In this paper we model the evolution of conjectures in an economy consisting of a large number of... more In this paper we model the evolution of conjectures in an economy consisting of a large number of firms which meet in duopolies. The duopoly game is modelled by the conjectural variation (CV) model. An evolutionary process leads to more profitable conjectures becoming more common (payoff monotone dynamics). Under this class of selection dynamics, convergence occurs to a small set of serially undominated strategies containing the consistent conjecture. This set can be made arbitrarily small by appropriate choice of the strategy set. If the game is dominance solvable, then the dynamics converge globally to the unique attractor.
The gas industry was first privatised in 1986, and the regulator, Ofgas, identified the contract ... more The gas industry was first privatised in 1986, and the regulator, Ofgas, identified the contract gas market as a possibility for introducing initial competition into the industry. Nevertheless, competing shippers were slow in entering the market. Subsequently, Ofgas introduced a series of procompetitive policies. It, however, invoked a series of strategic behaviour by the incumbent shipper, British Gas. The effectiveness of these measures are analysed here with respect to the evolving competitive process. The issues it raised, especially when formulating future regulatory policies and theories, are also considered.
This paper considers the existence and properties of approximate Bertrand equilibria in a replica... more This paper considers the existence and properties of approximate Bertrand equilibria in a replicated industry. Price setting firms produce a homogeneous product with weakly convex costs. The main results are that: (a) Given E > 0, an E-equilibrium exists if the industry is large enough; (b) If the e is small enough, and the industry large enough, any E-equilibrium is approximately competitive. These results depend on how contingent demand is specified.
THE IMPORTANCE of imperfect competition has long been recognised in many areas of economics, perh... more THE IMPORTANCE of imperfect competition has long been recognised in many areas of economics, perhaps most obviously in industrial economics and in the labour economics of trade unions. Despite the clear divergence of output and labour markets from the competitive paradigm in most countries, macroeconomics where it has used microfoundations has tended to stick to the Walrasian market-clearing approach. However, over the last decade a shift has begun away from a concentration on the Walrasian price-taker towards a world where firms, unions and governments may be strategic agents. This paper takes stock of this burgeoning literature, focusing on the macroeconomic policy and welfare implications of imperfect competition, and contrasting them with those of Walrasian models.
WHAT influence does trade union power have on the nature of macroeconomic equilibrium, and the ab... more WHAT influence does trade union power have on the nature of macroeconomic equilibrium, and the ability of the government to influence that equilibrium? Given the importance of unions in many industrialised economies, this is an issue of central importance for those who wish to adopt a macroeconomic approach to understanding macroeconomic equilibrium.
IT IS generally recognised that the flexibility of firms' production will influence the nature of... more IT IS generally recognised that the flexibility of firms' production will influence the nature of competition in an industry. For example, where production is very inflexible the Cournot outcome seems most appropriate: the Bertrand outcome, however, depends on production being perfectly flexible. The model presented makes both the firms' cost structure (flexibility of production) and the nature of competition endogenous, and thus provides a framework in which both elements of industrial structure and the conduct of firms are explained. We combine two ideas in the recent literature on oligopoly theory: models of strategic investment (Brander and Spencer (1983), Dixon (1985), Eaton and Grossman (1984), Yarrow (1985) inter alia) and notions of the consistency of conjectures (Bresnehan (1981) in particular). The fundamental idea underlying this synthesis is very simple. As we discuss below, there is a precise sense in which Bresnehan's consistency condition relates firm's conjectures about each other's responses-and hence the degree of competition in the product market-to the firms cost functions. Strategic investment models, on the other hand, provide a framework for making the firm's cost functions endogenous: by choosing a level of investment, the firm decides which short-run cost function it will have. By combining the strategic investment framework with Bresnehan's consistency condition, we have a model in which both firm's cost structures and the degree of competition in the product market are endogenously determined. Thus we have a framework in which both a structural characteristic of the market (firms costs), and the conduct of firms are endogenously determined.
