Cournot Firms Research Articles

Consumer environmental awareness and green R&D subsidy policy under Cournot–Bertrand comparisons

ABSTRACT This study examines the impacts of consumer environmental awareness on green R&D subsidy policies under different market competition modes when firms adopt green strategies for emissions-reduction activities. We demonstrate that governments grant fewer subsidies to Cournot firms than Bertrand firms. Thus, Cournot firms produce lower outputs and invest less in green R&D. However, firms’ profits and social welfare are higher (lower) in Cournot than in Bertrand firms if the product substitutability is high (low). We also investigate an endogenous competition mode game and find that a Cournot (Bertrand) competition is a socially desirable equilibrium when products substitutability is relatively high (low) while consumer environmental awareness is not sufficiently high (low). These findings suggest that through appropriate green subsidies, antitrust authorities should monitor not only consumer environmental awareness but also firms’ competition mode coordination.

Product liability and firm owners’ delegation to overconfident managers

Abstract This article analyzes the socially optimal liability allocation when strictly liable Cournot firms delegate their safety and output choices to managers whose potential biases are chosen by firm owners and consumers misperceive product risks. Firm owners always hire managers who are overconfident about their product safety’s effectiveness in reducing product-related accident risk. However, the extent of overconfidence depends on consumers’ risk perceptions and the allocation of liability. As a result, the socially optimal liability allocation hinges on whether consumers underestimate or overestimate product risk. When consumers overestimate product risks, firms should be held liable for all losses incurred by consumers. However, when consumers underestimate risk, firms should only be held liable for a part of consumer losses. We also show that, in some circumstances, negligence produces socially more desirable outcomes than strict liability (JEL: K13, L13, L14).

Cournot–Bertrand comparisons under double managerial delegation contracts with sales and environmental incentives

AbstractThis study investigates the effect of consumers' willingness to pay (WTP) for green products on double managerial delegation contracts with sales and environmental incentives. We illustrate that Cournot firms set higher sales and lower environmental incentives than Bertrand firms, yielding higher profits and better environmental performance under Cournot. We also examine an endogenous competition mode and discover that Cournot is an equilibrium when consumers' WTP is low, while the welfare‐inferior Bertrand appears unless consumers' WTP or product substitutability is high. Our finding suggests that antitrust authorities should monitor welfare‐distorting coordination when firms reformulate their strategies for emission‐reduction activities under double managerial delegation contracts.

Cournot–Bertrand comparisons under R&D competition: Output versus R&D subsidies

AbstractWe compare Cournot and Bertrand competitions with R&D investment under output versus R&D subsidy policies. We demonstrate that Cournot firms invest more (less) in R&D and the government grants more (less) subsidies than for Bertrand firms with output (R&D) subsidies. We also find that both competition modes yield the same welfare with output subsidy, while Bertrand yields higher welfare than Cournot with R&D subsidy. Finally, firms' profits and welfare in Cournot are higher under output subsidies, while they can be higher in Bertrand under R&D subsidies if the product substitutability is high and the firm's R&D investment is efficient.

Compensation disclosures and strategic commitment: Evidence from revenue-based pay

A 2006 rule change in the United States mandated that publicly traded firms provide more detailed disclosures about executives’ compensation plans. In response to the new disclosure requirements, Cournot firms with large market shares add revenue-based pay to their CEOs’ pay packages. This change in pay practices coincides with a shift towards more aggressive product market equilibria, characterized by greater production expenditures and lower margins. Jointly, these patterns are consistent with predictions from the theory of “strategic delegation,” and suggest that the new disclosure requirements enhanced the viability of committing through executive incentives. After adopting the new disclosure requirements, many firms appear to restructure their executives’ pay packages as strategic devices designed to make rivals curtail their competitive actions.

Network compatibility, intensity of competition and process R&D: A generalization

This paper analyzes implications of network compatibility and competition on process innovation in differentiated network goods duopoly. It shows that firms’ R&D investments are strategic substitutes (complements) if effective network compatibility is less (more) than product substitutability, regardless of the nature of product market competition. If R&D investments are strategic complements, firms always invest in process innovation and they invest more under Bertrand competition than under Cournot competition. If R&D investments are strategic substitutes, unlike Cournot firms, Bertrand firms do not always undertake process innovation; but when Bertrand firms also undertake process innovation, Cournot–Bertrand R&D ranking depends on the strength of network externalities. Presence of R&D spillover improves the case of strategic complementarity of R&D levels under both Bertrand and Cournot competition.

