Optimal bid-ask price strategies

Economic analysis has begun to focus on the implications of transaction costs to trading in capital assets. Specifically, the economics of market making and the price of liquidity has received considerable attention. This paper formulates the market maker's bid-ask price decision as a semi-Markov decision process with the reward being a function of expected return and risk. Risk is intimately related to dealer inventory and hence the solution of the analysis specifies bid-ask price strategies which are inventory dependent. Numerical examples indicate the market maker's optimal bid-ask prices will tilt around the ‘assets’ equilibrium price to control inventory as well as influence expected profit.     

Channel Strategies for Durable Goods: Coexistence of Selling and Leasing to Individual and Corporate Consumers

In durable goods markets, such as those for automobiles or computers, the coexistence of selling and leasing is common as is the existence of both corporate and individual consumers. Leases to corporate consumers affect the price of used goods on the second‐hand market which in turn affect the buying and leasing behavior of individual consumers. The setting of prices (or volumes) for sale and lease to individual and corporate consumers is a complicated problem for manufacturers. We consider a manufacturer who concurrently sells and leases a finitely durable good to both individual and corporate consumers. The interaction between the manufacturer and consumers is modeled as a dynamic sequential game, where each player seeks to maximize its own payoff over an infinite horizon. We study how the corporate channel substitutability of new goods and used goods and transaction costs in the second‐hand market affect the manufacturer's pricing decisions, consumer behavior, and social welfare in the retail market. Making a number of simplifying assumptions, including two‐period lifetime for the finitely durable goods, we consider Markov Perfect Equilibrium as the solution concept. We show that the manufacturer can maximize her profit by segmenting consumers according to their willingness to pay. Selling and leasing are the mechanisms used for price discrimination in the retail market. We show that as she leases a larger share of her production to the corporate consumer, (1) the manufacturer does not necessarily have to adjust the optimal selling price of new goods to individual consumers, and the volume of sales of new goods to individual consumers can stay the same; (2) the manufacturer does increase the retail lease price, and the number of individual leases decreases; (3) the net supply of used goods on the market increases, leading to a lower market price for used goods; and (4) more individual consumers are able to participate in the market, and their collective welfare or net utility improves. We also show that as production costs increase the manufacturer increases prices, reducing volumes across all channels. When transaction costs increase, the manufacturer reduces leasing in both corporate and retail channels.     

基于“搭便车”行为的双渠道供应链库存竞争和促销策略

本文建立了由一个制造商和一个零售商组成的双渠道供应链模型，研究了随机需求下"搭便车"行为和渠道间缺货替代行为对供应链库存竞争与促销决策的影响。结果表明：分散式决策下，网络渠道替代率越高，零售商的最优订购量越大，同样的零售渠道替代率越高，制造商会为网络渠道提供更多的库存；而"搭便车"行为对零售商与制造商订购量的影响则取决于渠道替代率的变化，但"搭便车"行为会降低零售商促销努力水平。数值分析发现：分散式决策下，零售商最优订购量随"搭便车"行为的增加而减少。然而制造商的最优库存量并非随着"搭便车"行为程度的增加而增加，不同的是制造商网络渠道最优库存量取决于市场需求对传统零售渠道促销努力水平的弹性系数，即制造商网络渠道最优库存量随"搭便车"行为的增加先增加后减少。通过比较发现在不同的"搭便车"行为程度、传统零售渠道替代率、网络渠道替代率下，集中式决策下供应链期望收益大于分散式决策下供应链期望总收益。     

Strategic Management of Distressed Inventory

It is well known that maximizing revenue from a fixed stock of perishable goods may require discounting prices rather than allowing unsold inventory to perish. This behavior is seen in industries ranging from fashion retail to tour packages and baked goods. A number of authors have addressed the markdown management problem in which a seller seeks to determine the optimal sequence of discounts to maximize the revenue from a fixed stock of perishable goods. However, merchants who consistently use markdown policies risk training customers to “wait for the sale.” We investigate models in which the decision to sell inventory at a discount will change the future expectations of customers and hence their buying behavior. We show that, in equilibrium, a single‐price policy is optimal if all consumers are strategic and demand is known to the seller. Relaxing any of these conditions can lead to a situation in which a two‐price markdown policy is optimal. We show using numerical simulation that if customers update their expectations of availability over time, then optimal sales limit policies can evolve in a complex fashion.     