IMPERFECT competition is a pervasive part of modern industrial economies, where high levels of co... more IMPERFECT competition is a pervasive part of modern industrial economies, where high levels of concentration in product markets often coexist with unionised labour markets. Most standard macroeconomic models, however, assume that markets are perfectly competitive. This paper provides a simple framework in which we are able to explore some of the implications of imperfect competition for the macroeconomy, and to evaluate the adequacy of competitive macroeconomic models as "convenient simplifications". The results of the paper suggest that whilst some general features of competitive macromodels do carry over to an imperfectly competitive framework, others do not. Imperfect competition in the labour and product market can have a significant impact on the level of employment and the effectiveness of macroeconomic policy. Imperfect competition provides an explicit account of price and wage determination, and thus gives us a far greater insight into the macroeconomic structure of macroeconomic equilibrium than is possible in competitive models. This paper presents a simple model of imperfect competition with Walrasian features. The model is "Walrasian" both in some of its assumptions,0 and also in the properties of the model. What we have attempted to do is to take a standard neoclassical synthesis macromodel (e.g. Patinkin (1965), Branson (1979)) and introduce imperfect competition into the product and labour markets. We feel that this is a useful exercise for two reasons. Firstly, it provides a simple macro model of imperfect competition in which the causal mechanisms are very clear. In general, models of imperfect competition have tended to be rather complex, despite a recent trend towards simpler versions (e.g. Hart (1982), d'Aspremont et al. (1985)). Secondly, by adopting the standard neoclassical synthesis framework, it is easy to relate the model of imperfect competition to more familiar models. Imperfect competition in the product is modelled using conjecturalvariations Cournot equilibrium which captures a wide range of possible market solutions, encompassing perfect competition, Cournot, and joint profit maximisation as special cases. This approach contrasts with existing I would like to thank Ben Lockwood and Dennis Snower for many useful conversations. The first section of the paper was used for the M.Sc. macroeconomics course at Birkbeck in March 1985. The current revision owes much to comments made at the time. Financial support from the ESRC is gratefully acknowledged. Faults, alas, remain my own.
This paper develops a new class of homothetic preferences which generate Marshallian demand curve... more This paper develops a new class of homothetic preferences which generate Marshallian demand curves for individual goods which can be concave, convex or linear in own price under the assumption that agents treat aggregate price indices as given (as in . The preferences are represented by a cost function which has two parameters: one determining the curvature of the Marshallian demand; the other determining the elasticity of demand when all prices are equal. The elasticity of demand varies with relative prices. Illustrative examples are given of Cournot duopoly and exchange rate pass-through.
This paper provides a simple solution to the problem of non-existence of pure-strategy equilibria... more This paper provides a simple solution to the problem of non-existence of pure-strategy equilibria in Bertrand-Edgeworth models with strictly convex costs. The voluntary-trading constraint in standard Bertrand-Edgeworth models is generalized to allow for there being costs incurred when customers are turned away. So long as the industry is sufficiently large, the presence of such costs ensures that the competitive price will be an equilibrium. There will be other single price equilibria, but if the offence costs are small, all equilibria will be close to the competitive outcome. * I would like to thank two most helpful referees, Michael Tiet Nielson, Peter Skott and other workshop participants at Aarhus, as well as seminar participants at Birkbeck/UCL, Cambridge and York for their helpful comments. ' For a comparison of these approaches with differentiated products, see Benassy [1989]. 131 132 HUW DIXON T > 0 to turning customers away: the standard Bertrand-Edgeworth model is a special case where Y = 0. It is very plausible to assume that there is some cost to failing to meet demand, in terms of loss of goodwill, reputation, or offence caused. The presence of such costs is absolutely standard in Operations Research and inventory models (see, for example, Taha [1982, ch. 13] for textbook treatment and references)
In this paper, we develop a general model of an imperfectly competitive small open economy. There... more In this paper, we develop a general model of an imperfectly competitive small open economy. There is a traded and non-traded sector, whose outputs are combined in order to produce a single ÿnal good that can be either consumed or invested. We make general assumptions about preferences and technology, and analyze the impact of ÿscal policy on the economy. We ÿnd that the ÿscal multiplier is between zero and one, and provide su cient conditions for it to be increasing in the degree of imperfect competition. We also are able to compare the multiplier under free-entry and with a ÿxed number of ÿrms and welfare. A simple graphical representation of the model is developed.
In this paper we study the e!ects of opening an economy, with increasing returns in the productio... more In this paper we study the e!ects of opening an economy, with increasing returns in the production of nontraded goods, on the existence of multiple Pareto-ranked stationary equilibria, local indeterminacy and bifurcations. We consider a standard overlapping generation model of a small open economy, with a "xed exchange rate, where labour is the only input and money the only asset. We "nd that when there are increasing returns, the open economy may display persistent equilibrium endogenous #uctuations (deterministic and stochastic) in the balance of trade and main macroeconomic aggregates.
In this paper we model the evolution of conjectures in an economy consisting of a large number of... more In this paper we model the evolution of conjectures in an economy consisting of a large number of firms which meet in duopolies. The duopoly game is modelled by the conjectural variation (CV) model. An evolutionary process leads to more profitable conjectures becoming more common (payoff-monotonic dynamics). Under this class of selection dynamics, convergence occurs to a small set of serially undominated strategies containing the consistent conjecture. This set can be made arbitrarily small by appropriate choice of the strategy set. If the game is dominance solvable, then the dynamics converge globally to the unique attractor.
