The effect of vertical integration on consumer price in the presence of inventory costs

This paper investigates the effect on consumer price of a vertical merger between a monopolist manufacturer and his retailer, when inventory costs are taken into consideration. We find that the traditional result (lower prices) remains true only when inventory costs are sufficiently small. The direction of the price change also depends on the market size.     

住房价格波动对自有住房家庭消费的区域异质性影响研究

为了解决八大类消费品价格数据不易得到的难题,本文构建投入产出价格模型,分别经验研究25个省(自治区和直辖市)住房价格同时变动不同幅度对八大类消费品价格的影响。25个省(自治区和直辖市)消费品价格变动幅度结果即为QUAIDS模型中的消费品价格变量。然后,本文采用CFPS2010数据,在QUAIDS模型中加入反映家庭所在地区的人口特征变量,研究住房价格波动对自有住房家庭消费的区域异质性影响。研究结果表明住房价格波动对自有住房家庭生存型消费需求区域异质性影响的财富效应显著,而对享受型和发展型消费需求区域异质性影响的挤出效应显著。在此基础上,本文进一步运用补偿变动研究住房价格波动对自有住房家庭福利的区域异质性影响。研究结果表明为了提高自有住房家庭的生活质量和促进社会的和谐稳定,政府应该把稳定东部地区住房价格放在首位。且当遇到如何优化家庭消费结构问题时,政府应该根据地区差异划分市场。     

Introduction of a second channel: Implications for pricing and profits

In this paper we study the optimal pricing strategies when a product is sold on two channels such as the Internet and a traditional channel. We assume a stylized deterministic demand model where the demand on a channel depends on prices, degree of substitution across channels and the overall market potential. We first study four prevalent pricing strategies which differ in the degree of autonomy for the Internet channel. For a monopoly, we provide theoretical bounds for these pricing strategies. We also analyze the duopoly case where an incumbent mixed retailer faces competition with a pure retailer and characterize price equilibria. Finally, through a computational study, we explore the behavior (price and profits) under different parameters and consumer preferences for the alternative channels.     

Designing coalition-based fair and stable pricing mechanisms under private information on consumers’ reservation prices

We model the relation between an aggregator and consumers joining a coalition to reduce the risk resulting from the unpredictability of their base load demand, as a Stackelberg game formulated as a mathematical bilevel program with private information on the consumers’ reservation prices. At the upper-level of the Stackelberg game, the aggregator optimizes his daily price profile so as to reach a net targeted profit which is the maximum value guaranteeing that no consumer will leave the coalition - to contract with a conventional retailer considered here as a fixed alternative - while meeting fairness criterion imposed by the cost-sharing mechanism. At the lower-level, the consumers are asked to provide in day ahead an estimate of their base load hourly demand profile and to schedule their shiftable loads depending on the price signal sent by the aggregator. We provide algorithms that determine the unique price profile and consumer shiftable load schedules as functions of the reservation price estimates. The Stackelberg game between the aggregator and the consumers being repeated for a period of time, the aggregator has the possibility to update his estimates of the reservation prices relying on a feedback function which depends on the percentage of activated loads. A randomized algorithm for consumers’ reservation price learning based on regret minimization is provided. For four cost-sharing mechanisms such as uniform allocation, stand-alone cost, Shapley value, separable and non-separable costs, we determine the closed form of the aggregator’s optimal net targeted profit guaranteeing the stability of the coalition. We also determine conditions guaranteeing the core non-emptiness and prove that for a profit-maximizing aggregator, the stand-alone cost is always preferable to the Shapley value, which coincides with the uniform allocation. Furthermore, the optimal size of the coalition - in terms of the aggregator’s profit - can be determined analytically when the Shapley value is implemented as cost-sharing mechanism. The results are illustrated on a case study where we show that there exists an optimal net targeted profit below which the consumers energy bill is lower when joining the aggregator than with the conventional retailer. Coalition dynamics is also analyzed numerically depending on the consumer inertia in their energy supplier choice process, for each cost-sharing mechanism.     

