Symmetric Oligopoly Research Articles

Modelling advertising budgeting and allocation decisions using modified multinomial logit market share models

Previous research suggests that a multinomial logit model of market share (MNL) is inappropriate for equilibrium analyses of advertising competition. This article shows that when employing simple transformations of the advertising effort, the modified MNL model becomes useful in representing situations of diminishing returns to advertising and appropriate for advertising equilibrium analyses without additional difficulties in its empirical estimation. Using the modified MNL model, optimal advertising budgets together with their allocation over time are derived for both the cases of concave and S-shaped attraction (response) functions in a symmetric oligopoly.

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.

Sunk Costs, Market Structure And Growth

I discuss a model of endogenous innovation that brings to the forefront the in-house R&D activity of the modern corporation. In a symmetric oligopoly, firms undertake cost-reducing R&D subject to a research technology with incomplete spillovers. Concentration of sales and R&D resources determine the optimal scale and the efficiency of firms' R&D operations and, thus, the rate of productivity growth. In addition, R&D expenditures (a sunk cost) are one component of total fixed costs and determine the number of active firms in zero-profit equilibrium. This feed-back makes the price, investment, entry, and exit decisions interdependent. A rich characterization of the balanced growth path, defined as the rate of growth and the number of firms that the market supports in general equilibrium, emerges. Multiple equilibria may exist and firms' expectations about rivalry determine the economy's performance.

Analyses of sensitivity and competition of an EOQ model

Min (1992) proposed a symmetric Cournot-like oligopoly model consisting of sellers who are profit maximizing EOQ-based decision makers. In this paper Min's 1992 model is extended by means of sensitivity and equilibrium analyses. The primary objective of such extensions is to enhance the general understanding of relationships between critical quantities in inventory theory (such as the order quantity) and in microeconomic theory (such as the number of competing sellers). In particular, for EOQ-based decision making sellers, the effects on each seller's profitability caused by the entry of an additional competitor, as well as the maximum number of competitors the entire market can sustain, are examined.

A competitive inventory model with options to reduce setup and inventory holding costs

In this paper, the profit maximizing economic order quantity (EOQ) model is extended to the case of a symmetric oligopoly consisting of several producers who compete with each other for the same potential buyers. For each producer, we assume that the options of investing in reducing the setup and inventory holding costs are available. A primary goal of this paper is to understand economic implications of the resulting equilibrium in terms of critical elements of EOQ models such as the setup and inventory holding costs as well as critical elements of the microeconomic market theory such as the market price and the number of competing producers. For an example, we present a unique insight as to why several Japanese and American producers are striving to reduce the setup costs under ever increasing competition. Specifically, it will be shown that, for a profit maximizing producer, as the number of competing producers increases, his optimal strategy dictates that he reduce his setup and inventory holding costs.

Strategic trade policy under asymmetric oligopoly

Models of trade policy under oligopoly usually assume symmetry, in each country all firms are identical, but this paper analyses trade policy under asymmetric oligopoly. It is shown that under asymmetric oligopoly trade policy has a rationalisation effect which does not occur under symmetric oligopoly. The size of the rationalisation effect depends upon the convexity of demand and the variation of industry output. The rationalisation effect may strengthen or weaken the argument for strategic trade policy.

Inventory and pricing policies under competition

We extend the profit maximizing economic order quantity (EOQ) model to the case of a symmetric oligopoly consisting of sellers of a homogeneous product who complte with each other for the same potential buyers. The key feature differentiating this paper from the extant EOQ literature is that, for both uniform pricing and quantity discount pricing cases, the formulations and equilibrium strategies of our models explicitly depend on the number of competing sellers. From the resulting symmetric equilibria, we derive interesting economic implications.

Supply Function Equilibria in Oligopoly under Uncertainty

We model an oligopoly facing uncertain demand in which each firm chooses as its strategy a relating its quantity to its price. Such a strategy allows a firm to adapt better to the uncertain environment than either setting a fixed price or setting a fixed quantity; commitment to a supply function may be accomplished in practice by the choice of the firm's size and structure, its culture and values, and the incentive systems and decision rules for its employees. In the absence of uncertainty, there exists an enormous multiplicity of equilibria in supply functions, but uncertainty, by forcing each firm's supply function to be optimal against a range of possible residual demand curves, dramatically reduces the set of equilibria. Under uncertainty, we prove the existence of a Nash, equilibrium in supply functions for a symmetric oligopoly producing a homogeneous good and give sufficient conditions for uniqueness. We perform comparative statics with respect to firms' costs, the industry demand, the nature of the demand uncertainty, and the number of firms, and sketch the extension to differentiated products. Firms' equilibrium supply functions are steeper with marginal cost curves that are steeper relative to demand, fewer firms, more highly differentiated products, and demand uncertainty that is relatively greater at higher prices. The steeper are the supply functions firms choose in equilibrium, the more closely competition resembles the Cournot model (which exogenously imposes vertical supply functions-fixed quantities); with flatter equilibrium supply functions, competition is closer to the Bertrand model (which exogenously imposes horizontal supply functions-fixed prices).

Optimal regulation of a consistent conjectures duopoly

Previous regulatory incentive schemes have focused on monopoly or on competition with externalities. This note examines a consistent conjectures duopoly, deriving a specific tax function that induces optimal output even if the regulator is ignorant of demand and knows the cost function only up to an affine transformation. The solution readily generalizes to symmetric oligopoly.

Price adjustment within a framework of symmetric oligopoly: An analysis of pricing in 380 U.S. manufacturing industries, 1958–71

This paper is concerned with the generation and testing of predictions on price adjustment from a model of symmetric oligopoly. Two types of industry demand regimes are considered, linear and iso-elastic. It is shown that these can be distinguished by a simple test, and linear demand is given strong support. It is then shown that the industry conjectural variation may be treated as a function whose properties can be established by non-linear estimation of the price adjustment equation.

Competitive nonlinear tariffs

This paper generalizes the study of nonlinear tariffs, i.e., those depending nonlinearly on the quantity purchased, to the case of a symmetric oligopoly. Competitive equilibria and the corresponding tariffs are analyzed in a Cournot framework. Various equilibria are obtained, which depend both upon the number of competing suppliers and the choice of market parameters used to characterize the competitors' strategies. Buyers are classified by type, each selecting an optimal consumption level in response to the prevailing tariff. The phenomena of buyer self-selection found in monopoly nonlinear pricing and the scaling of equilibrium demand elasticity found in Cournot models both appear in the results.