STOCHASTIC COST-VOLUME-PROFIT ANALYSIS WITH A LINEAR DEMAND FUNCTION

In this paper we incorporate a linear demand function to model the price-volume causal relationship into stochastic cost-volume-profit (CVP) analysis. We assume that the objective function is to maximize expected profit; other objective functions are also discussed and compared. A linear stochastic model follows from which probabilistic statements can be easily obtained if the random variables are assumed to be multivariate normal. The basic framework is shown to be a special case of project value maximization where project value is the cash flow of the project discounted for time and risk according to the capital asset pricing model. Moreover, an intertemporal extension that considers inventory is developed. In summary, a new approach to stochastic CVP analysis that incorporates the management decision process in an uncertain environment is developed.     

Location models for ceding market share and shrinking services

New location models are presented here for exploring the reduction of facilities in a region. The first of these models considers firms ceding market share to competitors under situations of financial exigency. The goal of this model is to cede the least market share, i.e., retain as much of the customer base as possible while shedding costly outlets. The second model considers a firm essentially without competition that must shrink it services for economic reasons. This firm is assumed to close outlets so that the degradation of service is limited. An example is offered within a competitive environment to demonstrate the usefulness of this modeling approach.     

A ONE-PERIOD STOCHASTIC INVENTORY PROBLEM WITH A LUMP-SUM PENALTY COST

This paper presents an inventory problem related to the one-period stochastic inventory (or “newsboy”) problem. In this problem, the firm has to decide how much product to order to meet a random one-period demand. The version of the problem presented is novel in two respects. First, demand is explicitly permitted to be negative, and second, the penalty (or shortage) cost is assumed to be independent of the magnitude of the shortage. This situation is shown to change the form of the cost function and to complicate the determination of optimal policies. The form of the optimal policy is developed, and two example problems are presented in some detail.     

Technical Note – Pricing Below Cost Under Exchange‐Rate Risk

Pricing below cost is often classified as “dumping” in international trade and as “predatory pricing” in local markets. It is legally prohibited from practice because of earlier findings that it leads to predatory behavior by either eliminating competition or stealing market share. This study shows that a stochastic exchange rate can create incentives for a profit‐minded monopoly firm to set price below marginal cost. Our result departs from earlier findings because the optimal pricing decision is based on a rational behavior that does not exhibit any malicious intent against the competition to be considered as violating anti‐trust laws. The finding is a robust result, because our analysis demonstrates that this behavior occurs under various settings such as when the firm (i) is risk‐averse, (ii) can postpone prices until after exchange rates are realized, (iii) is capable of manufacturing in multiple countries, and (iv) operates under demand uncertainty in addition to the random exchange rate.     

公司价值的随机优化模型

本文研究了净现金流为随机过程情况下的企业价值,并建立了企业价值的随机优化模型。探讨了在一定的风险水平和其它相关约束条件下,确定企业的资本结构、企业债务的承担能力等,使得公司价值最大化,并应用于实际项目中。     

Seeking Closure: Competition in Complementary Markets*

When offering a product that has a complementary product in a different market, a firm must consider the interdependence between the complementary products as well as the competition within markets. If the firm participates in both markets, the balancing act becomes even more challenging. This article provides insights about strategies in this latter setting: when should the firm seek to keep its products closed to competing complementary products, and when would the firm be better off by accepting a common standard? To address these questions, we employ standard game theoretic analysis to a simple spatial model that captures aspects of both intermarket externalities and intramarket competition. We find that if a firm participates in both markets and chooses a closed standard, it achieves lower profits compared to an open standard, but gains greater market share. Surprisingly, we find that customers are better off when standards are kept closed.     