Integrating inventory control and a price change in the presence of reference price effects: a two-period model

Demand and procurement planning for consumer electronics products must cope with short life cycles, limited replenishment opportunities and a willingness to pay that is influenced by past prices and decreases over time. We therefore propose the use of an integrated pricing and inventory control model with a two-period linear demand model, in which demand also depends on the difference between a price-history-based reference price and the current price. For this model we prove that the optimal joint pricing/inventory policy for the replenishment opportunity after the first period is a base-stock list-price policy. That is, stock is either replenished up to a base-stock level and a list-price is charged, or it is not replenished and a discount is given that increases with the stock-level. Furthermore, we use real-world cell phone data to study the differences between an integrated policy and traditional sequential optimization, where prices are initially optimized based on the expected demand and ordering cost, and the resulting demand distribution is used to determine an optimal inventory policy. Finally, we discuss possible extensions of the model.     

考虑产品绿色度的双渠道供应链协调研究

本文在消费者需求受价格和产品绿色度影响的背景下,考虑制造商通过提高产品绿色度来扩大需求的情况以及双渠道需求之间的搭便车效应,构建了集中式和分散式博弈模型,并设计了收益共享和成本共担的联合契约协调供应链。研究发现:直销渠道价格和传统渠道价格都会随着产品绿色度的提高而上升,其中直销渠道价格的上升幅度随着搭便车消费者比例的增大而下降,传统渠道价格的上升幅度随着搭便车消费者比例的增大而加快;联合契约的引入能有效地降低直销渠道价格和传统渠道价格,提高产品绿色度和供应链总需求,使供应链总利润达到集中决策时的水平。     

低碳双渠道供应链的需求信息共享策略研究

在需求不确定环境下,研究考虑消费者低碳意识的双渠道供应链的需求信息共享策略。论文考虑由单个零售商和单个进行碳减排的制造商构成的两级双渠道供应链,构建三种情形的模型:信息不共享、信息共享和只有零售商作预测。通过三种情形下供应链中成员最优决策和利润的比较,得到需求信息共享策略对供应链的影响;并进一步研究消费者低碳意识等参数对供应链运营的影响。研究发现,需求信息共享未必使得供应链成员利润均提高,当制造商预测准确度优于零售商时,零售商会选择信息共享,制造商选择信息不共享情形;当零售商比制造商预测准确时,零售商会选择信息不共享的情形,而制造商会选择仅有零售商预测,此时制造商应采取一定的激励措施以获得零售商的预测信息;消费者低碳意识对批发价、零售价、单位产品减排量、供应链成员利润均产生正向影响。     

基于CCAPM框架的财富不平等与房价关系研究

运用含有房屋的CCAPM模型,在同时考虑房屋的消费属性与投资属性基础上分析了财富(或收入)分配对房价的影响;并通过数值模拟解释了我国房价高企的根源.结论表明,我国房价高企是财富分配不均所致,财富不均等程度加剧致使房屋从消费属性向投资属性转变进而推高了房价.文章也分析了财富分配对居民消费结构的影响,财富分配不均等程度加剧使得贫穷阶层的房屋消费比重下降而富裕阶层的投资性购房比重增加,进而拉高房价.文章最后指出,要调控我国当前房地产市场价格,必须从财富(或收入)分配入手,明晰产权.     

低碳双渠道供应链的需求信息共享策略研究

在需求不确定环境下,研究考虑消费者低碳意识的双渠道供应链的需求信息共享策略。论文考虑由单个零售商和单个进行碳减排的制造商构成的两级双渠道供应链,构建三种情形的模型:信息不共享、信息共享和只有零售商作预测。通过三种情形下供应链中成员最优决策和利润的比较,得到需求信息共享策略对供应链的影响;并进一步研究消费者低碳意识等参数对供应链运营的影响。研究发现,需求信息共享未必使得供应链成员利润均提高,当制造商预测准确度优于零售商时,零售商会选择信息共享,制造商选择信息不共享情形;当零售商比制造商预测准确时,零售商会选择信息不共享的情形,而制造商会选择仅有零售商预测,此时制造商应采取一定的激励措施以获得零售商的预测信息;消费者低碳意识对批发价、零售价、单位产品减排量、供应链成员利润均产生正向影响。     

