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.     

Consumer search with asymmetric price sampling

We explore asymmetries in the way consumers sample prices in a simple sequential search framework. In equilibrium, the price distribution of a firm catering to more local consumers first-order stochastically dominates that of its rival. Prices rise in the degree of asymmetry.     

Buyer search and price dispersion: a laboratory study

We study markets with costly buyer search in which sellers simultaneously post prices. Buyers costlessly observe one or (with probability 1−q) two of the posted prices, and can accept one or pay to search again. The experiment varies q, the search cost, and the number of buyers. Equilibrium theory predicts a unified very low (high) price for q=0 (q=1) and predicts specific distributions of dispersed prices for q=1/3 and 2/3. Actual prices conform closely to the predictions in some treatments. Buyers’ reservation prices are biased away from the extremes, however, and sellers’ prices have positive autocorrelation and cross-sectional correlation.     

Modelling price competition across many markets (An application to the Spanish loans market)

The purpose of this work is the structural modelling of price competition in a product-differentiated industry in which many firms of varying size compete across many independent small markets, with the target of identifying price behaviour. We apply it to model competition among the more than 79 banks that were active in the Spanish loans market during the period 1983-1991, using micropanel data. A model in which national banks (as opposed to regional and local banks) fully internalize their cross-rate effects in pricing is selected as the model that best fits the data. Our framework allows us to estimate the dead-weight loss due to market power, and to decompose it assessing the part attributable to price coordination.     

A public firm in a model of spatial duopoly with price discrimination

We visit the role of privatization in the location decision of firms in an industry where no firm can produce all varieties demanded. We demonstrate that the Nash equilibrium locations are socially optimal, in the presence of a publicly owned firm, notwithstanding the degree of privatization.     

Paradoxical price effects on insurance markets

In this paper we analyze a paradox phenomenon in certain insurance markets of some countries: in spite of there being strong competition, increasing prices can be found in some submarkets. As a reason for this, we need to note the special distribution of insurance products, a distribution primarily based on intermediaries — and, as a result, there is an increasing part for ‘intermediation’ costs within insurance products' cost structure due to competition for the intermediaries. We build an oligopolistic model assuming that the market is saturated, which is able to explain the overemployment of intermediaries and the high commissions involved. We analyze possible interventions and laws/regulations and suggest that the problem can be solved only with major regulation. Finally, we have come up with an empirical analysis to test the model.     

Protecting consumers through protection: The role of tariff-induced technology transfer

We consider a duopolistic trade model where a tariff induces the foreign firm to transfer its superior technology to the domestic rival. Contrary to the conventional wisdom, such a tariff raises consumers’ surplus relative to the free trade situation. We characterize the optimal tariff with and without precommitment on the part of the local government. Possibility of technology transfer reduces the optimal tariff rate compared to the no-transfer situation.     

Mixed pricing in oligopoly with limited monopoly

We analyze price competition between two brands. Buyers consist of switchers and two segments of customers with limited brand loyalty. We identify a unique symmetric mixed-strategy price equilibrium and find that competition is most relaxed when there exists some switchers.     

The dynamics of a differentiated duopoly with quantity competition

We analyse the dynamics of a Cournot duopoly with heterogeneous players to investigate the effects of micro-founded differentiated products demand on stability. The present study, which indeed modifies and extends Zhang et al. (2007) (Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148) and Tramontana, F., (2010) (Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357), reveals that a higher degree of product differentiation may destabilise the market equilibrium. Moreover, we show that a cascade of flip bifurcations may lead to periodic cycles and ultimately chaotic behaviours. Since a higher degree of product differentiation implies weaker competition, then a theoretical implication of our findings, that also constitute a policy warning, is that a fiercer (weaker) competition tends to stabilise (destabilise) the unique positive Cournot–Nash equilibrium.     

Unilateral effects of mergers with general linear demand

We derive the formula for the unilateral price effects of mergers of two products with linear demand in the general asymmetric situation. The formula uses the same information required to calculate upward pricing pressure in the 2010 Horizontal Merger Guidelines.     

Uncertain spatial demand and price flexibility: A state space approach to duopoly

Sufficient conditions for a unique price equilibrium, in terms of the uncertainty distribution and the state contingent consumer distributions, are given for spatial duopoly. Also considered are efficiency and endogenous locations for the symmetric case and comparative statics on price flexibility.     

Selling licences for a process innovation: the impact of the product market on the selling mechanism

Abstract.  This article considers the sale by a research lab of licences for a cost-reducing innovation. The marginal cost of a firm that wins a licence is private information and the acquisition of a licence imposes a negative externality on the other firms. The lab's optimal revenue is determined from a class of mechanisms in which the lab selects the number of licences and the reserve price before the sale. The role of the downstream product market in the determination of the number of licences is analyzed. Furthermore, it is also shown that the optimal reserve price may be zero.     