Endogenizing the Cost Parameter in Cournot Oligopoly

We study the effects of endogenous cost formation in the classic Cournot oligopoly through an extended two-stage game. The competing Cournot firms produce low-cost but limited quantities of a single homogeneous product. For additional procurements, they may refer to a revenue-maximizing supplier who sets a wholesale price prior to their orders. We express this chain as a two-stage game and study its equilibrium under two different information levels: complete and incomplete information on the side of the supplier about the actual market demand. In the deterministic case, we derive the unique subgame-perfect Nash equilibrium for different values of the retailers’ capacity levels, supplier’s cost and market demand. To study the incomplete information case, we model demand uncertainty via a continuous probability distribution. Under mild assumptions, we characterize the supplier’s optimal pricing policy as a fixed point of a proper translation of his expectation about the orders that he will receive from the retailers. If this expectation is decreasing in his price, then such an optimal policy always exists and is unique. Based on this characterization, we are able to proceed with comparative statics and sensitivity analysis, both analytically and numerically. Incomplete information gives rise to market inefficiencies because the supplier may ask for a too high price. Increasing supplier’s cost results in increasing wholesale prices, decreasing orders from the retailers and hence decreasing consumer surplus. Increasing retailers’ production capacities results in decreasing wholesale prices and increasing consumer surplus. Finally, as the number of second-stage retailers increases, the supplier’s profit may initially rise but eventually drops.

Network externalities and process R&D: A Cournot–Bertrand comparison

This paper examines the implication of the nature of competition in a market with network externalities on strategic investment in process R&D by firms. It shows that network externalities have a larger positive effect on process R&D under Bertrand competition than that under Cournot competition. If network externalities are sufficiently strong, regardless of the degree of product differentiation, Bertrand firms have a stronger incentive for process R&D than Cournot firms. Further, Bertrand R&D can be higher than Cournot R&D even in the presence of weak network externalities. These results hold true regardless of whether networks are incompatible or imperfectly compatible.

When Multiple Merged Entities Lead in Stackelberg Oligopolies

I study a merger model among symmetric Cournot firms where—before a merger occurs—firms choose output simultaneously and in which a merged entity acquires the market leadership. I find conditions under which a single or multiple mergers are profitable and solve the free-riding problem. The model connects to Liu and Wang (Econ Lett 129:1–3, 2015), who show that a single leading entity can profitably merge with an arbitrary number of firms. The current paper extends their results in two directions: first, I find the conditions under which the free-riding issue is solved; second, I study the implications of multiple mergers, in which the merged entities are allowed to be heterogeneous in the number of merging firms. A welfare analysis shows that mergers may be welfare-enhancing—even without efficiency gains. Moreover, the set of welfare-enhancing mergers is the same irrespective of the measure that is used: consumer surplus only, or the sum of consumer surplus and industry profits. This suggests caution for the antitrust authorities in evaluating the overall effect of these mergers.

Stable manifold market sequences

In this article, we construct examples of discrete-time, dynamic, partial equilibrium, single product, competition market sequences, namely, $\{m_{t}\}_{t = 0}^{∞}$, in which, potentially active firms, are countably infinite, the inverse demand function is linear, and the initial market $m_0$ is null. For Cournot markets, in which, the number of firms is defined exogenously, as a finite positive integer, namely $n: n>3$, the long term behavior of the quantity supplied, into the market, by Cournot firms is not well explored and is unknown. In this article, we conjecture, that in all such cases, the Cournot equilibrium, provided that it exists, is unreachable. We construct Cournot market sequences, which might be viewed, as appropriate resource tools, through which, the 'unreachability' of Cournot equilibrium points is being resolved. Our construction guidelines are, the stable manifolds of Cournot equilibrium points. Moreover, if the number of active firms, increases to infinity and the marginal costs of all active firms are identical, the aggregate market supply, increases to a competitive limit and each firm, at infinity, faces a market price equal to its marginal cost. Hence, the market sequence approaches a perfectly competitive equilibrium. In the case, where marginal costs are not identical, we show, that there exists a market sequence, $\{m_{t}\}_{t = 0}^{∞}$, which approaches an infinite dimensional Cournot equilibrium point. In addition, we construct a sequence of Cournot market sequences, namely, $\{m_{it}\}_{t = 0}^{∞}, i ≥ 1$, which, for each, $i$, approaches an imperfectly competitive equilibrium. The sequence of the equilibrium points and the double sequence, $\{m_{it}\}$, both approach, the equilibrium, at infinity, of the market sequence, $\{m_t\}$.