需求弹性、抗衡势力与价格歧视

构建完全信息动态博弈模型,考察下游市场需求弹性、零售商抗衡势力对中间产品价格歧视的影响问题。结果表明,低弹性市场中零售商抗衡势力会削弱价格歧视,且改善低弹性市场消费者福利,而高弹性市场中零售商抗衡势力会增强价格歧视,且损害低弹性市场消费者福利。而高弹性市场消费者福利的变化则依赖于零售商的抗衡势力强度,只有当抗衡势力较强时,高弹性市场消费者福利才能够得到改善。     

Dynamic Pricing via Dynamic Programming<Superscript>1</Superscript>

This article specifies an efficient numerical scheme for computing optimal dynamic prices in a setting where the demand in a given period depends on the price in that period, cumulative sales up to the current period, and remaining market potential. The problem is studied in a deterministic and monopolistic context with a general form of the demand function. While traditional approaches produce closed-form equations that are difficult to solve due to the boundary conditions, we specify a computationally tractable numerical procedure by converting the problem to an initial-value problem based on a dynamic programming formulation. We find also that the optimal price dynamics preserves certain properties over the planning horizon: the unit revenue is linearly proportional to the demand elasticity of price; the unit revenue is constant over time when the demand elasticity is constant; and the sales rate is constant over time when the demand elasticity is linear in the price. ¹We acknowledge professor robert e. kalaba for initiating this work and suggesting solution methods.     

A stochastic delay financial model

We compute the logarithmic utility of an insider when the financial market is modelled by a stochastic delay equation. Although the market does not allow free lunches and is complete, the insider can draw more from his wealth than the regular trader. We also offer an alternative to the anticipating delayed Black-Scholes formula, by proving stability of European call option prices when the delay coefficients approach the nondelayed ones.

     

CIR框架下的投资组合效用微分博弈(英文)

建立了Cox-Ingersoll-Ross随机利率下的关于两个投资者的投资组合效用微分博弈模型.市场利率具有CIR动力,博弈双方存在唯一的损益函数,损益函数取决于投资者的投资组合财富.一方选择动态投资组合策略以最大化损益函数,而另一方则最小化损益函数.运用随机控制理论,在一般的效用函数下得到了基于效用的博弈双方的最优策略.特别考虑了常数相对风险厌恶情形,获得了显示的最优投资组合策略和博弈值.最后给出了数值例子和仿真结果以说明本文的结论.     

The value of information for price dependent demand

Predicting demand and determining optimal pricing are essential components of operations management. It is often useful to think in terms of the price elasticity of demand when reasoning about the demand curve. Firms wishing to invest in demand prediction and information gathering should reason about the relationship between the expected value of perfect information (EVPI) on demand and demand elasticity. Should firms pay more/less for information on demand if elasticity is high/low? Furthermore, when considering different product prices, correlation may exist between demand at different prices. Should firms pay more/less for information if the correlation between demand at different prices is high or low? This paper derives analytic and numeric results to answer these questions. We start with the assumption that demand is uncertain and follows a uniformly distributed band around a deterministic demand curve where the upper and lower bounds of the demand distribution vary with price. This formulation enables a closed form expression for EVPI that provides a useful benchmark. We find nuanced behavior of EVPI that depends on both the elasticity and the initial price preference. The EVPI approaches zero as elasticity increases (decreases) for a firm that initially prefers the low (high) price. Numerical results using the truncated normal and beta distributions relax assumptions about the uniform distribution and show EVPI is similar when the distribution variances are similar. Finally, we relax the assumption of perfect information and show the expected value of imperfect information (EVOI) follows similar patterns as EVPI with respect to demand elasticity.     

Market Price Calculations in Restructured Electricity Markets

In the traditional organisation of the power market, the generation Unit Commitment and Dispatch problem was solved as a cost minimisation problem. After deregulation of the electricity sector, the problem must be solved as a profit maximising problem. It is necessary to find feasible market prices. This is difficult, because simple marginal cost based prices not always cover startup and operation-independent costs, with the result that the generator would choose not to run with such prices. In this paper a market structure is proposed with a central market operator computing the market equilibrium for both energy and reserves, based on generator offers and consumer bids. It is shown that it is possible to find feasible market prices. Using a simple test system, it is shown that demand elasticity can have a profound impact on prices and generator revenues and profits during peaking hours.     

