Price or quantity setting under uncertain demand and capacity constraints: An examination of the profits

This article considers price formation and quantity setting of a capacity-constrained risk-neutral firm facing uncertain demand. It is shown that the optimal price of a price-setting risk-neutral monopolist decreases with demand uncertainty. With a strictly convex demand function expected profits increase with uncertainty for a quantity-setting monopolist whereas expected profits decrease for a price-setting monopolist. Furthermore, similar results on the effect of uncertainty are derived for a differentiated goods industry.     

策略性采购联盟、集体谈判与最优贸易政策选择——基于广义Cournot-Nash谈判函数的分析

文章发展了一个关于由本国企业组成的中间品策略性采购联盟与外国垄断性供给者进行集体谈判的模型一—该模型以中国的制造业外包服务,即出口加工贸易实践为基础,其中,中间品的采购价格与数量通过有效的Nash谈判过程同时决定。当采购联盟的效用函数的数量弹性高于（低于）价格弹性,则该联盟的偏好为数量（价格）导向的。文章证明：（1）当本国与外国的中间品与最终产品贸易具有互补性时,政府贸易政策调整的价格、数量以及福利效应是不确定的,它们依存于本国采购联盟的偏好、最终产品需求曲线的弹性与曲率、外国企业的技术以及生产专业化程度;（2）政府贸易政策的干预功能与企业策略性联盟的自主调整功能存在重叠与冲突。     

THE DETERMINANTS OF THE QUANTITY‐QUALITY BALANCE IN MONOPOLY*

This paper describes how a monopolist manipulates the balance of quantity and quality in order to increase revenue when its customers treat quantity and quality as substitutes. This ‘skewing’ of quality depends on the characteristics of customer's demand for quality. Customers differ in demand for quality, because they differ in either (i) their preferences and/or (ii) their time cost per unit. The monopolist is constrained to supply the same quality of good to all customers. The price and quality per unit are described under the assumption the monopolist (i) profit maximises; (ii) maximises social welfare subject to a profit constraint. The determinants of the skewing of quantity and quality are found under third‐degree price discrimination and uniform pricing.     

Natural monopoly and differential pricing

Under uniform pricing a monopolist cannot make a positive profit in equilibrium. I analyze how differential pricing can be exploited by a natural monopolist to deter entry when entry is costless. In a two-stage game with price competition before quantity competition I show that the incumbent firm can deter entry and make a positive profit in equilibrium. The incumbent sets two different prices, the low price to deter entry and the high price to generate profit. Entry is not possible because of scale effects. If dumping is allowed for all firms no positive profits are realizable, but welfare is reduced. I show that for some parameter values the incumbent is forced to engage in a stunt (i.e., set a negative low price) to keep entrants out.     

RISKY PRODUCTION WITH EX-ANTE PRICES UNDER MONOPOLY ANALYTICAL AND SIMULATION RESULTS

This paper concerns the case of a monopolist facing multiplicative uncertainty in demand. Karlin and Carr (1962), henceforth KC, show that, when price and production are both chosen ex ante , the uncertainty price exceeds the certainty price. They also give a sufficient condition under which the firm locates above the certainty demand curve, but they do not consider the effect on the output level. In this note we replicate the KC results and then go further. In the special case that the price elasticity of certainty demand is constant, and the probability distribution for the uncertainty parameter in the demand function is uniform, output is unambiguously lower under uncertainty, and KC's condition for the firm to locate above the certainty demand curve can be strengthened to one that is both necessary and sufficient. The robustness of these results is tested under less stringent assumptions on demand, abandoning symmetry for a lognormal distribution of the uncertainty parameter. Simulation confirms that the results hold up, and also determines the effects upon the firm's decisions of an increase in demand uncertainty.     

THE POTENTIAL FOR SHORT‐RUN SHIFTING OF A CORPORATE PROFITS TAX

Can the owners of a firm shift a corporate profits tax to consumers? Not in the short run if the tax is stated as a proportion of profits and the firm is a profit maximizer. But what if the firm wishes to pursue a strategy other than profit maximization, say revenue maximization subject to a profit constraint? Under such a condition the firm's reaction to a tax or tax increase might be a price rise that captures part of the foregone profits. We show that firms which operate at a point on their demand curve that differs from profit maximization have an incentive to raise price in response to the tax – and that high cost firms have a greater incentive to raise price than do low cost firms. Our empirical analysis of the US beer industry confirms this finding, and sheds light on the Krzyzaniak–Musgrave analysis of the 1960s which suggested that the corporation income tax produced significant short‐run shifting.     

Dynamic control of a monopolist’s product and process innovation with reference quality

ABSTRACT

Our main purpose is to investigate the dynamic control problem of a monopolist’s product and process innovation under reference quality. The main features of this article are: (i) a monopolist dealing with customer behaviour in the spirit of the principle of behaviour economics determines the product price, and carries out the activities of product and process innovation; (ii) the consumers’ demand depends on price, product quality and reference quality, and adopts an additive separable demand function form. Our main results show that under the cases of the monopolist optimum and the social planner optimum, (i) there exists an unique stable, which is a saddle-point steady-state equilibrium; (ii) the change rates of the monopolist’s investments in product and process innovation are increasing with the reference quality, while the monopolist’s steady-state investments in product and process innovation are decreasing with the reference quality; (iii) as the memory parameter increases with other parameters kept constant, it is very likely that the monopolist’s investment in process innovation be greater than the investment in product innovation; and (iv) the social incentive towards both investments in product and process innovation is always larger than the private incentive characterizing the profit-seeking monopolist.     