Supply Chain Management of Fresh Products with Producer Transportation*

This article considers a class of fresh‐product supply chains in which products need to be transported by the upstream producer from a production base to a distant retail market. Due to high perishablility a portion of the products being shipped may decay during transportation, and therefore, become unsaleable. We consider a supply chain consisting of a single producer and a single distributor, and investigate two commonly adopted business models: (i) In the “pull” model, the distributor places an order, then the producer determines the shipping quantity, taking into account potential product decay during transportation, and transports the products to the destination market of the distributor; (ii) In the “push” model, the producer ships a batch of products to a distant wholesale market, and then the distributor purchases and resells to end customers. By considering a price‐sensitive end‐customer demand, we investigate the optimal decisions for supply chain members, including order quantity, shipping quantity, and retail price. Our research shows that both the producer and distributor (and thus the supply chain) will perform better if the pull model is adopted. To improve the supply chain performance, we propose a fixed inventory‐plus factor (FIPF) strategy, in which the producer announces a pre‐determined inventory‐plus factor and the distributor compensates the producer for any surplus inventory that would otherwise be wasted. We show that this strategy is a Pareto improvement over the pull and push models for both parties. Finally, numerical experiments are conducted, which reveal some interesting managerial insights on the comparison between different business models.     

The myth of price convergence under economic integration: A proposed explanation for the difference in food prices across European countries

Conventional globalization theory states that regional economic integration will precede price standardization across participating countries due to the increased buying power of large retail groups and parallel imports. The resulting price corridor should merely reflect differences in logistic costs and short-term, local competitive actions. Yet, this study uses panel data from 25 European countries to examine how hefty food and beverage price differentials between regions remained constant over the last decade. Income, store productivity, and market concentration all contribute to the explanation for regional price differences. These findings suggest that, contrary to straight-line globalization theory, large European retailers’ decisions can influence price convergence and maintain important price dispersion between economically integrated countries. We provide recommendations to enhance market integration.     

Joint Ordering and Pricing Strategies for Managing Substitutable Products

Starr and Rubinson (1978) develop a model to establish the relationship between product demand and relative prices. The notion of relative prices motivates us to consider a situation in which a retailer would either charge the same retail price for all products if he adopts a ‘fixed’ pricing strategy or charge different prices for different products if he adopts a ‘variable’ pricing strategy. In this paper, we develop a base model with deterministic demand that is intended to examine how a retailer should jointly determine the order quantity and the retail price of two substitutable products under the fixed and variable pricing strategies. Our analysis indicates that the optimal retail price under the variable pricing strategy is equal to the optimal retail price under the fixed pricing strategy plus or minus an adjustment term. This adjustment term depends on product substitutability and price sensitivity. We also present two different extensions of our base model. In the first extension, our analysis indicates that the underlying structure of the optimal retail price and order quantity is preserved when there is a limit on the total order quantity. The second extension deals with the issue of retail competition. Relative to the base case, we show that the underlying structure of the optimal retail price and order quantity is preserved in a duopolistic environment. Moreover, our analysis suggests that both retailers would adopt the variable pricing strategy at the equilibrium.     

Markdown Budgets for Retail Buyers: Help or Hindrance?

For many retailers, markdown decisions are taken by retail buyers whose compensation is based on sales revenue so their objective is to maximize it through the season. This implies that the buyers' objectives are not perfectly aligned with the overall profitability the firm. Many retailers set markdown budgets prior to the season to control margin erosion and increase profitability. Markdown budget constrains the buyers on the amount of discounts that they can apply on a given inventory of merchandise and sets a limit on the dollar value of markdowns for the season. While markdown budgets may be useful in preventing excessive discounts, they can have a detrimental effect on the buyers' ability to respond to poor market and remove distressed inventory. We investigate the effectiveness of this practice in aligning the incentives of buyers with that of the firm, and provide guidance on how these budgets should be established ahead of time. We consider a firm with a fixed inventory of a seasonable item, and a single chance to mark the price down. The retailer knows only the demand distribution at the beginning of the season, but the market information is revealed during the season to the buyer. We first characterize the buyer's markdown policy and understand the circumstances under which this can be different from the retailer's markdown policy. We use our model to determine the optimal markdown budget and quantify its effectiveness considering different factors such as the level of demand uncertainty, initial markup, and market's responsiveness to markdowns.     