Investing in a Shared Supplier in a Competitive Market: Stochastic Capacity Case

When firms invest in a shared supplier, one key concern is whether the invested capacity will be used for a competitor. In practice, this concern is addressed by restricting the use of the capacity. We consider what happens when two competing firms invest in a shared supplier. We consider two scenarios that differ in how capacity is used: exclusive capacity and first‐priority capacity. We model firms' investment and production decisions, and analyze the equilibrium outcomes in terms of the number of investing firms and capacity levels for each scenario; realized capacity is a stochastic function of investment levels. We also identify conditions under which the spillover effect occurs, where one firm taps into the other firm's invested capacity. Although the spillover supposedly intensifies competition, it actually discourages firms' investment. We also characterize the firms' and supplier's preference about the capacity type. While the non‐investing firm always prefers spillovers from the first‐priority capacity, the investing firm does not always want to shut off the other firm's access to its leftover capacity, especially when allowing spillover induces the other firm not to invest. The supplier's preference depends on the trade‐off between over‐investment and flexibility.     

A Two-Period Repeated Game Advertising Investment Model for Oligopolistic Markets with an Application to the Beer Industry*

This paper proposes a simple analytical model of advertising competition in oligopoly markets. The widely used log-log sales response function underlies the model specification. Advertising carryover effects are assumed to persist for one period following the period in which the expenditure occurs. Firms are assumed to be engaged in a repeated competitive game in which in every period advertising levels are set such that they maximize current and next period (i.e., two-period) profits. A Nash equilibrium solution is sought for the game. Compared with previous empirical studies of advertising competition in a game theoretic framework, the proposed model offers the following advantages: (1) oligopoly, not duopoly, markets are analyzed; (2) industry sales is allowed to vary over time as a function of advertising expenditures; (3) non-zero discount rates are used for the players. An empirical application is provided using data from the beer market on sales and advertising expenditures of Anheuser-Busch and Miller Brewing. Comparisons are provided with policies that ignore the dependence of next period profits on current advertising levels, reaction function strategies and spending levels obtained from a market share game. Extension of the model formulation to multiple marketing instruments is briefly discussed.     

Markov Perfect Industry Dynamics With Many Firms

We propose an approximation method for analyzing Ericson and Pakes (1995)‐style dynamic models of imperfect competition. We define a new equilibrium concept that we call oblivious equilibrium, in which each firm is assumed to make decisions based only on its own state and knowledge of the long‐run average industry state, but where firms ignore current information about competitors' states. The great advantage of oblivious equilibria is that they are much easier to compute than are Markov perfect equilibria. Moreover, we show that, as the market becomes large, if the equilibrium distribution of firm states obeys a certain “light‐tail” condition, then oblivious equilibria closely approximate Markov perfect equilibria. This theorem justifies using oblivious equilibria to analyze Markov perfect industry dynamics in Ericson and Pakes (1995)‐style models with many firms.     

排污权价格随机情境下基于CVaR 准则的企业生产决策

面向排污权市场价格随机情境,通过提取理性企业在产品生产、污染削减、排污权交易等方面决策行为与排污权市场价格之间的关联性,推导了排污权市场价格随机情境下的企业随机利润函数;基于条件风险价值(CVaR)风险度量准则,推导了任意置信水平下随机利润的风险价值(VaR)解析表达式,建立了不同排污权预期价格和置信水平下的CVaR测度模型;基于此,深入论证了给定置信水平下实现随机利润CVaR最大化的企业最优决策及其特征,并系统分析了外部情景要素变动对最优决策及其优化结果的影响。主要结论表明：在企业分别作为排污权出售者与购买者两种情况下,随机利润CVaR的具体测度因利润下行风险存在的排污权市场价格区间不同而存在差异;基于CVaR准则,考虑决策风险的最优决策受到决策主体置信水平、排污权初始配额、排污权市场价格均值及标准差等多因素的复杂影响,进而系统性地偏离风险中性最优决策,并表现出风险规避特征;通过算例分析对所得结论进行全面验证,进一步说明该模型能较好地刻画与反映排污权交易企业决策风险及其现实决策行为。     

Replacement Decisions for Potentially Hazardous Substances

As public awareness of environmental hazards increases, a growing concern for corporations is the potential negative environmental impact of their products and the chemicals these products contain. In this study, we analyze the optimal decisions of a firm when a substance within its product is identified as potentially hazardous. Although the substance is not currently regulated, regulation may occur in the future. Therefore, the firm must devise a strategy for the development and implementation of a replacement substance. In an environment where replacement costs can be millions of dollars, regulation is uncertain, and both consumer and non‐governmental organization pressures exist, a carefully developed plan that balances costs and risks is critical for a firm. Our results demonstrate that as long as a threat of regulation exists, a firm should always dedicate resources toward developing a replacement substance. However, it is not always optimal for a firm to implement a developed replacement. Regarding competitive dynamics, we find that competition between firms can offset a low chance of a shift in consumer perception about a substance and compel firms to replace; however, competition can lead to inefficient outcomes in which firms incur avoidable costs to implement ahead of potential regulation.     

