Commitment and price competition in a dynamic differentiated-product duopoly

This paper characterizes linear Markov-perfect equilibrium in a duopolistic environment where firms engage in dynamic price competition. Firms have constant (but potentially different) marginal costs and produce differentiated products. We show that, for the case of linear demand, dynamically stable Markov-perfect equilibrium prices are strictly higher than one-shot Nash equilibrium prices, but lower than fully collusive (monopoly) prices. We provide closed-form solutions for the Markov-perfect equilibrium prices which, in principle, can be estimated given data on firm demand and costs. Our results suggest that static two-stage models of price commitment are on reasonably solid ground in that they might be viewed as a reduced form for more complicated dynamic models.     

AN ELEMENTARY PROOF OF ARROW'S IMPOSSIBILITY THEOREM*

This paper deals with a situation where a quantity-setting Coumot firm and a price- setting Bertrand firm coexist in the same industry. Under a set of regularity conditions
on demand and cost, we compute equilibrium prices on Cournot-Bertrand "mixed" duopolies, and compare them with those of "pure"Cournot and Bertrand duopolies.     

Price competition,free entry,and welfare in congested markets

In this paper we study the problem of price competition and free entry in congested markets. In particular, we consider a network with multiple origins and a common destination node, where each link is owned by a firm that sets prices in order to maximize profits, whereas users want to minimize the total cost they face, which is given by the congestion cost plus the prices set by firms. In this environment, we introduce the notion of Markovian Traffic Equilibrium to establish the existence and uniqueness of a pure strategy price equilibrium, without assuming that the demand functions are concave nor imposing particular functional forms for the latency functions. We derive explicit conditions to guarantee existence and uniqueness of equilibria. Given this existence and uniqueness result, we apply our framework to study entry decisions and welfare, and establish that in congested markets with free entry, the number of firms exceeds the social optimum.     

Collusion and Price Rigidity

We consider an infinitely repeated Bertrand game, in which prices are publicly observed and each firm receives a privately observed, i.i.d. cost shock in each period. We focus on symmetric perfect public equilibria, wherein any "punishments" are borne equally by all firms. We identify a tradeoff that is associated with collusive pricing schemes in which the price to be charged by each firm is strictly increasing in its cost level: such "fully sorting" schemes offer efficiency benefits, as they ensure that the lowest-cost firm makes the current sale, but they also imply an informational cost (distorted pricing and/or equilibrium-path price wars), since a higher-cost firm must be deterred from mimicking a lower-cost firm by charging a lower price. A rigid-pricing scheme, where a firm's collusive price is independent of its current cost position, sacrifices efficiency benefits but also diminishes the informational cost. For a wide range of settings, the optimal symmetric collusive scheme requires (i) the absence of equilibrium-path price wars and (ii) a rigid price. If firms are sufficiently impatient, however, the rigid-pricing scheme cannot be enforced, and the collusive price of lower-cost firms may be distorted downward in order to diminish the incentive to cheat. When the model is modified to include i.i.d. public demand shocks, the downward pricing distortion that accompanies a firm's lower-cost realization may occur only when current demand is high.     

Exchange rates and perfect competition

The purpose of this note is to demonstrate that the commonly held belief that incomplete and perverse pass-through are incompatible with perfect competition is wrong! To this end, we consider two types of firms both operating in two countries. The demand sides of the markets of the two countries are separated and each type of firm produces its good in one of these countries. We study the effect of an exchange-rate change on the competitive equilibrium prices in each country. When producing for the foreign market causes the same costs as producing for the home market then the law of one price holds and an exchange-rate change is completely offset by price changes. Furthermore, when cost functions neither exhibit economies nor diseconomies of scope between producing for the home and producing for the foreign market then prices move in the right directions in response to an exchange-rate change. However, with general cost structures, even in this simple perfectly competitive model, perverse directions of price changes can result from an exchange-rate change.     

Exchange rates and bertrand oligopoly

The impact of exchange-rate changes on industrial prices seems ambiguous. Incomplete and even perverse pass-through has been observed: the import prices in the depreciating country decrease while those in the appreciating country increase. To explain these counterintuitive price reactions we consider a situation of international Bertrand competition: two firms, based in different countries, are selling in both countries simultaneously. The profit-maximizing duopolists set the prices for their products in each of the two markets which are segmented on the demand side. We then study the qualitative effect of an exogenous exchange-rate change on the Bertrand-Nash equilibrium. Under the strong assumption of linear demand and cost functions we have normal exchange-rate pass-through. However, allowing for more general cost structures in this simple static model enables us to show that the import prices in both countries might move in counterintuitive directions.     