Distributing a Product Line in a Decentralized Supply Chain

Although there is a rich literature on single product distribution in decentralized supply chains, the incentive problems that arise in distributing a product line have largely not been investigated. In practice, most manufacturers distribute a line of products with different features and qualities and not just a single product. Consider a manufacturer who distributes a product line through competing downstream retailers. In this setting, we investigate how and why the retailers' price and inventory decisions deviate from the centrally optimal decisions. Due to substitution between different product variants, as well as between different retailers, the incentive problems associated with distributing a product line are more complicated than that of distributing a single product. We characterize retailers' incentive distortions under a residual‐claimancy contract, and construct contracts that achieve channel coordination. We show that retail price floors or inventory buybacks, appropriately tailored to each product variant, are among the contracts that can achieve coordination. Using numerical simulations, we demonstrate how the optimal contract terms (such as wholesale prices and buyback prices) for each variant are influenced by the parameters of an underlying consumer choice model.     

Coordinating a Supply Chain System with Retailers Under Both Price and Inventory Competition

We investigate a supply chain system with a common supplier selling to downstream retailers who are engaged in both price and inventory competition. We establish the existence and uniqueness of the pure‐strategy Nash equilibrium for the retailer game and study how a supplier can coordinate the system to achieve the best performance. Our main conclusions are as follows: First, a buyback contract can be used to coordinate retailers competing on both price and inventory in a sense that optimal retail prices and inventory levels arise as the Pareto‐dominant equilibrium. With symmetric retailers, the system optimum arises as the unique symmetric equilibrium. Second, the particular type of competition experienced by retailers (price versus inventory competition) affects the characteristics of the contract. Specifically, strong price competition leads to a coordination mechanism with a positive buyback rate, where the supplier subsidizes retailers for leftover inventories; however, strong inventory competition leads to a negative buyback rate, where retailers are punished for overstocking. Using a linear expected demand function, we further explore the impact of system parameters on the coordination contract and the competitive equilibrium. We also find that the performance of the supplier's optimal contract is asymptotic to the system optimal coordination contract as competition becomes fierce.     

买方市场时效性产品的供应链弹性契约优化模型

在买方市场环境下,产品越来越具有时效性,寿命周期越来越短,为了规避风险,经销商往往不以实际预测量来订货。针对该问题,本文在已有的数量弹性契约研究的基础上,以激励相容理论和供应链理论为理念,引入回购契约的方法,提出了一个可以激励经销商的弹性契约优化模型,弥补了弹性契约的不足。用一个算例分析检验了该模型,结果表明,通过调节批发价格和返利比例来引导经销商的订货量趋势,当经销商期望利润最大的订货量与市场平均需求相等时,经销商会客观地估测未来需求量并报给制造商,同时制造商还在此基础上确定具体批发价格和返利比例以使自己利润最大化,从而使经销商与制造商共担供应链环节中的市场风险,并共同为优化整体供应链做出努力。     

Hedging through index-based price contracts in commodity-based supply chains

This paper studies the optimal hedging strategy of risk-neutral firms in supply chain settings. We model a retailer procuring goods through index-based price contracts from two commodity processors. The processors’ input commodity prices are random and correlated. The retailer faces price-sensitive demand curves; therefore, it controls product demand through retail pricing in the final product market. We characterize the optimal contracting terms for the processors and show that they prefer to hedge part of their exposure to the commodity price risk. The optimal contract for processor comprises a processing margin independent of the commodity price volatility and a hedge ratio that is a function of the commodity price volatility and the products substitution factor. We uncover a new rationale for hedging in settings where downstream firms have pricing power; both processors and the retailer benefit from the retailer’s pricing power when their margins are linked to input prices; an index-based price contract is a means to link the processors’ and the retailer’s margins. We further investigate how different market parameters affect the optimal hedge ratios and extend our model to settings with random market sizes and asymmetric substitution for final products.     