The Cournot-Bertrand model and the degree of product differentiation

We consider a duopoly model with a Cournot-type firm and a Bertrand-type firm. Both survive and the equilibrium is stable when there is sufficient product differentiation. With no differentiation, only the Cournot-type firm survives, and the outcome is perfectly competitive.     

Environmental Taxation and Induced Structural Change in an Open Economy: The Role of Market Structure

Abstract. Studies of structural change induced by environmental taxation usually proceed in a perfect-competition framework and typically find structural change to be quite moderate under realistic emission reduction scenarios. By observing that some of the industries affected are likely to operate under imperfect rather than perfect competition, additional mechanisms emerge which may amplify structural change beyond the extent identified as yet. Especially, changes in economies of scale may arise which weaken or strengthen the competitive position of industries over and above the initial cost effect. Using a computable general equilibrium model for Germany to examine the effects of a unilaterally introduced carbon tax, we find that induced structural change is more pronounced under imperfect competition than under perfect competition. At the macroeconomic level, we find that aggregate losses in economies of scale are larger than aggregate gains, implying that the total costs of environmental regulation are higher under imperfect competition than under perfect competition.     

The effects of market structure on industry growth: Rivalrous non-excludable capital

We analyze imperfect competition in dynamic environments where firms use rivalrous but non-excludable industry-specific capital that is provided exogenously. Capital depreciation depends on utilization, so firms influence the evolution of the capital equipment through more or less intensive supply in the final-goods market. Strategic incentives stem from, (i) a dynamic externality, arising due to the non-excludability of the capital stock, leading firms to compete for its use (rivalry), and, (ii) a market externality, leading to the classic Cournot-type supply competition. Comparing alternative market structures, we isolate the effect of these externalities on strategies and industry growth.     

On input market surplus and its relation to the downstream market game

Abstract In order to analyze the welfare effects of price changes in input markets – following for example a price‐fixing conspiracy – economists have studied the relationship between the surplus measured in the input markets and the surplus in the output markets. The latest results hinge on simplifying assumptions, which are relaxed here by linking the input markets surplus question to another stream of literature, which characterizes functions that oligopolists collectively, yet unintentionally, maximize. It is shown that the area under the input demands is equal to the change in a function for which critical points coincide with the equilibria of the downstream game. A particular case of these functions is the exact potential function.     

Intertemporal market division:: A case of alternating monopoly

In this paper, we report on an equilibrium with market dominance that exists in a simple two-firm model that features neither entry barriers nor sophisticated punishment strategies. This equilibrium induces an intertemporal market division in which the two firms alternate as monopolists - despite the fact that the model also sustains a Cournot duopoly. Even when initially both firms are active in the market, the alternating monopoly reveals itself rather quickly. Moreover, it Pareto dominates the Cournot equilibrium - as it is close to the cartel outcome. Several examples of what well may be such alternating monopolies are presented.     

Competing auctions with endogenous quantities

Two sellers decide on their discrete supply of a homogenous good. There is a finite number of buyers with unit demand and privately known valuations. In the first model, there is a centralized market place where a uniform auction takes place. In the second, there are two distinct auction sites, each with one seller, and buyers decide where to bid. Using the theory of potential games, we show that in the one-site auction model there is always an equilibrium in pure-strategies. In contrast, if the distribution of buyers values has an increasing failure rate, and if the marginal cost of production is relatively low, there is no pure-strategy equilibrium where both sellers make positive profits in the competing sites model. We also identify conditions under which an equilibrium with a unique active site exists. We deal with the finite and discrete models by using several results about order statistics developed by Richard Barlow and Frank Proschan [R. Barlow, F. Proschan, Mathematical Theory of Reliability, Wiley, New York, 1965; R. Barlow, F. Proschan, Inequalities for linear combinations of order statistics from restricted families, Ann. Math. Statist. 37 (1966) 1593-1601; R. Barlow, F. Proschan, Statistical Theory of Reliability and Life Testing, McArdle Press, Silver Spring, 1975].     

Comparative statics for oligopoly: A generalized result

We perform comparative statics for a general model of asymmetric oligopoly and derive a concise formula for the response of one firm to a marginal change in its rival’s strategic variable, taking into account the responses of all other firms. We obtain the conditions under which the sign of this response coincides with that of the mixed second-order partial derivative of the firm’s payoff function. We then propose a distinction between gross and net strategic relationships (i.e., strategic substitute and complement).     

Spatial Cournot Competition in a Linear City with Directional Delivery Constraints

This study investigates a sequential game of location and transportation mode choices, as well as the subsequent quantity choice. The results show that spatial Cournot competition with directional delivery constraints yields a richer set of spatial configurations, involving midpoint agglomeration, maximum differentiation and asymmetric dispersion, and a richer set of transportation mode selections, involving delivery in different directions, asymmetric delivery between duopoly firms, and delivery in two directions by each firm, depending on the fixed cost of a transportation instrument. This paper concludes with an investigation of welfare analysis on optimal locations and transportation modes.