Abstract
Pricing for new products is usually a difficult task for a firm, for there always exists uncertainty of consumers’ valuation with respect to the new products. Moreover, the presence of strategic consumers even complicates the situation, due to their inter-temporal purchase choice behavior and their uncertain proportion in the whole demand pool. In this paper, facing the twofold uncertainty, we develop a stylized model to study the optimal pricing for new fashion products in the presence of strategic consumers. The optimal pricing strategy for the firm and the optimal purchase timing for strategic consumers are obtained; a framework is also built to investigate the expected value of demand information. Through numerical studies, we find that the price skimming strategy dominates the penetration strategy only when the firm’s discount factor is large enough, consumers’ strategic purchasing behavior diminishes the firm’s ability to adopt skim pricing, and the revealing strategy is most valuable when the firm is (almost) indifferent between skimming and penetration. In addition, some other managerial insights are also derived.
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Notes
In reality, the penetration strategy also involves the possibility of raising the price gradually after the launch. As we consider fashion products, it is hard to perform the inverse case of price skimming without rationing effect. So we do not incorporate raising price.
On shopping websites, it is quite common to see the complaints about the price drop from consumers who have already purchased the product, especially for fashion products, such as electronic gadgets. When Apple decided to cut price for iPhone after ten weeks from the launch, Steve Jobs received hundreds of complaint e-mails. Consequently, he had to apologize personally and provide refunds for the early buyers.
Consumers’ valuation or reservation price with respect to a product can be the reservation price of combinations of other goods, and is mainly affected by consumers’ disposal income. The consumers with low income have relatively small amount of choices in combinations of consumption, so it is relatively easier to locate their reservation price. In contrast, consumers with high income have much more alternatives, without additional information the firm does not know how strong the taste of consumers with high income is, and which set of combinations can be regarded as equal to her product.
Here we only define strategic consumers and myopic consumers for high-end group. As for the low-end group, from the analysis in Sect. 4.1, we can see that it does not matter whether the low-end consumers are strategic or myopic, since in our setting the firm would always set the clearance price at the low-end valuation.
We use the uncertainty over the proportion of myopic consumers instead of the proportion of strategic consumers for expositional convenience. It does not matter much with the analysis since the total volume of myopic consumers and strategic consumers always equals \(\alpha \), which is a constant.
In fact, the firm should always undercut \(v_H\, (v_L)\) by an infinitesimal value \(\varepsilon \) to induce the myopic (low-end) consumers to buy. For ease of exposition, we should drop \(\varepsilon \) during the analysis and assume consumers choose to buy when they are indifferent between buying and not buying, strategic consumers choose to buy early when they are indifferent between buying early and delaying purchase.
We still refer to \(\arg \{v_L -c\}\) as \(v_L\) whenever \(E_{\Pi 1} =v_L -c\) or \(E_{\Pi 2} =v_L -c\) at some \(p_1\) larger than \(v_L\).
For the sake of clarity, we display the figures of optimal launching price and optimal expected discounted profit with the range of \((0.7,\,1)\) for the dimension of \(\gamma \). All the omitted parts belong to the “plain” area.
Since in Sect. 6.3 we assume \(\beta \) conforms to uniform distribution, \(\hbox {E}(\beta )=\frac{\alpha }{2}\) in the cases of Fig. 4. Thus when we compare Fig. 2 with Fig. 4, only those sub-figures with \(\{\alpha =0.2,E(\beta )=0.1\}\) and \(\{\alpha =0.4,E(\beta )=0.2\}\) in Fig. 2 are involved.
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Acknowledgments
The authors would like to thank the editor and the reviewers for the helpful comments. This work is supported by National Nature Science Foundation of China under Grant 71172071 and 61403213, and the Specialized Research Fund for the Doctoral Program of Higher Education, China (No. 20120031110036).
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Du, P., Chen, Q. Skimming or penetration: optimal pricing of new fashion products in the presence of strategic consumers. Ann Oper Res 257, 275–295 (2017). https://doi.org/10.1007/s10479-014-1717-0
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DOI: https://doi.org/10.1007/s10479-014-1717-0