In this paper we model the evolution of conjectures in an economy consisting of a large number of... more In this paper we model the evolution of conjectures in an economy consisting of a large number of firms which meet in duopolies. The duopoly game is modelled by the conjectural variation (CV) model. An evolutionary process leads to more profitable conjectures becoming more common (payoff monotone dynamics). Under this class of selection dynamics, convergence occurs to a small set of serially undominated strategies containing the consistent conjecture. This set can be made arbitrarily small by appropriate choice of the strategy set. If the game is dominance solvable, then the dynamics converge globally to the unique attractor.
The gas industry was first privatised in 1986, and the regulator, Ofgas, identified the contract ... more The gas industry was first privatised in 1986, and the regulator, Ofgas, identified the contract gas market as a possibility for introducing initial competition into the industry. Nevertheless, competing shippers were slow in entering the market. Subsequently, Ofgas introduced a series of procompetitive policies. It, however, invoked a series of strategic behaviour by the incumbent shipper, British Gas. The effectiveness of these measures are analysed here with respect to the evolving competitive process. The issues it raised, especially when formulating future regulatory policies and theories, are also considered.
This paper considers the existence and properties of approximate Bertrand equilibria in a replica... more This paper considers the existence and properties of approximate Bertrand equilibria in a replicated industry. Price setting firms produce a homogeneous product with weakly convex costs. The main results are that: (a) Given E > 0, an E-equilibrium exists if the industry is large enough; (b) If the e is small enough, and the industry large enough, any E-equilibrium is approximately competitive. These results depend on how contingent demand is specified.
THE IMPORTANCE of imperfect competition has long been recognised in many areas of economics, perh... more THE IMPORTANCE of imperfect competition has long been recognised in many areas of economics, perhaps most obviously in industrial economics and in the labour economics of trade unions. Despite the clear divergence of output and labour markets from the competitive paradigm in most countries, macroeconomics where it has used microfoundations has tended to stick to the Walrasian market-clearing approach. However, over the last decade a shift has begun away from a concentration on the Walrasian price-taker towards a world where firms, unions and governments may be strategic agents. This paper takes stock of this burgeoning literature, focusing on the macroeconomic policy and welfare implications of imperfect competition, and contrasting them with those of Walrasian models.
WHAT influence does trade union power have on the nature of macroeconomic equilibrium, and the ab... more WHAT influence does trade union power have on the nature of macroeconomic equilibrium, and the ability of the government to influence that equilibrium? Given the importance of unions in many industrialised economies, this is an issue of central importance for those who wish to adopt a macroeconomic approach to understanding macroeconomic equilibrium.
IT IS generally recognised that the flexibility of firms' production will influence the nature of... more IT IS generally recognised that the flexibility of firms' production will influence the nature of competition in an industry. For example, where production is very inflexible the Cournot outcome seems most appropriate: the Bertrand outcome, however, depends on production being perfectly flexible. The model presented makes both the firms' cost structure (flexibility of production) and the nature of competition endogenous, and thus provides a framework in which both elements of industrial structure and the conduct of firms are explained. We combine two ideas in the recent literature on oligopoly theory: models of strategic investment (Brander and Spencer (1983), Dixon (1985), Eaton and Grossman (1984), Yarrow (1985) inter alia) and notions of the consistency of conjectures (Bresnehan (1981) in particular). The fundamental idea underlying this synthesis is very simple. As we discuss below, there is a precise sense in which Bresnehan's consistency condition relates firm's conjectures about each other's responses-and hence the degree of competition in the product market-to the firms cost functions. Strategic investment models, on the other hand, provide a framework for making the firm's cost functions endogenous: by choosing a level of investment, the firm decides which short-run cost function it will have. By combining the strategic investment framework with Bresnehan's consistency condition, we have a model in which both firm's cost structures and the degree of competition in the product market are endogenously determined. Thus we have a framework in which both a structural characteristic of the market (firms costs), and the conduct of firms are endogenously determined.