期货市场涨跌停板幅度设置的模型研究

涨跌停板幅度规定了期货交易中每日价格波动的范围,是涨跌停板制度的核心,过高的停板幅度不利于抑制价格的剧烈波动,过低的停板幅度又会妨碍期货市场价格发现功能的实现。尽管涨跌停板制度已被期货交易所广泛采用,但对如何设置合理的涨跌停板幅度的研究尚不成熟,实用性较差。本文在国内外学者研究的基础上,基于自履行合约理论和极值理论构建期货涨跌停板幅度设置模型。模型通过合约自履行条件下涨跌停板幅度与保证金水平的关系,获得合理的涨跌停板幅度,并应用极值理论修正了以往模型中期货收益率的正态分布假设,提高了实用性。最后,本文应用该模型对我国铜和天然橡胶期货涨跌停板幅度进行了实际测算。     

Promotion Planning and Supply Chain Contracting in a High–Low Pricing Environment

Demand forecast errors threaten the profitability of high–low price promotion strategies. This article shows how to match demand and supply effectively by means of two‐segment demand forecasting and supply contracts. We find that demand depends on the path of past retail prices, which leads to only a limited number of reachable demand states. However, forecast errors cannot be entirely eliminated because competitive promotions entail some degree of random (i.e., last‐minute) pricing. A hedging approach can be deployed to distribute demand risk efficiently over multiple promotional campaigns and within the supply chain. A retailer that employs a portfolio of forward, option, and spot contracts can avoid both stockouts and excess inventories while achieving the first‐best solution and Pareto improvements. We provide an improved forecasting method as well as stochastic programs to solve for optimal production and purchasing policies such that the right amount of inventory is available at the right time. By connecting a stockpiling model of demand with the supply side, we derive insights on optimal risk management strategies for both manufacturers and retailers in a market environment characterized by frequent price promotions and multiple discount levels. We employ a data set of the German retail market for a key generator of store traffic—namely, diapers.     

考虑策略性消费者的生鲜农产品定价和库存决策

消费者的策略性行为使零售商的生鲜农产品的定价和库存决策面临更大挑战。本文基于报童模型,综合考虑消费者的策略性行为,对生鲜农产品价值下降进行离散化处理。刻画策略性消费者的决策行为,构建零售商的单阶段和两阶段定价及库存决策模型,分析了产品价值剩余率对消费者行为、零售商最优定价、最优库存水平以及零售商利润的影响机理。研究发现,在单阶段模型中零售商最优价格和最优库存水平均随产品价值剩余率的递增而递增;而在两阶段模型中,第二阶段最优价格随价值剩余率的变化趋势可能存在阈值。     

The Dynamics of Domestic Gray Markets and Its Impact on Supply Chains

Gray markets are created by unauthorized retailers selling manufacturer's branded products. Similar to international gray markets, domestic gray markets are a growing phenomenon whose impact on supply chains is not clear. We consider a supply chain with one manufacturer and several authorized retailers who face a newsvendor problem and a domestic gray market. While a gray market provides an opportunity for retailers to clear their excess inventory (inventory‐correction effect), it also can be a threat to their demand (demand‐cannibalization effect). We first characterize the emerging equilibrium by assuming an MSRP environment. Comparing a decentralized and centralized system, we show that a wholesale pricing contract is quite efficient in a gray market environment; we explain the underlying mechanism and note some of the operational decisions that could hurt that efficiency. We show that the gray market price determines the degree of both the negative effects of demand‐cannibalization and the positive effects of inventory correction, which in turn determines the net impact of gray markets on the retailer's stocking choice and, ultimately, the manufacturer's profit. We then study the authorized retailers' problem as a price‐setting newsvendor. We observe that the gray market creates price competition between the authorized and unauthorized retailers, causing a drop in the primary market price. However, this price competition can be counteracted by the authorized retailers' stocking decision. Finally, we extend our model to consider the cases where the demand can be correlated across retailers.     