Choosing Price or Quantity? The Role of Delegation and Network Externalities in a Mixed Duopoly

This paper considers a differentiated goods managerial mixed duopoly composed of one social welfare‐maximising public firm and one profit‐maximising private firm. We model the firm choice of the strategic contract. We find that when the strength of network effects is sufficiently strong, the price competition can become the unique equilibrium market structure. Furthermore, we show that there exists an area of the degree of product differentiation and the strength of network effects such that the situation wherein the public firm chooses its price contract whereas the private firm chooses its quantity contract can become the unique equilibrium structure.     

Competition and regulation with product differentiation

We consider a market for differentiated products, where one good is supplied by a regulated monopolist and competitive firms operate in an unregulated segment. In this setting we investigate the issue of whether to allow the monopolist to diversify into the unregulated segment by owning a competitive firm. Under asymmetric cost information, if goods are substitutes a diversified monopolist, which exaggerates its costs in the regulated segment to charge a higher regulated price, stimulates the demand for the competitive affiliate. This strengthens the firm??s incentive to inflate costs, since doing so generates a positive informational spillover to its profits in the competitive segment. Consequently, a regime of separation, which prevents the firm from operating in the competitive segment, is welfare-enhancing. Conversely, with complements, cost exaggeration in the regulated monopoly reduces the demand and harms profits in the competitive segment, and allowing the monopolist to diversify into the competitive segment therefore generates countervailing incentives, which weaken the firm??s interest in cost manipulation and improve social welfare.     

On complex dynamics of monopoly market

The equilibrium state of a bounded rational monopolist model is studied in this paper. It is assumed that the entire demand function is considered based on some market experiments to produce a quantity which maximizes profit. The stability of equilibrium state of the model is discussed. In addition, some complex dynamical behaviours of the model are illustrated.     

RETAIL PRICE REGULATION AND THE OPTION TO DELAY

ABSTRACT ** :  This paper examines a two-period model of an investment decision in a network industry characterized by demand uncertainty, economies of scale and sunk costs. In the absence of regulation we identify the market conditions under which a monopolist decides to invest early as well as the underlying overall welfare output. In a regulated environment, we consider a monopolist who faces no downstream (final good) competition but is subject to retail price regulation. We identify the welfare-maximizing regulated prices when the unregulated market outcome is set as the benchmark. We show that if the regulator can commit to ex post regulation – that is, regulated prices that are contingent to future demand realization – then regulated prices that allow the firm to recover its total costs of production are welfare-maximizing. Thus, under ex post price regulation there is no need to compensate the regulated firm for the option to delay that it foregoes when investing today. We argue, however, that regulators cannot make this type of commitment and, therefore, price regulation is often ex ante – that is, regulated prices are not contingent to future demand. We show that the optimal ex ante regulation, and the extent to which regulated prices need to incorporate an option to delay, depend on the nature of demand uncertainty.     

MONOPOLY POWER AND DOWNWARD PRICE RIGIDITY UNDER COSTLY PRICE ADJUSTMENT

A method of 'backward deduction' is used to analyse the decisions of a firm, setting price and quantity before demand observations are made, with the option to adjust price at a cost after demand is observed. It is shown for such a firm that the events of (1) downward price rigidity; (2) overproduction; and (3) a high degree of monopoly power are closely related. The paper distinguishes itself from the previous literature on costly price adjustment in its treatment of disequilibrium situations and focus on monopoly power in relation to price rigidity. The main results are obtained for a linear demand curve and a uniform demand distribution.     

TAXES ON PAYROLL, REVENUES AND PROFITS IN THREE MODELS OF COLLECTIVE BARGAINING

Variations in company taxes are analysed for a right-to-manage model, an efficient bargaining setting and a seniority approach. Taxes cannot be shifted forward by the risk-neutral firm. Alternative income and bargaining power are allowed to vary with taxes. Employing asymmetric Nash solution it is found that changes in a payroll, revenue or profit tax can have differing implications for labour demand curve models and efficient bargaining solutions. This distinction might provide a novel basis for empirical work. Variations in bargaining power and-within a labour demand curve setting-the union's objective function do not change results.     