产权结构、企业类型与企业行为——日本电气机械产业上市企业的实证研究

给出 S型、O型和 M型三种企业类型的分类标准 ,而后对日本电器机械产业的 1 41家企业 90年代的产权结构和企业行为进行了实证研究 .研究结果表明 :(1 )尽管三类企业在产权结构上存在显著差异 ,但三类企业利润率均值不存在显著差异 ;(2 )三类企业的管理者行为存在显著差异 .M型企业的管理者追求企业规模的最大化 ,S型企业的管理者追求资本周转率的最大化 ,O型企业的管理者追求销售利润率的最大化     

How Should a Firm Manage Deteriorating Inventory?

Firms selling goods whose quality level deteriorates over time often face difficult decisions when unsold inventory remains. Since the leftover product is often perceived to be of lower quality than the new product, carrying it over offers the firm a second selling opportunity, a product line extension to new and unsold units, and the ability to price discriminate. By doing so, however, the firm subjects sales of its new product to competition from the leftover product. We present a two period model that captures the effect of this competition on the firm's production and pricing decisions. We characterize the firm's optimal strategy and find conditions under which the firm is better off carrying all, some, or none of its leftover inventory. We also show that, compared to a firm that acts myopically in the first period, a firm that takes into account the effect of first period decisions on second period profits will price its new product higher and stock more of it in the first period. Thus, the benefit of having a second selling opportunity dominates the detrimental effect of cannibalizing sales of the second period new product.     

SOME STATISTICAL ISSUES IN THE ESTIMATION OF A SIMPLE COST-VOLUME-PROFIT MODEL*

This paper presents point and interval estimators of both long-run and single-period target quantities in a simple cost-volume-profit (C-V-P) model. This model is a stochastic version of the “accountant's break-even chart” where the major component is a semivariable cost function. Although these features suggest obvious possibilities for practical application, a major purpose of this paper is to examine the statistical properties of target quantity estimators in C-V-P analysis. It is shown that point estimators of target quantity are biased and possess no moments of positive order, but are consistent. These properties are also shared by previous break-even models, even when all parameters are assumed known with certainty. After a test for positive variable margins, Fieller's [6] method is used to obtain interval estimators of relevant target quantities. This procedure therefore minimizes possible ambiguities in stochastic break-even analysis (noted by Ekern [3]).     

A Contingent Claims Model of Corporate Pension Obligations*

This study develops a contingent claims model for valuing the implicit market value of the pension claim associated with defined benefit pension plans. In this model, the firm issues pension, debt, and equity claims. These claims have joint access to two underlying portfolios: corporate and pension. The changes in the market values of these two portfolios are assumed to follow a joint lognormal diffusion process. By imposing terminal boundary conditions implied by Employment Retirement Income Security Act (ERISA) rules and the pension insurance provisions of the Pension Benefit Guaranty Corporation (PBGC) on the partial differential equation, a solution for the pension value is obtained. This quasi-market measure of the value of the pension claim may be represented by a portfolio consisting of four components: (1) a risk-free discount bond with face value equal to promised pension benefits; (2) a short put on pension assets with exercise price equal to pension benefits; (3) a long call on 30 percent of corporate assets with exercise price equal to the face value of secured corporate debt; and (4) a short call on 30 percent of corporate assets with a stochastic exercise price which depends on the terminal value of the pension fund. A numerical example using 1992 and 1993 financial statement data from six major U.S. corporations is provided. This example illustrates the usefulness of the model's prediction and the potential effect of theoretical pension values on corporate debt-equity ratios.     