Rationing rule, imperfect information and equilibrium

Summary. The impact of imperfect information on the price setting behaviour of firms is analysed. Specifically, consumers support an information cost to become informed about prices. Firms are endowed with U-shaped average cost curves. If a firm does not supply more than its competitive supply as determined by its marginal cost schedule, then we show that the existence of a pure strategy equilibrium is conditional on the rationing rule employed. If uninformed consumers are served first then the monopoly price is the sole equilibrium whenever consumers' information costs are high enough. Otherwise, a pure strategy equilibrium fails to exist contrary to the results of Salop and Stiglitz (1977) or Braverman (1980) who implicitly suppose that firms supply all the demand at a given price. Received: May 17, 1999; revised version: September 15, 2000     

The price normalization problem in imperfect competition and the objective of the firm

Summary. General equilibrium models of oligopolistic competition give rise to relative prices only without determining the price level. It is well known that the choice of a numéraire or, more generally, of a normalization rule converting relative prices into absolute prices entails drastic consequences for the resulting set of Nash equilibria when firms are assumed to maximize profits. This is due to the fact that changing the price normalization amounts to altering the objective functions of the firms. Clearly, the objective of a firm must not be based on price normalization rules void of any economic content. In this paper we propose a definition of the objective of a firm, called maximization of shareholders' real wealth, which takes shareholders' demand explicitly into account. This objective depends on relative prices only. Real wealth maxima are shown to exist under certain conditions. Moreover, we consider an oligopolistic market and prove the existence of a Nash equilibrium in which each firm maximizes the real wealth of its shareholders. Received: July 10, 1997; revised version: July 27, 1998     

ON COURNOT-BERTRAND MIXED DUOPOLIES*

This paper deals;with a situation where a quality-setting Cournot firm and a price-seeting Bertrand firm coexist in the same industry. Under a set of regularity conditions on demand and coast, we compute equilibrium prices on Cournot-Bertrand "mixed"duopolies, and compare them with those of "pure" Cournot and Bertrand duopolies.     

General equilibrium effects of environmental policy: A CGE-modeling approach

Estimation of emission control cost functions is often carried out in a partial equilibrium framework, i.e., under the assumption that emission control measures have negligible effects on input and output prices. In this paper a computable general equilibrium model is used for simulation of the impact on factor prices and resource allocation of reductions of SO _infx ^sup- , NO _infx ^su- and CO₂-emissions. Thus the model includes markets for tradable emission permits, and the equilibrium prices of permits reflect the marginal costs of emission control. The results suggest that major emission reductions are likely to have general equilibrium effects, and thus that emission control cost functions that fail to take these effects into account may give a distorted picture of the economic impact of emission control.     

Sraffa and the Assumption of Constant Returns to Scale: A Critique of Samuelson and Etula

In a recent paper Samuelson and Etula claim to have providedthree examples of the presence of a constant returns to scaleassumption in Sraffa's Production of Commodities. The presentpaper is a refutation of their interpretation of Sraffa's propositions.It shows that they mistakenly take Sraffa's logical propositionsfor empirical propositions. This article also provides evidenceto refute Samuelson's hypothesis that Sraffa consistently confusedthe concept of Marshallian "constant cost" with the generalequilibrium concept of "constant returns to scale". The paperalso argues that Sraffa's prices are not necessarily "equilibrium"prices, and that it is not true that Sraffa maintained thatchanges in demand had no impact on prices; his position appearsrather to be that the impact of demand on prices is unpredictable.     

Full-cost pricing in the classical competitive process: A model of convergence to long-run equilibrium

In the last 10–15 years a lot of attempts has been devoted to study the calssical process of convergence of market prices toward natural prices. The two forces that one has thought could achieve this target were capital mobility, that determines the dynamics of output, and demand-supply forces, that determine the dynamics of prices. In this article a model of classical competition is proposed in which a full-cost pricing mechanism is adopted in the rule of evolution of market prices. An asymptotical stability result of long-run equilibrium is proved for a two-commodity model with and without a final demand.     

Personalized pricing and advertising: An asymmetric equilibrium analysis

We study personalized price competition with costly advertising among n quality-cost differentiated firms. Strategies involve mixing over both prices and whether to advertise. In equilibrium, only the top two firms advertise, earning “Bertrand-like” profits. Welfare losses initially rise then fall with the ad cost, with losses due to excessive advertising and sales by the “wrong” firm. When firms are symmetric, the symmetric equilibrium yields perverse comparative statics and is unstable. Our key results apply when demand is elastic, when ad costs are heterogeneous, and with noise in consumer tastes.     

