The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining

This paper compares Cournot and Bertrand equilibria in a downstream differentiated duopoly in which the input price (wage) paid by each downstream firm is the outcome of a strategic bargain with its upstream supplier (labor union). We show that the standard result that Cournot equilibrium profits exceed those under Bertrand competition - when the differentiated duopoly game is played in imperfect substitutes - is reversible. Whether equilibrium profits are higher under Cournot or Bertrand competition is shown to depend upon the nature of the upstream agents’ preferences and on the distribution of bargaining power over the input price. We find that the standard result holds unless unions are both powerful and place considerable weight on the wage argument in their utility function.     

Profit sharing as entry deterrence mechanism

In a right-to-manage framework, this paper analyzes the optimal choice of the pay scheme (profit sharing vs. fixed wage) in a unionized duopoly with potential market entry and decentralized bargaining. The paper shows that, depending on the institutional features, both pay systems can arise as equilibria in Nash strategies. Under duopoly with committed bargaining, the fixed wage is the Nash equilibrium; with flexible bargaining, an agreement between the incumbent firm and its union about profit sharing arises as Nash equilibrium, if the union is not too strong. A monopoly with threat of entry reinforces the selection of profit sharing as a deterrent mechanism.     

A bargaining model in general equilibrium

The goal of the paper is to present a simple model of rational endogenous household formation in a general equilibrium framework in which Pareto optimality at the economy level is not necessarily obtained. The simplest example of household formation is the case in which pairs of individuals engage themselves in a bargaining process on the division of some wealth: if an agreement on the distribution is (not) reached, we can say that the household is (not) formed. The vast majority of existing bargaining models predicts agreements on an efficient outcome. A seminal paper by Crawford (Econometrica 50:607–637, 1982) describes a very simple game with incomplete information in which, even with rational agents, disagreement causes welfare losses. We embed that model in a general equilibrium framework and present some results on equilibria both in the bargaining game and the associated exchange economy. Crawford’s results support Schelling’s intuition on the reasons of disagreement: it may arise if players’ commitments are reversible. Crawford shows that high probabilities of reversibility tend to favor the bargaining impasse, in fact with low probability. We prove that even if those probabilities are arbitrarily close to zero, disagreement is an equilibrium outcome, with high probability. That conclusion seems to be an even stronger support to Schelling’s original viewpoint. In the exchange economy model with that noncooperative bargaining game as a first stage, we present significant examples of economies for which equilibria exist. Because of disagreement, Pareto suboptimal exchange economy equilibria exist for all elements in the utility function and endowment spaces and they may coexist with Pareto optimal equilibria even at the same competitive prices.     

RAISING WAGES TO DETER ENTRY INTO UNIONIZED MARKETS*

This paper investigates entry under a unionized oligopoly when entry and wage negotiations are sequential. We find the incumbent has incentives to raise the wage, which strengthens the bargaining position of the union relative to the entrant at subsequent negotiations and thus discourages entry. We show that entry is more likely to be deterred (accommodated) if the union is wage (employment) oriented and that raising unemployment compensation during recession not only reduces the burden of the unemployed but also induces new entry, creating more employment opportunities. However, during a business boom, reducing unemployment compensation is a better policy.     

Comparing new Keynesian models in the Euro area: a Bayesian approach

This paper estimates and compares four versions of the sticky price New Keynesian model for the Euro area using a Bayesian approach. We find that the average duration of price contracts is between two and four quarters, while the average duration of wage contracts is estimated to be below two quarters. Both mechanisms of price and wage indexation are not important when autocorrelated price markup shocks are introduced in the model. These results are in stark contrast to Smets and Wouters (2003): when we use their priors, our estimated posterior distributions are similar to theirs, but the models’ fit to the data is worse. We are thankful to the Econometric Modelling Unit at the European Central Bank for providing us with the Euro area data. We also thank two anonymous referees for helpful suggestions. The views expressed in this paper are those of the authors and do not necessarily reflect the views of Caixa d’Estalvis i Pensions de Barcelona (“la Caixa”).     