Inventory Sharing in the Presence of Commodity Markets

This study investigates the value of inventory sharing in the presence of spot and forward markets. We consider a multi‐period setting where two firms process a common commodity to meet stochastic demands. They can buy and sell the commodity through both the spot and forward markets. They can also share the commodity if one has leftover inventory while the other has excess demand. We first characterize the equilibrium strategies of the two firms. Our analysis reveals that in such a context, the value of inventory sharing is low when the forward price is directly used to value the sharing transactions. We then develop a structured trans‐shipment price scheme that uses a linear combination of the spot and forward prices. We show that this method can substantially increase the value of inventory sharing. Our analysis also reveals that in the presence of liquid spot and forward markets, the value of inventory sharing mainly results from the difference of the transaction costs, and it increases if the market in which firms operate becomes more competitive.     

Dynamic Pricing and Demand Estimation for a Single Unique Asset*

We address the situation of a firm that needs to dispose of a large, expensive asset (e.g., car, machine tool, earth mover, turbine, house, airplane), with or without a given deadline (and either known or unknown to the buyer). If a deadline exists, the asset is salvaged at a known value which may be zero, or even negative if there is a disposal cost. The asset has a known holding cost and may also have an initial nominal (undiscounted) price. The question is how, if at all, the price should be discounted as time progresses to maximize the expected proceeds. We use a dynamic recursion where each decision stage can be optimized based on classic economic monopoly pricing theory with a demand intensity function estimated from sales data, and show that the model is well‐behaved in the sense that the optimal price and optimal expected revenue monotonically decline as the deadline approaches. We test the model by comparing its optimal price pattern to the official pricing policy practiced at a used‐car dealer. We then extend the model to situations where the buyer knows the seller's deadline and thus may alter his behavior as the deadline approaches.     

Betriebsformen im Automobilhandel �C Resultate einer empirischen Untersuchung

Whereas most retail industries are characterized by a great diversity of competitive retail formats, the automotive industry largely relies on one single retail format, the authorized car dealer. However, both automobile manufacturers and car dealers are trying to expand sales activities for automobiles by implementing new and innovative retail formats. A focal point raised within this context is the question about (potential) customers?? expectations regarding retail formats in the automotive industry. To be able to analyze these expectations, eleven attributes which are specific to automotive retail formats have been derived from a literature overview. The resulting taxonomy of attributes has then been used to systematically identify current and future retail formats in this particular industry. Using an hierarchical adaptive conjoint analysis model, the attributes describing different automotive retail formats have being extensively analyzed. By developing this specific conjoint analysis model, it is possible to both analyze single attributes and entire retail formats regarding their impact on the automotive market as well as particular market segments.     

Promotional pricing and online business model choice in the presence of retail competition

Online promotional channels provided by competitive conventional reselling or novel agency selling e-tailers are widely used by firms to stimulate significant sales in retail. Compared with reselling, agency selling gives firms the power to directly control prices, but it involves costly platform fees. Given the unique features of the reselling and agency selling business models, we develop game theoretic models to explore how the firm and e-tailers, under consideration of retail competition, should strategically use these two business models in promotion. Our analysis generates several insights. We demonstrate that the agency selling model might lead to a higher price than the reselling model, a result contrary to the double marginalization. We also present that without retail competition, there exists a “win-win” promotional strategy, which is also a Pareto-optimal situation for the firm and e-tailer. Specifically, this situation occurs when the e-tailer is in the reselling model under a moderate inventory level or in the agency selling model with a moderate platform fee under a high inventory level. However, under conditions of competitive e-tailers, both e-tailers being in the reselling model is no longer a “win-win” promotional strategy, while the hybrid selling model, i.e., one in the reselling model and the other in the agency selling model, can generate a Pareto improvement. In addition, low platform fees, customers’ high price sensitivities, increased selling costs or decreased competitive intensities will drive supply chain participants to seek direct pricing power in the agency selling model.