumer valuations when they make their decisions. Some valuations will be idiosyncratic and depend on the tastes, moods and circumstances of each consumer. For instance, a prepaid meal at Disneyland may not be desirable if they are not sure they will like the food on offer.

But other valuations depend on external circumstances that affect everybody equally at the time of consumption, such as tickets to a popular Broadway show on a limited run or the World Series.

Sellers could sell to advance under each of these scenarios, but they will need different strategies for each, such as a better price or guaranteed availability, the authors said. “The interdependence of consumer valuations creates very different markets for the seller even when the valuation distribution of an individual consumer remains the same,” they said.

To demonstrate this, they devise a model that looks at different levels of interdependence of consumer valuations in advance selling, and show how this interacts with the seller’s capacity.

When the seller has unlimited capacity, he or she does not need to worry about interdependence and can safely offer advance selling with a discount in order to increase sales.

A discount in advance is also viable if capacity is limited but interdependence is low, although the quantity sold in advance should be rationed.

But if capacity is limited and there is high interdependence of consumer valuations, then the opposite holds: the seller should charge a premium in advance and make the entire supply available in advance.

The authors explained the rationale using examples. “When individual differences largely determine the consumer’s valuation, such as the value of pre-purchased meal tickets in Disneyland or of an airline ticket, and the valuations are diverse, the seller can set the spot price to avoid major shortages in the spot market. Consequently, consumers are not willing to pay a premium price in advance.

“But when consumers’ valuations are highly interdependent, advance selling can be beneficial to the seller at any capacity level, even when the capacity is tight. The seller can exploit consumers’ uncertainty about product availability in the spot period and charge a premium price in advance. This matches much-hyped or award-winning Broadway shows and concerts, or sports events, for which the advance price can be much higher than spot price. Some Broadway shows, for example, can charge 40 per cent higher in advance.”

These are the extreme cases and the seller’s policy will gradually change with the degree of valuation interdependence, they said. But sellers must identify the right scenario or their profits could suffer.

“When capacity is limited, valuation interdependence always hurts the seller’s overall profitability but enhances the average gain from advance selling. In such cases, the seller who fails to recognise the valuation interdependence when choosing selling strategies suffers a significant loss of profit,” they said.

“Therefore, the seller with limited capacity should explicitly consider how the valuations are derived for their product, for example, largely from environmental or idiosyncratic factors, before deciding on an advance-selling strategy.”