Unionized oligopoly and vertical integration

Labor market structures may have important effects on imperfectly competitive rivalries between firms. This paper examines the consequences of unionization for the rivalry between duopoly firms in two types of contracts: vertical integration and vertical separation. If a franchise fee is used to extract the retailer’s profit, then it is in the individual interest of each manufacturer to choose vertical separation and charge his retailer a wholesale price in excess of the unit production cost, depending on the specific time structures. These arguments could make integration preferable for the manufacturer if the wage bargaining power of the union is relatively powerful.     

Pollution Abatement Subsidies and the Eco-Industry

This paper considers the combination of pollution taxes and abatement subsidies when some polluting firms procure their abatement goods and services from an oligopolistic eco-industry. The regulator must here cope with two simultaneous price distortions: one that comes from pollution and the other which is caused by the eco-industry’s market power. In this context, we show that taxing emissions while subsidizing polluters’ abatement efforts cannot lead to first-best, but the opposite occurs provided it is the eco-industry’s output which is subsidized. When public transfers also create distortions, welfare can be higher if the regulator uses only an emission tax, but subsidizing abatement suppliers while taxing emissions remains optimal when the eco-industry is concentrated.     

Optimal Factor Taxation under Wage Bargaining: A Dynamic Perspective

Abstract. We consider the issue of steady-state optimal factor taxation in a Ramsey-type dynamic general equilibrium setting with two distinct distortions: (i) taxes on capital and labour are the only available tax instruments for raising revenues and (ii) labour markets are subject to an inefficiency resulting from wage bargaining. If considered in isolation, the two distortions create conflicting demands on the wage tax, while calling for a zero capital tax. By combining the two distortions, we arrive at the conclusion that both instruments should be used, implying that the zero capital tax result in general is no longer valid under imperfectly competitive labour markets.     

Search,Concave Production,and Optimal Firm Size

This paper demonstrates that in a free entry search and bargaining economy with concave production firms over-employ. Bargaining allows the worker's wage to depend upon marginal productivity. As such, with strictly concave production, the wage declines as firms employ more labor. Firms react to this declining wage function by choosing an inefficiently large number of workers. However, in equilibrium, fewer firms are likely to enter causing aggregate employment and vacancies to fall.Journal of Economic LiteratureClassification Numbers: J30, J41, J50.     

Union–firm bargaining: Order of play and efficiency

This paper shows that a modified alternating offers Rubinstein model can provide a Pareto superior outcome in the context of the right-to-manage union–firm bargaining. Two examples of bargaining protocols that yield a superior outcome are provided. In the first example, the parties engage in a game in which the order of play is determined as part of the bargaining. We show that the game has a unique subgame perfect equilibrium in which the firm always moves first in the wage bargaining game. The equilibrium wage is, therefore, unique. In the second example, we examine a two-part-tariff alternating offers bargaining protocol, where the parties bargain over the wage and transfer payments. We show that this bargaining protocol has a Pareto efficient, unique subgame perfect equilibrium. Thus, although the parties do not bargain over the level of employment, the outcome under this protocol is, nevertheless, socially optimal.     

Strategic Interactions of Monetary Policymakers and Wage/Price Bargainers: A Review with Implications for the European Common-Currency Area

This paper reviews recent work on macroeconomic management with varying organization of wage/price bargaining and degrees of credible monetary conservatism. The emerging literature synthesizes and extends theory and empirics on central bank independence (CBI) and coordinated wage/price bargaining (CWB), arguing that the degrees of CBI and CWB interact with each other and with other political-economic conditions (sectoral composition, international exposure, etc.) to structure the incentives facing actors involved in monetary policy and wage/price bargaining. The core implication, theoretically surprising but empirically supported, is that even perfectly credible monetary conservatism has long-run, equilibrium, on-average real effects, even with fully rational expectations, and that these effects depend on the organization of wage/price bargaining. Conversely, wage/price-bargaining structure has real effects that depend on the degree of credible conservatism reflected in monetary-policy rules. Each also has interactive nominal effects though this is less surprising. Some disagreement remains over the precise nature of these interactive effects, but all emerging theory and evidence agree that a common, credibly conservative European monetary policy has nominal and real effects that depend on the Europe-wide institutional-structural organization of wage/price bargaining. Indeed, the one specific piece of theoretical and empirical agreement suggests that, for many member countries, the nominal gains from monetary-policy delegation to a credibly conservative European Central Bank will worsen these bargaining-policy interactions.     