IMPERFECT competition is a pervasive part of modern industrial economies, where high levels of co... more IMPERFECT competition is a pervasive part of modern industrial economies, where high levels of concentration in product markets often coexist with unionised labour markets. Most standard macroeconomic models, however, assume that markets are perfectly competitive. This paper provides a simple framework in which we are able to explore some of the implications of imperfect competition for the macroeconomy, and to evaluate the adequacy of competitive macroeconomic models as "convenient simplifications". The results of the paper suggest that whilst some general features of competitive macromodels do carry over to an imperfectly competitive framework, others do not. Imperfect competition in the labour and product market can have a significant impact on the level of employment and the effectiveness of macroeconomic policy. Imperfect competition provides an explicit account of price and wage determination, and thus gives us a far greater insight into the macroeconomic structure of macroeconomic equilibrium than is possible in competitive models. This paper presents a simple model of imperfect competition with Walrasian features. The model is "Walrasian" both in some of its assumptions,0 and also in the properties of the model. What we have attempted to do is to take a standard neoclassical synthesis macromodel (e.g. Patinkin (1965), Branson (1979)) and introduce imperfect competition into the product and labour markets. We feel that this is a useful exercise for two reasons. Firstly, it provides a simple macro model of imperfect competition in which the causal mechanisms are very clear. In general, models of imperfect competition have tended to be rather complex, despite a recent trend towards simpler versions (e.g. Hart (1982), d'Aspremont et al. (1985)). Secondly, by adopting the standard neoclassical synthesis framework, it is easy to relate the model of imperfect competition to more familiar models. Imperfect competition in the product is modelled using conjecturalvariations Cournot equilibrium which captures a wide range of possible market solutions, encompassing perfect competition, Cournot, and joint profit maximisation as special cases. This approach contrasts with existing I would like to thank Ben Lockwood and Dennis Snower for many useful conversations. The first section of the paper was used for the M.Sc. macroeconomics course at Birkbeck in March 1985. The current revision owes much to comments made at the time. Financial support from the ESRC is gratefully acknowledged. Faults, alas, remain my own.
This paper develops a new class of homothetic preferences which generate Marshallian demand curve... more This paper develops a new class of homothetic preferences which generate Marshallian demand curves for individual goods which can be concave, convex or linear in own price under the assumption that agents treat aggregate price indices as given (as in . The preferences are represented by a cost function which has two parameters: one determining the curvature of the Marshallian demand; the other determining the elasticity of demand when all prices are equal. The elasticity of demand varies with relative prices. Illustrative examples are given of Cournot duopoly and exchange rate pass-through.
This paper provides a simple solution to the problem of non-existence of pure-strategy equilibria... more This paper provides a simple solution to the problem of non-existence of pure-strategy equilibria in Bertrand-Edgeworth models with strictly convex costs. The voluntary-trading constraint in standard Bertrand-Edgeworth models is generalized to allow for there being costs incurred when customers are turned away. So long as the industry is sufficiently large, the presence of such costs ensures that the competitive price will be an equilibrium. There will be other single price equilibria, but if the offence costs are small, all equilibria will be close to the competitive outcome. * I would like to thank two most helpful referees, Michael Tiet Nielson, Peter Skott and other workshop participants at Aarhus, as well as seminar participants at Birkbeck/UCL, Cambridge and York for their helpful comments. ' For a comparison of these approaches with differentiated products, see Benassy [1989]. 131 132 HUW DIXON T > 0 to turning customers away: the standard Bertrand-Edgeworth model is a special case where Y = 0. It is very plausible to assume that there is some cost to failing to meet demand, in terms of loss of goodwill, reputation, or offence caused. The presence of such costs is absolutely standard in Operations Research and inventory models (see, for example, Taha [1982, ch. 13] for textbook treatment and references)
In this paper, we develop a general model of an imperfectly competitive small open economy. There... more In this paper, we develop a general model of an imperfectly competitive small open economy. There is a traded and non-traded sector, whose outputs are combined in order to produce a single ÿnal good that can be either consumed or invested. We make general assumptions about preferences and technology, and analyze the impact of ÿscal policy on the economy. We ÿnd that the ÿscal multiplier is between zero and one, and provide su cient conditions for it to be increasing in the degree of imperfect competition. We also are able to compare the multiplier under free-entry and with a ÿxed number of ÿrms and welfare. A simple graphical representation of the model is developed.
In this paper we study the e!ects of opening an economy, with increasing returns in the productio... more In this paper we study the e!ects of opening an economy, with increasing returns in the production of nontraded goods, on the existence of multiple Pareto-ranked stationary equilibria, local indeterminacy and bifurcations. We consider a standard overlapping generation model of a small open economy, with a "xed exchange rate, where labour is the only input and money the only asset. We "nd that when there are increasing returns, the open economy may display persistent equilibrium endogenous #uctuations (deterministic and stochastic) in the balance of trade and main macroeconomic aggregates.
In this paper we model the evolution of conjectures in an economy consisting of a large number of... more In this paper we model the evolution of conjectures in an economy consisting of a large number of firms which meet in duopolies. The duopoly game is modelled by the conjectural variation (CV) model. An evolutionary process leads to more profitable conjectures becoming more common (payoff-monotonic dynamics). Under this class of selection dynamics, convergence occurs to a small set of serially undominated strategies containing the consistent conjecture. This set can be made arbitrarily small by appropriate choice of the strategy set. If the game is dominance solvable, then the dynamics converge globally to the unique attractor.
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