Conjectures between Two Cournot Firms with Symmetric Information and Their Risk-taking Behaviours

This paper introduces the simple and standard Cournot duopoly model in a symmetric situation in which each firm has the same information on the cost function of its rival. This paper considers two types of firms’ risk-taking behaviours and two classes of symmetric information. First, we consider that both firms are risk neutral and have perfect information. In this case, we obtain a unique Cournot equilibrium. Second, when both firms are risk neutral and have partial information, that is, each firm’s set of information changes from perfect to partial information, the number of equilibrium changes from one to four compared to case 1. Third, when both firms are risk averse and have perfect information, that is, firms’ risk taking behaviours change from risk neutral to risk averse, the number of equilibrium changes from one to three compared to case 1. Therefore, both firms’ information structure and risk taking behaviours affect their optimal output strategies.

Hidden Costs of Offshore Outsourcing: an Analysis of Offshoring Decisions

Offshore outsourcing has grown as a form of industrial organisation to increase profitability of firms. However, offshoring may be less lucrative than envisaged, due to the presence of hidden costs. We study the strategic interaction amongst onshore Cournot firms in the decision to offshore when they receive signals about offshore hidden costs. The analysis helps suggest policy implications for countries which are potential offshoring locations. We find the precision of signals and the range of possible hidden costs to be crucial in determining offshoring destinations. Updating of information about hidden costs leads to different equilibria including herding in offshoring.

Does environmental regulation create merger incentives?

This paper studies merger incentives for polluting Cournot firms under a competitive tradable emission permits market. We find that when firms are symmetric and marginal costs are constant, an horizontal merger is welfare enhancing if efficiency gains are high enough for the merger to take place. The presence of a competitive (or monopolistic) outside market that also trades in the permits market makes profitable a merger that would not happen otherwise. When firms are vertically related in an input-output chain, an horizontal merger in one of the markets increases profits in the other market due to the permits price decrease. Finally we consider an oligopoly-fringe model in which firms differ in their marginal production costs. A merger between the dominant oligopolistic firms decreases the permits price and is always profitable. Such setting is relevant to assess the observed mergers between power generators in several market for permits, like the Regional Greenhouse Gas Initiative (RGGI), allowing us to derive some policy recommendations.

When Should Firms Expose Themselves to Risk?

I analyze a firm making a decision whether to expose itself to risk in an exogenous parameter when the firm can change a choice variable after observing the realization of the exogenous parameter. For example, the firm decides whether to choose an advertising campaign with a less certain outcome (conditional on the same expected outcome) when it can adjust the product’s price after seeing the effects of the campaign. I show that in many cases, the firm wants to expose itself to risk, and I outline general conditions that need to be satisfied for this result. I then analyze the strategic version of this setup with two competing firms, provide a general characterization, and show that in many cases both firms want to expose themselves to risk, as long as the risks are not too positively correlated. This is the case for many linear demand and constant marginal cost settings (monopolies, differentiated Bertrand firms, or differentiated Cournot firms selling substitutes) where the exogenous parameter is a demand, or a marginal cost shifter results in the monopoly (or both of the competitors if the risks are not too positively correlated) voluntarily exposing itself to risk. This paper was accepted by J. Miguel Villas-Boas, marketing.