Competition network as a source of competitive advantage: The dynamic capability perspective and evidence from China

The search for competitive advantage is the defining inquiry of strategic management research. In this study, we draw on the dynamic capability lens to develop a counterintuitive view that positions competitors of a firm as an important source of competitive advantage. We argue that a firm's competitors form a competition network from which it can collect information about innovative ideas, product market, and related industries. Such information helps it calibrate market opportunities, update the resource base, and, eventually, strengthen its competitive advantage. This positive effect of competition network on competitive advantage will reasonably be contingent upon the proactive information search by the firm. The empirical results based on the survey data of 631 Chinese firms strongly support our theoretical model. This study identifies another distinctive source of competitive advantage than industry context or organizational resources as well as advancing our understanding of competition network.     

COST-VOLUME-PROFIT ANALYSIS IN STOCHASTIC PROGRAMMING MODELS

This paper applies mathematical programming to cost-volume-profit (CVP) analysis under contribution margin uncertainty. Three CVP probabilistic chance-constraint models based on various safety-first criteria for decisions under uncertainty are presented and compared. It is shown that a break-even segment of the mean-standard deviation frontier is a set of optimal solutions for the proposed models. An operational parametric quadratic programming (QP) model is constructed, and the efficiency frontier is generated. The procedures for locating an optimal solution on the efficiency frontier are then presented. The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.     

竞争环境下客户服务投入对企业利润影响的均衡分析

客户服务投入是企业吸引新顾客和维持现有顾客的重要手段之一。然而,服务投入究竟是否能给企业带来价值？对于这一问题,业界和学界都没有明确的答案。本文通过建模的方法研究在竞争的市场环境下,固有的市场因素对客户服务投入价值的影响。研究发现,服务竞争的市场均衡结构是两家厂商都投入客户服务。服务投入给企业带来的价值随着产品差异度的提高而提高,随着厂商自身市场份额的增加而增加。即,在产品差异度高的市场,服务投入更容易给企业带来价值。而在集中度高的市场,服务投入更容易给市场份额大的企业带来价值。     

Horizontal capacity sharing between asymmetric competitors

A common practice to address supply-demand mismatch is capacity sharing, whereby a firm possessing excessive capacity collaborates with its rival that is incapable of meeting captured demand. However, previous studies have seldom focused on the role of capacity sharing in shaping market competition. In this paper, we investigate coopetition strategies under two widely used contracting mechanisms of capacity sharing, namely, the linear transfer payment contracting mechanism and the revenue sharing contracting mechanism. In a model of two competitors with asymmetric capacities, we find that the larger firm becomes less aggressive in market competition and benefits more from capacity sharing. Competition between the firms will be softened by capacity sharing. Moreover, competition intensity is more likely to be higher under the linear transfer payment contracting mechanism than under the revenue sharing contracting mechanism, while it may be lower if the total capacities are slightly larger than the aggregate demand.     

The Effect of Competition on the Efficient–Responsive Choice

In determining their operations strategy, a firm chooses whether to be responsive or efficient. For firms competing in a market with uncertain demand and varying intensity of substitutability for the competitor's product, we characterize the responsive or efficient choice in equilibrium. To focus first on the competitive implications, we study a model where a firm can choose to be responsive at no additional fixed or marginal cost. We find that competing firms will choose the same configuration (responsive or efficient), and responsiveness tends to be favorable when demand uncertainty is high or when product competition is not too strong. Intense competition can drive firms to choose to be efficient rather than responsive even when there is no additional cost of being responsive. In such a case, both firms would be better off by choosing to be responsive but cannot credibly commit. We extend the basic model to study the impact of endogenized production timing, multiple productions and product holdback (or, equivalently, postponed production). For all these settings, we find structurally similar results; firms choose the same configuration, and the firms may miss Pareto‐improvements. Furthermore, through extensions to the basic model, we find that greater operational flexibility can make responsiveness look less attractive in the presence of product competition. In contrast to our basic model and other extensions, we find it is possible for one firm to be responsive while the other is efficient when there is either a fixed cost or variable cost premium associated with responsive delivery.