Communication in bargaining over decision rights

This paper develops a model of bargaining over decision rights between an uninformed principal and an informed but self-interested agent. We introduce two different bargaining mechanisms: tacit and explicit bargaining. In tacit bargaining, an uninformed principal makes a take-it-or-leave-it price offer to the agent, who then decides whether to accept or reject the offer. In the equilibrium of the game, the principal inefficiently screens out some agent types so that the agent's private information cannot be fully utilized when the decision is made. In explicit bargaining in which parties can communicate explicitly via cheap talk before tacit bargaining, however, an equilibrium with no such inefficient screening exists even when the conflict of interest is arbitrarily large. We also follow a mechanism design approach, showing that under certain conditions, explicit bargaining is an optimal bargaining mechanism that maximizes the joint surplus of the parties.     

WAGE BARGAINING AND MERGER INCENTIVES WITH ASYMMETRIC COSTS

This paper examines how wage bargaining within each firm influences the relationship between an equilibrium ownership structure and the most preferred ownership structure from the viewpoint of social welfare, in a unionized oligopoly of asymmetric firms with respect to productivity of capital. We consider the merger incentive of each firm’s owner when the wage level is determined through bargaining between the firm’s owner and union. We derive a condition for both the degree of cost asymmetry among existing firms and the relative bargaining power of each firm’s owner to her/his union such that each ownership structure can be observed in equilibrium. We also show that although the two types of ownership structures with the merger involving the least efficient firm can be equilibria and socially optimal, these structures are observed only when both the degree of cost asymmetry and the relative bargaining power of each firm’s owner are moderate. Finally, we analyse the relationship among the cooperative game approach employed in this paper and two non‐cooperative merger formation approaches, and examine the robustness of the results obtained in this paper against the change in the assumption regarding each firm’s cost function.     

Entry Threats and Inefficiency in ‘Efficient Bargaining’

We study limit pricing in a model of entry with asymmetric information, where the incumbent firm's wage is endogenously determined through ‘efficient bargaining’ with its union. In the presence of entry threat, the incumbent firm‐union pair may face a conflict between rent sharing and transmitting its cost information. When the wage is not observable to outsiders and employment is the only signalling instrument, over‐employment features in all entry deterring contracts. When the wage is also observable, information transmission becomes easier. Most of the time, then, but not always, the efficient contract deters (induces) entry against the low (high) cost incumbent.     

Endogenous wage bargaining institutions in oligopolistic sectors

Summary. This paper explores the endogenous emergence of wage bargaining institutions in a union-oligopoly framework. Technological asymmetries among firms are shown to be the driving force for the emergence of alternative wage bargaining centralization structures that are observable in real life. As wage deals at the sector-level obtain the consensus of all unions and the efficient firms, a regulator has an incentive to authorize those deals by activating/establishing a Minimum Sectoral Wage Institution(MSWI). If productivity differences are high enough, wage setting above the established wage floor may subsequently occur in efficient firms. Otherwise, a completely centralized wage bargaining structure emerges and the sector-level wage deal is simply confirmed as the firms wage rate. If, however, productivity asymmetries are rather insignificant, firms and unions have conflicting interests and a completely decentralized wage bargaining regime prevails in equilibrium.Received: 17 December 2001, Revised: 9 June 2003, JEL Classification Numbers: J50, J31, L13.Correspondence to: Emmanuel PetrakisParticular appreciation is expressed to an anonymous referee who has greatly helped us to improve our work upon an earlier draft of this paper. We also wish to thank T. Kollinzas, J. Padilla, H. Bester, J. Sakovics, K. Uwe-Kühn, J. J. Dolado, J. L. Ferreira, A. Matsui and C. Martinelli for their helpful comments and suggestions.     