Biased managers as strategic commitment: The relative profit approach

This paper analyzes a duopolistic model wherein each firm׳s owner can hire a biased manager for strategic reasons. We focus on the situation wherein each firm׳s owner evaluates the performance of her/his manager on the basis of her/his relative profit, which is equal to the weighted sum of her/his absolute profit and the absolute profit of her/his opponent firm. We show that in both price-setting and quantity-setting competitions, the owners of the two private firms employ aggressive managers rather than absolute profit maximizing managers regardless of the degree of importance of each firm׳s relative performance. Furthermore, in both the price competition and the quantity competition, as the degree of importance of each firm׳s relative performance increases, we show that the firms׳ owners tend to hire more aggressive managers when the degree of importance of each firm׳s relative performance is sufficiently low, whereas in both the price competition and the quantity competition, the firms׳ owners tend to hire less aggressive managers otherwise. Thus, in both the price competition and the quantity competition, the type of each firm׳s manager is not monotone with respect to the degree of each firm׳s relative performance. Thus, in both the price competition and the quantity competition, we find that the change in the optimal type of manager hired by each firm is non-monotone against the change of competitiveness in the market with the increase in the degree of importance of each firm׳s relative performance.     

PHILANTHROPY AS A CORPORATE STRATEGY*

An attempt to formulate the implications of corporate “philanthropy” by private firms is made in this paper. By philanthropy we mean the public activities of private agents, which are not carried out through the ordinary price mechanism. From the point of view of social roles, corporate philanthropy complements the price mechanism as do the government sector, non-profit organizations and individuals. Here we formulate corporate philanthropy as the product of two possible motivations: either as a means of long-term profit maximization, or as a direct element in an objective function of a firm.     

Raising rivals' costs: The entry of an upstream monopolist into downstream markets

A regulated upstream monopolist provides an input to firms in a downstream market. If the monopolist enters the downstream market, a natural concern is that it will act so as to raise its downstream rivals' costs. An offsetting incentive is that a higher downstream price will reduce demand for the input, which reduces the monopolist's profit. Conditions under which one incentive dominates the other are derived. The monopolist may desire to lower its downstream rivals' costs rather than raise them. These findings suggest that regulatory policy towards such downstream entry should not focus exclusively on the ability to discriminate.     

Relative standards: A positive and normative analysis

The paper considers relative standards which limit the level of emissions per unit of output. The representative firm is characterized by a cost function describing the actual production process, a separate abatement technology, and the fact that (gross) emissions are proportional to output. At first, the implications of a relative standard and of its marginal change for a single firm are examined. It is shown that the standard cannot be replaced by a corresponding tax. Afterwards a positive analysis is performed for an industry consisting of identical firms under perfect competition. Comparative statics are used to analyze the impacts of changes in the relative standard in a short-run and long-run equilibrium. It turns out that the standard always possesses a price effect. Moreover the relevant factors which govern price, quantity, and profit changes are revealed. Then the paper characterizes the optimal standard for the same framework. A main result is that the first-best allocation can never be obtained by means of a relative standard, even if firms are identical. The influence of the demand and supply side on an optimal standard can be demonstrated since the underlying model is simple and transparent. The resulting market price is compared to social marginal costs. Finally the investigation is extended to monopoly and symmetric oligopoly.     

Socially responsible firms and endogenous choice of strategic incentives

In this paper we are analyzing a mixed quantity-setting duopoly consisting of a socially concerned firm and a profit-maximizing firm. The socially concerned firm considers one group of stakeholders in its objective function and maximizes its profit plus a share of consumer surplus. Both firms have the option to hire a manager who determines the production quantity on behalf of the firm's owner. We find that in the subgame-perfect equilibrium of this game both firms hire a manager and delegate the production choice. If the unit production costs of the firms are similar, then the socially concerned firm has a higher market share and even higher profit. Interestingly, we observe that the relationship between the share of consumer surplus taken into account by the socially concerned firm and its profit is non-monotonic. As the share increases, the socially concerned firm's profit first increases and then decreases. The conclusion is that it pays off to take stakeholder interests into account, but not too much.     

随机需求下考虑排污权交易的制造商最优生产与定价联合决策研究

在考虑排污权交易的情况下,研究了具有价格依赖需求特征的排污制造商如何进行单周期生产和定价联合决策的问题。研究表明:制造商的最优生产量和最优定价存在且唯一;制造商的最大期望利润既是排污权交易一级市场排污权交易价格的减函数,也是二级市场排污权交易价格的减函数(当最优生产量大于排污上限时)或增函数(当最优生产量小于排污上限时);与不考虑排污权交易的情况相比,排污权交易二级市场的存在可以促进制造商进行减排投资、提高排污生产效率;由制造商决策对排污权交易政策的反应函数可知,排污权交易中的各种政策因素和市场因素都会对制造商的生产经营决策产生显著影响。     

Differentiable Technology,the Curvature of the Profit Function,and the Response of Supply to Own-Price Changes

The author establishes a property of supply for a competitive firm: Assuming differentiability of the production frontier, linearly independent price vectors have disjoint image sets under the supply mapping. This property supports the main results. First, the author drew a simple proof of McFadden's proposition that differentiability of the production frontier is necessary and sufficient for strict quasiconvexity of the profit function. This proposition rules out linearity of the profit function on any subset of price domain, in turn ruling out supply and input- demand functions that are constant and have zero values for all price effects. Second, for discrete price changes, own-price effects in supply are strictly positive, assuming a differentiable technology. In this context, strict convexity of the production set is irrelevant. The author indicates implications for cost and demand theory.