Entrepreneurship,search costs,and ecological rationality in an agent-based economy

Since Coase’s paper on the firm, transaction costs have occupied much attention as a field of economic inquiry. Yet, with few exceptions, neoclassical theory has failed to integrate transaction costs into its core. The dominant mode of theorizing depends upon Brouwer fixed points which cannot integrate transaction costs in more than a superficial manner. Agent-based modeling presents an opportunity for researchers to investigate the nature of transaction costs and integrate them into the core of economic theory. To the extent that transaction costs reduce economic efficiency, they provide opportunities for entrepreneurs to earn a profit by reducing these costs. We employ an extension of Epstein and Axtell’s (1996) Sugarscape to demonstrate this point one type of transaction costs: search costs. When agents do not face the cost of finding a trading partner, the system quickly reaches a steady state with tightly constrained prices regardless of agent production strategies. When search costs are present, entrepreneurs may use competing strategies for production and exchange that allow them to earn higher revenues than they would earn otherwise. These cost reducing innovations tend to promote concatenate coordination (Klein 2012). The agent’s production strategies represent technology in the form of mental models (Denzau and North 1994) that shape agent action with regard to the agent’s environment. The success of these are dependent on their ability to overcome search costs. The average profit, market rate of return, earned by each of these mental structures tends to equalize as a result of competition.     

Intertemporal pricing in markets with differential information

Summary This paper provides a theory of intertemporal pricing in a small market with differential information about the realizations of a stochastic process which determines demand. We study the sequential equilibria in stationary strategies of the stochastic game between a seller and buyer. The seller has zero cost of producing one unit of a non-durable good in all market periods. The buyer's value for the good is a random variable governed by a simple Markov process. At the beginning of each period the unit's value is determined by nature and is privately revealed to the buyer. The seller posts a single price offer each period, which the buyer either accepts or rejects. Only two types of price paths emerge in equilibrium: either prices are constant, or they have persistent cycles between a low and a high value. In both cases, however, prices are sticky in the sense that changes in price are less frequent than changes in the economy's fundamentals.We thank John Rust and Asher Wolinsky for helpful comments. We also gratefully acknowledge financial support from NSF grant SES 89-09242.     

On Intertemporal Subsidy-Free Prices and Economic Depreciation: Constrained Market Pricing Revisited

The constrained market pricing approach to regulating monopolies maintains that prices should be subsidy-free, lying between the often expansive bounds of stand alone and incremental costs. For a simple two-good/two-period model of a monopolist subject to a zero profit constraint, it is shown that subsidy-free prices are those which rise to the amortized opportunity cost of the currently optimal asset configuration required to meet both current and future demand, providing—in some circumstances—justification for accelerated depreciation. Such intertemporal subsidy-free prices recognize that the stand alone cost of existing assets to current consumers depends on the value of those assets to future consumers. Hence, if a feasible resale price for the fixed costs of capacity exists within or between periods, then intertemporal stand alone costs and intertemporal incremental costs are driven to equality.     

Environmental Policy, Tax Incidence, and the Cost of Public Funds

This paper studies under what conditions a double dividend may occur in the sense that both environmental quality and employment rise. A simple static general equilibrium model is employed in which tax policy faces the dual task of internalising a negative environmental externality and raising revenue to finance public consumption. The model features a clearing labour market with both labour demand and supply and a fixed factor of production (e.g. capital). Hence, we can study tax incidence and its effect on employment, environmental quality, and the marginal cost of public funds. It is shown for the case of an upward sloping labour supply curve and less than full tax shifting by employers that a shift towards greener preferences cannot yield a double dividend, even if the fixed factor is important. However, if labour supply curve bends backwards, more environmental concern confers a double dividend.     

Competitive supply behavior when price information is fuzzy

The theory of fuzzy sets is applied to the output decisions of a price-taking firm facing imprecise information about expected future prices. Accepting risk resulting from the randomness of prices, the manager is interested in expected profits only. Since the set of possible expected-price vectors is fuzzy, a suitable defuzzification strategy is defined in analogy to the pessimism-optimism index proposed by L. Hurwicz. It depends on the manager's willingness to accept surprises resulting from a deviation of the true expected prices from the values that guided output decisions. Despite a linear cost function, well specified solutions to the optimization problem are possible without resorting to capacity constraints.     

Risk,variety and volatility: growth,innovation and stock prices in early industry evolution

The paper studies the patterns of volatility in firm growth rates and stock prices during the early phase of the life-cycle of an old economy industry, the US automobile industry from 1900-1930, and a new economy industry, the US PC industry from 1974-2000. In both industries, firm growth rates are more volatile in the period in which innovation is the most radical. This is also the period in which stock prices are more volatile. The comparison sheds light on the co-evolution of industrial and financial volatility and the relationship between this co-evolution and mechanisms of Schumpetarian creative destruction. Results provide insight into the debate on whether the statistical behavior of firm growth rates is well represented by Gibrats Law.JEL Classification: L11, 030, G12I thank Massimiliano Tancioni for his excellent research assistance. Support from the following grants is much appreciated: European Commission Key Action Improving the socio-economic knowledge basecontract HPSE-CT-2002-00146, and the Open University RDF Grant contract no. 793.