Growth cycles and inflation in a model of the class struggle

The problems of price and wage inflation and unemployment are discussed here in a context of a model of class struggle developed by R. M. Goodwin. The basic Goodwin model which is an analog of the Volterra-Lotka preypredator model is extended to include actual and anticipated price inflation and excess capacity. Cyclical behavior of labor's share in national income and the employment ratio is studied around a Harrodian steady state. It is found that the presence of money illusion with respect to the actual rate of inflation in the wage bargaining equation is a stabilizing influence. With respect to anticipated inflation, local stability of equilibrium is no longer assured. The implications of this for Phillips curve analysis are also derived.     

The codetermined firm in a Cournot duopoly: A stability analysis

This paper aims to study the stability issue in a Cournot duopoly with codetermined firms. We show that when both firms codetermine employment together with decentralised employees' representatives, a rise in wages acts as an economic (de)stabiliser when the wage is fairly (high) low, while under profit maximisation a rise in wages always acts as a stabilising device because the parametric stability region monotonically increases with the wage in such a case. Moreover, a rise in the union's bargaining power has a de-stabilising effect, except when the wage is low and the firm power is already high. Therefore, under codetermination a change either in the wage or firm power in the Nash bargaining plays an ambiguous role on stability. We also show with numerical simulations that complex dynamics can also occur.     

A multi-agent bilateral bargaining model with endogenous protocol

People do bargain over how to bargain. We examine the role of individuals’ ability to pursue certain bargaining protocols in a multi-agent bilateral bargaining model. Bargaining protocols are not completely settled, but will emerge endogenously in equilibrium. We show that players’ ability to partially influence bargaining protocols plays a crucial role in determining equilibrium outcomes. When discounting is not too high, there are multiple subgame perfect equilibria, including inefficient ones. As the number of players increases, both the set of discount factors that support multiple equilibrium outcomes and the set of the first proposing player’s equilibrium payoffs expand. The maximum loss of efficiency increases with respect to the discount factor. We would like to thank Hongbin Cai, John Conlon, Andrew Daughety, Taiji Furusawa, Byoung Heon Jun, Akira Okada, Ping Wang, and two anonymous referees for their comments and suggestions. Both authors gratefully acknowledge financial support from the Social Sciences and Humanities Research Council of Canada.     

Efficiency wages and union-firm bargaining with private information

We consider efficiency wage effects in a union-firm bargaining model with private information. We show that an increase in the efficiency wage effects does not necessarily increase the wage level at equilibrium, even when the wage bargaining with private information is close to one with complete information. However, if it is commonly known that the firm is stronger than the union and the demand is sufficiently elastic, then an increase in the efficiency wage effects increases for sure the wage at equilibrium.JEL Classification: J41, J50, J52We thank Juan Dolado and two anonymous referees for valuable comments. Vincent Vannetelbosch is Chercheur Qualifié at the Fonds National de la Recherche Scientifique. The research of Ana Mauleon has been made possible by a fellowship of the Fonds Européen du Développement Economique Régional (FEDER). Financial support from the Belgian French Communitys program Action de Recherches Concertée 99/04-235 (IRES, Université catholique de Louvain) is gratefully acknowledged.     

Wage Bargaining Versus Efficiency Wages: A Synthesis

We construct a model integrating the efficiency wage model of Shapiro–Stiglitz (1984) (SS), with an individual wage bargaining model in the Diamond–Mortensen–Pissarides (DMP) tradition where firms and workers form pairwise matches. We show that when workers may threaten to shirk on the job and there is individual wage bargaining, the wage is always higher and employment lower than in either the SS model, or the (appropriately modified) DMP model. When firms determine workers' efforts unilaterally, efforts are set inefficiently low in the SS model. In the bargaining model, effort is higher, and is first best when the worker non–shirking constraint does not bind. The overall equilibrium allocation may then be more or less efficient than in the SS model, but is always less efficient than in a pure bargaining model with no moral hazard.