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Intertemporal Price Discrimination Via Reference Price Effects

Intertemporal Price Discrimination Via Reference Price Effects
Author: Zizhuo Wang
Publisher:
Total Pages: 21
Release: 2015
Genre:
ISBN:

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We consider the dynamic pricing problem a monopolistic seller faces when customers arrive in heterogeneous time periods and their purchase decisions are affected by reference prices formed from their past purchase experiences. We illustrate that a new form of price discrimination opportunity exists in such situations, where the seller's optimal pricing strategy is a cyclic one, even when the customers are loss-neutral and their demand functions are identical. This result differs from those in prior studies where the optimal price paths are shown to be asymptotically constant when customer arrival times are homogeneous or when there are no reference price effects, thus is unique due to the interaction between the heterogeneous arrivals and the reference price effects. We also provide the length of the cycle when the demand function is linear. In this era where customer information becomes easier accessible, our results suggest the seller consider this new dimension of price discrimination in conjunction with the old ones, in order to take advantage of the full power of customer data.


Dynamic Pricing

Dynamic Pricing
Author: Mark Stenius Roberts
Publisher:
Total Pages:
Release: 1977
Genre:
ISBN:

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Intertemporal Price Discrimination in Storable Goods Markets

Intertemporal Price Discrimination in Storable Goods Markets
Author: Igal Hendel
Publisher:
Total Pages: 36
Release: 2011
Genre: Economics
ISBN:

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Abstract: We study intertemporal price discrimination when consumers can store for future consumption needs. To make the problem tractable we offer a simple model of demand dynamics, which we estimate using market level data. Optimal pricing involves temporary price reductions that enable sellers to discriminate between price sensitive consumers, who anticipate future needs, and less price-sensitive consumers. We empirically quantify the impact of intertemporal price discrimination on profits and welfare. We find that sales: (1) capture 25-30% of the profit gap between non-discriminatory and third degree price discrimination profits, and (2) increase total welfare


Intertemporal Price Discrimination with Multiple Products

Intertemporal Price Discrimination with Multiple Products
Author: Jean-Charles Rochet
Publisher:
Total Pages: 52
Release: 2017
Genre: Monopolies
ISBN:

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We study the multiproduct monopoly profit maximisation problem for a seller who can commit to a dynamic pricing strategy. We show that if consumers' valuations are not strongly-ordered then optimality for the seller requires intertemporal price discrimination and it can be implemented by dynamic pricing on the cross-sell to the bundle. If consumers are perfectly negatively correlated, reducing the cross-sell price at a single point in time is optimal. For general valuations we show that if the cross-partial derivative of the profit function is negative then dynamic pricing on the cross-sell is more profitable than fixing prices. So we show that the celebrated Stokey (1979) no-discrimination-across-time result does not extend to multiple good sellers when consumers' valuations are drawn from the tilted uniform, the shifted uniform, the exponential, or the normal distribution. We extend our results to welfare, to complementarities in demand, and to the determination of optimal discount schedules.


Intertemporal Price Discrimination with Time-Varying Valuations

Intertemporal Price Discrimination with Time-Varying Valuations
Author: Victor F. Araman
Publisher:
Total Pages: 41
Release: 2020
Genre:
ISBN:

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A firm that sells a non perishable product considers intertemporal price discrimination in the objective of maximizing the long-run average revenue. Each period, a number of interested customers approach the firm and can either purchase on arrival, or remain in the system for a period of time. During this time, each customer's valuation changes following a discrete and homogenous Markov chain. Customers leave the system if they either purchase at some point, or their valuations reach an absorbing state v0. We show that, in this context, cyclic strategies are optimal, or nearly optimal. When the pace of intertemporal pricing is constrained to be comparable to customers patience level, we have a good control on the cycle length and on the structure of the optimizing cyclic policies. We also obtain an algorithm that yields the optimal (or near optimal) cyclic solutions in polynomial time in the number of prices. We cast part of our results in a general framework of optimizing the long-run average revenues for a class of payoffs that we call weakly coupled, in which the revenue per period depends on a finite number of neighboring prices.


Dynamic Allocation and Pricing

Dynamic Allocation and Pricing
Author: Alex Gershkov
Publisher: MIT Press
Total Pages: 209
Release: 2024-06-11
Genre: Business & Economics
ISBN: 0262552442

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A new approach to dynamic allocation and pricing that blends dynamic paradigms from the operations research and management science literature with classical mechanism design methods. Dynamic allocation and pricing problems occur in numerous frameworks, including the pricing of seasonal goods in retail, the allocation of a fixed inventory in a given period of time, and the assignment of personnel to incoming tasks. Although most of these problems deal with issues treated in the mechanism design literature, the modern revenue management (RM) literature focuses instead on analyzing properties of restricted classes of allocation and pricing schemes. In this book, Alex Gershkov and Benny Moldovanu propose an approach to optimal allocations and prices based on the theory of mechanism design, adapted to dynamic settings. Drawing on their own recent work on the topic, the authors describe a modern theory of RM that blends the elegant dynamic models from the operations research (OR), management science, and computer science literatures with techniques from the classical mechanism design literature. Illustrating this blending of approaches, they start with well-known complete information, nonstrategic dynamic models that yield elegant explicit solutions. They then add strategic agents that are privately informed and then examine the consequences of these changes on the optimization problem of the designer. Their sequential modeling of both nonstrategic and strategic logic allows a clear picture of the delicate interplay between dynamic trade-offs and strategic incentives. Topics include the sequential assignment of heterogeneous objects, dynamic revenue optimization with heterogeneous objects, revenue maximization in the stochastic and dynamic knapsack model, the interaction between learning about demand and dynamic efficiency, and dynamic models with long-lived, strategic agents.


Intertemporal Price Discrimination

Intertemporal Price Discrimination
Author: Omar Besbes
Publisher:
Total Pages: 0
Release: 2015
Genre:
ISBN:

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We study a firm's optimal pricing policy under price commitment. The firm's objective is to maximize its long-term average revenue given a steady arrival of strategic customers. In particular, customers arrive over time, are strategic in timing their purchases and are heterogeneous along two dimensions: their valuation for the firm's product and their willingness to wait before purchasing or leaving. The customers' patience and valuation may be correlated in an arbitrary fashion. For this general formulation, we prove that the firm may restrict attention to cyclic pricing policies, which have length at most twice the maximum willingness to wait of the customer population. To efficiently compute optimal policies, we develop a dynamic programming approach which uses a novel state space which is general, enabling to handle arbitrary problem primitives, and that generalizes to finite horizon problems with non-stationary parameters. We analyze the class of monotone pricing policies and establish their suboptimality in general. Optimal policies are, in a typical scenario, characterized by nested sales, where the firm offers partial discounts throughout each cycle, offers a significant discount halfway through the cycle, with the largest discount offered at the end of the cycle. We further establish a form of equivalence between the problem of pricing for a stream of heterogeneous strategic customers and pricing for a pool of heterogeneous customers who may stockpile units of the product.