Pricing in an equilibrium based model for a large investor

We study a financial model with a non-trivial price impact effect. In this model we consider the interaction of a large investor trading in an illiquid security, and a market maker who is quoting prices for this security. We assume that the market maker quotes the prices such that by taking the other side of the investor’s demand, the market maker will arrive at maturity with the maximal expected utility of the terminal wealth. Within this model we provide an explicit recursive pricing formula for an exponential utility function, as well as an asymptotic expansion for the price for a “small” simple demand.     

Wait or buy? The strategic consumer: Pricing and profit implications

Using tools from operations research, airlines have, for many years, taken a strategic approach to pricing the seats available on a particular flight based on demand forecasts and information. The result of this approach is that the same seat on the same flight is often offered at different fares at different times. Setting of these prices using yield-management approaches is a major activity for many airlines and is well studied in the literature. However, consumers are becoming increasingly aware of the existence of pricing strategies used by airlines. In addition, the availability of airline travel pricing on the Internet affords consumers the opportunity to behave more strategically when making purchase decisions. The onset of the information age makes it possible for an informed consumer or a third party, such as a travel agent, to obtain demand information similar to that used by the airlines. In particular, it is possible for consumers or travel agents to purchase historical data or to obtain it by monitoring the seats that are available at various prices for a given flight. If a consumer understands the pricing strategy and has access to demand information, he/she may decide to defer purchase of a ticket because they believe that a cheaper seat may yet become available. If consumers were to make use of this information to make such strategic purchasing decisions, what would be the impact on airline revenues? The purpose of this paper is to investigate these impacts. This work indicates that use of standard yield management approaches to pricing by airlines can result in significantly reduced revenues when buyers are using an informed and strategic approach to purchasing. Therefore, when airlines are setting or presenting prices, they should investigate the effect of strategic purchasing on their decisions.     

需求不确定影响下政府为绿色产品提供补贴的最优策略

考虑需求不确定因素的影响,应用报童模型,分析了政府为刺激绿色产品消费应该如何给消费者或供应企业提供补贴的问题。研究结果表明:政府部门希望实现政府补贴支出最小化的情况下,应该选择为消费者提供固定额度补贴。最优补贴额度由需求不确定因素以及政府制定目标销量共同决定。政府希望企业提高绿色产品产量的情况下,价格折扣为其最优选择。对消费者来说,随着需求不确定性增加,企业确定的最优产量将会增加,政府为绿色产品提供的补贴额度也将会提高,消费者实际购买价格将会降低,在需求不确定性较高的情况下,消费者购买绿色产品比较有利。     

Optimal Advertising and Pricing in a Dynamic Durable Goods Supply Chain

Cooperative advertising is an incentive offered by a manufacturer to influence retailers’ promotional decisions. We study a dynamic durable goods duopoly with a manufacturer and two independent and competing retailers. The manufacturer, as a Stackelberg leader, announces his wholesale prices and his shares of retailers’ advertising costs, and the retailers in response play a Nash differential game in choosing their optimal retail prices and advertising efforts over time. We obtain the feedback equilibrium policies for the manufacturer and the retailers in explicit form for a linear demand formulation. We investigate issues, like channel coordination and antidiscriminatory legislation, and also study a case, when the manufacturer sells through only one retailer and the second retailer sells a competing brand.     

Dynamic inventory system with pricing adjustment for price-comparison shoppers

With numerous price-comparison websites and applications, consumers today are frequently conducting price-comparison shopping. As a result, retailers face an increasing challenge in predicting consumer demand and determining the optimal product price and inventory level accordingly. To address this issue, this paper proposes an inventory model with joint decisions of price and inventory to optimize the retailer's long-run average profit under price-comparison consumer shopping. We first formulate the demand arrival process for a retailer under price-comparison shopping to be affected by not only its own price but also its competitors'. Based on this demand arrival process, we then formulate the retailer's long-run average profit and derive properties of its optimal solution. Our model focuses on capturing the impact of price-comparison consumers on a retailer's optimal price and inventory decisions. In particular, we allow competitors' prices to affect the retailer's demand via two key factors: the manufacturer's suggested price and the variability of the outside lowest price. According to our results, when the suggested price increases, the retailer should lower its price to obtain more price-comparison customers from competitors, whereas when the variability of outside lowest price increases, the retailer should raise its price to increase per unit profit from nonprice-comparison customers.