Welfare-Improving Effect of a Small Number of Followers in a Stackelberg Model

AbstractWe investigate a Stackelberg oligopoly model in which m leaders and $N - m$ followers compete. We find an important welfare effect that relates to anti-monopoly policies when we move from the Cournot model ($m = N$) to the Stackelberg model: Exchanging a small number of Cournot firms for Stackelberg followers always improves welfare under moderate conditions. This contrasts with the welfare effect that can reduce welfare when a small number of Cournot firms are exchanged for Stackelberg leaders. The key result behind this asymmetry is the contrasting limit results in the cases where m converges to N and m converges to 0. We also discuss the optimal number of leaders and the integer constraint for the number of firms.

Simulating a Homogenous Product Merger: A Case Study on Model Fit and Performance

This paper studies Tesoro’s 2013 acquisition of British Petroleum’s Los Angeles refinery. We present a merger simulation model tailored to the gasoline market, which includes Cournot firms and a price-taking fringe. This hybrid model generates margins that are more plausible than those generated by a standard Cournot model. We also test the predictive accuracy of the models relative to empirical estimates of the acquisition’s price effect. We estimate the effect of the acquisition using both difference-in-differences estimation and the synthetic control method. Both methods suggest the acquisition had little if any effect on Los Angeles gasoline prices. We can reject the price effect predicted by the standard Cournot model, but not that of the hybrid model.

Intra-industry trade with Bertrand and Cournot oligopoly: The role of endogenous horizontal product differentiation

This paper investigates the effect of endogenous horizontal product differentiation on trade patterns and the gains from trade under Bertrand and Cournot oligopoly. If trade occurs, Bertrand firms always differentiate their products more that Cournot firms. However, sufficiently high differentiation costs can prevent product differentiation. Trade in homogeneous products never takes place under Bertrand competition. Bertrand firms will either differentiate their products or will not export. Cournot firms, however, may trade in either homogeneous or differentiated products. Product differentiation can significantly increase the gains from trade under both Cournot and Bertrand oligopoly.

Market power in emissions trading: Strategically manipulating permit price through fringe firms

Tradable emission permits have received considerable attention recently. One emerging issue is its interaction with electricity markets, specifically, market power in the permit markets. One challenge in studying market power in the permit markets is that the demand for permits is implicitly determined by the system conditions. Traditional ways of modeling market power (e.g., standard Cournot model) cannot directly apply. This paper develops a model in which Cournot firms in the market can manipulate the permit price through fringe firms. We have two central findings in this paper. First, diverting emission permits from Cournot to fringe producers always reduce the power and the permit prices, which could improve social surplus. Second, when the fringe producer’s emission rate is low, diverting permits from the “dirty” (i.e., more-polluting) Cournot producer to the “clean” (i.e., less-polluting) Cournot producer leads to a decline of both power and permit prices. Therefore, the initial allocation of the emission permits could be a useful regulatory tool to mitigate the abuse of market power. We also illustrate these results through a numerical simulation of the California electricity market.

Firms Should be Risky at the Margin

I analyze a firm making a decision of whether to expose itself to risk in an exogenous parameter when the firm can change a choice variable after observing the realization of the exogenous parameter. For example, whether to choose an advertising campaign with a less certain outcome, when the firm can adjust the product's price after seeing the effects of the campaign. I show that in many cases the firm wants to expose itself to risk and I outline general conditions that need to be satisfied for this result. I then analyze the strategic version of this setup with two competing firms, provide a general characterization, and show that in many cases both firms want to expose themselves to risk, as long as the risks are not too positively correlated. For example, many linear demand and constant marginal cost settings (monopoly, differentiated Bertrand, or differentiated Cournot firms selling substitutes) where the exogenous parameter is a demand or a marginal cost shifter results in the monopolist (or both of the competitors if the risks are not too positively correlated) voluntarily exposing themselves to risk.

Corporate Social Responsibility in a Mixed Oligopoly

This paper investigates how CSR firms influence a Cournot oligopoly with pollution. We define as CSR a firm that takes into account not only its profits but also internalises its own share of the externality and is sensitive to consumer surplus. The CSR firm obtains higher profits compared to profit-seeking firms. Also, the presence of at least one CSR firm improves social welfare and makes the first best Pigouvian taxation more lenient for Cournot firms. Finally, the CSR firm may induce the other firms to invest in green technology.