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Pricing, Supply, Mechanism Selection and Ration in the Presence of Strategic Purchase Demands
LI He, LIN Zhong-gao, WU Jin-nan
2021, 29 (3):
153-167.
doi: 10.16381/j.cnki.issn1003-207x.2019.0700
Once the sales period of perishable assets (such as vehicle and ship seat services, seasonal vegetable and flower products) expires, its market value is extremely low, even zero. Dynamic pricing for improving sales revenue in uncertain demand often incur consumers' strategic purchase countermeasures. Since strategic purchases depend on reference prices, while prices depend on supply and demand, dynamic pricing is a combination of static pricing and rationing is about the distribution of supply. Therefore, there should be a unified decision on the pricing, supply, mechanism selection and rationing of perishable assets with consumer behavior. This is what the existing studies ignore.
In this paper, sales process is manifested as a two-stage pricing form (the prices in two stages are equal when static pricing is selected). Market players include the firm and high-end and low-end consumers with reserved prices of VH and VL respectively, and high-end consumers include the w strategic consumers who definitely arrived in the first stage and the X random consumers who randomly appeared in the second stage. Each consumer can only buy at most one, and enough low-end consumers can buy all the remaining goods as long as P1 or ${\tilde P_2}$ ≤ VL.The firm decides the supplyc, pricing mechanism and first-stage price P1 before sales,and the arriving strategic consumers purchase immediately when they find P1 ≤ E(${\tilde P_2}$) (the mathematical expectation of price ${\tilde P_2}$ in the second stage),otherwise, wait to become the potential demand w2 for the second stage. At the moment between the two stages,X becomes an observable value, the remaining quantity of the goods is c2,and the firm chooses the second stage price ${\tilde P_2}$(${\tilde P_2}$=VH when X+w2 ≥ $\frac{{{V_L}}}{{{V_H}}}{c^2}$, others ${\tilde P_2}$=VL) according to the remaining supply and demand. In short, the firm decides perishable asset prices, supply, mechanism selection and ration strategies based on profit maximization goal,and strategic consumers set the chance of strategic purchase by anchoring the expected price. Different from the usual thinking of pricing based on utility theory, the market expected demand curve and dynamic and static pricing areas of different waiting purchase scales are firstly explored based on the anchor effect and intertemporal price equilibrium. Secondly, the frontier of effective market pricing (i.e. effective demand curve) in many expected demand curves is studied. Third, the capacity expansion line (i.e. the maximum profit curve) corresponding to the effective pricing frontier on the profit surface is found. Finally, the maximum expected profit and corresponding strategies along the capacity expansion line and the frontier of effective pricing are provided.
The results show that the heterogeneity of consumer reserve price and the uncertainty of demands are the fundamental reasons for the existence of dynamic pricing and strategic purchases. The market has different expected demand curves in different scales of strategy waiting for purchase, and the expected demand curve in the largest-scale strategy waiting for purchase is the market effective pricing frontier. Dynamic pricing mechanism and static pricing mechanism each have their own applicable capacity and price space. Specifically, the level of the consumer's reservation price and the scale of strategic consumers determine the size of dynamic pricing space, while the different distributions of random demands only affect the shape of dynamic pricing space, i.e. affecting the demand elasticity. Meanwhile, both price increase and capacity expansion would intensify the strategic purchase degree of consumers in the area of intertemporal price equilibrium, that is, the larger the supply, the lower the pricing. Further, strategic purchases would not only reduce the supply, pricing and profits of firm, change the purchase opportunities of the high and low prices among different types of consumers, but also affect the selection of pricing mechanisms and ration strategies. Finally, reducing excess supply and virtual high price space can reduce the loss of profits caused by strategic purchases. The numerical results are consistent with the conclusions derived from the model. The results obtained from this paper can provide references for relevant studies and firms in practice.
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