Book titles, because they are compromises between concision and precision, provide but an approximate description of real content. For this book an al­ ternative and more comprehensive title would be: An investigation of spatial arbitrage as an introduction to the theory of commodity markets: trade and space-time patterns of price fluctuations. In this title, both the specificities and the limitations of our approach are emphasized. Firstly, our approach con­ centrates on the basic mechanisms of spatial arbitrage, leaving aside a number of accessory facets of international trade such as the impact of quotas or of ex­ change rates. Secondly, for the sake of simplicity we restrict ourselves to single commodity markets; the interrelationship of different goods on multi-commodity markets are only occasionally mentioned. The previous restrictions, however drastic they may at first appear delimit and define what can be considered as the core of the process of trade and of spatial transactions. Having thus simplified the object of our study, we are able to tackle the problem in a systematic way and to model spatial differentials along with their relationships to the volume of trade both in eqUilibrium and in non-equilibrium situations. As far as the subtitle of the book is concerned, we shall postpone the discussion of what is meant by the expression "analytical economics" until the concluding chapter.

Inhalt

I Prologue.- 1 Introduction.- 1 Smith's "invisible hand" in commodity markets.- 2 Spatial interaction in economic theory.- 3 Spatial interaction in geographical analysis.- 4 Regional market integration and famines.- 5 Organization of commodity markets.- 5.1 The twentieth century wheat market.- 5.2 Which prices?.- 5.3 Long term evolution of ocean freight rates.- 6 Spatial price differentials.- 6.1 Three examples of spatial price differentials.- 6.2 Evolution of spatial price differentials.- 7 The concept of market integration.- 8 Defining and delimiting the problems to be investigated.- 9 The methodology of our approach: parsimony as a condition of testability.- 10 Empirical findings.- 10.1 Interdependence between markets.- 10.2 Price intercorrelations.- 10.3 Variations in trade with respect to transportation costs.- 10.4 The evolution of market integration.- 10.5 The evolution of price volatility.- 11 Outline of the book.- 2 Pricing models.- 1 Dynamic market models with exogenous price expectations.- 1.1 Cobweb models without inventories.- 1 Conservative price anticipation.- 2 Extrapolative price anticipation.- 3 Adaptative price anticipation.- 4 The problem of mixed time scales.- 1.2 Cobweb models with inventories.- 1 A linear model.- 2 An example: the FAO cocoa price model.- 3 Comparison with empirical evidence.- 4 Nonlinear models.- 2 Rational expectations models.- 2.1 Origins of the concept of rational expectations.- 2.2 Rational expectations in commodity markets without inventories.- 2.3 Rational expectation with inventories.- 2.4 More about expectional equations.- 3 Oligopoly theory and spatial competition.- 3.1 The monopoly optimum.- 1 The firm is able to sell all it wishes.- 2 The firm cannot sell all it wishes.- 3.2 The duopoly equilibrium.- 1 Cournot's model.- 2 Nash equilibrium.- 3 Spatial competition: two marketplaces.- 4 Spatial competition: several marketplaces.- A Appendix A: Conditional expectation: a mathematical reminder.- A.1 Conditional expectation: two random variables.- 1 Definitions.- 2 Basic properties of conditional expectation.- A.2 Conditional expectation: generalization to n random variables.- B Appendix B: Consumption, closing stocks and prices of cocoa, sugar and wheat.- II Equilibrium models.- 3 The stochastic Enke-Samuelson arbitrage model.- 1 Defining the stochastic Enke-Samuelson model.- 1.1 The spatial price equilibrium model.- 1 General presentation.- 2 The spatial price equilibrium model for two markets.- 3 Algebraic solution.- 4 Variational solution.- 1.2 Possible generalizations to more than two markets.- 1 The algebraic solution.- 2 The variational solution.- 1.3 The stochastic Enke-Samuelson model.- 1 The rationale of a stochastic model.- 2 Smoothing and linearization of the model.- 3 Consistency tests of the model.- 4 Predictions of the model.- 2 The stochastic Enke-Samuelson model for two markets.- 2.1 Basic equations.- 2.2 Solutions of the linear model.- 1 Uncorrelated local shocks (identical means).- 2 Correlated local shocks (identical means).- 3 Correlated local shocks (different means).- 4 Linear versus nonlinear model.- 3 Chain of markets.- 3.1 Chain of markets: direct trade relations restricted to closest neighbours.- 1 Solving the linear model.- 2 Proof.- 3 Price differentials as a function of distance.- 4 Linear versus nonlinear model.- 3.2 Chain of markets with an arbitrary exchange pattern.- 1 Equations and results.- 2 Roots of reciprocal equation.- 3 Covariance function.- 4 Variance.- 5 Trade.- 6 Discussion.- 4 Market networks.- 4.1 Solving the linear Enke-Samuelson model.- 1 Equations of the model.- 2 Solution by Fourier transformation.- 3 Integral representation of the covariance function.- 4 Asymptotic expressions of the price covariance function.- 5 Approximation formula.- 4.2 Process of market integration.- 4.3 Price differentials as a function of inter-market distance.- A Appendix A: Covariance function of a network of markets.- A.1 Development for vanishing transportation costs.- A.2 Asymptotic expression for large transportation costs.- A.3 Approximation formula.- 4 Empirical evidence about transport costs.- 1 Transportation costs.- 1.1 European nineteenth century wheat markets.- 1 Inter-regional trade.- 2 International trade.- 1.2 Twentieth century commodity markets.- 1 Inter-regional trade in the United States.- 2 International trade.- 1.3 Long term evolution of transportation costs.- 1 Rail and waterways freight rates.- 2 Ocean freight rates.- 3 Tariffs.- 2 The spatial patterns of price differentials.- 2.1 European nineteenth-century wheat markets.- 1 Comparison between the evolution of price differentials and of transportation costs.- 2 Methodology for the observation of price differentials.- 3 Price differentials at the regional level.- 4 Price differentials at the national level.- 5 Price differentials at the international level.- 2.2 Twentieth-century commodity markets.- 1 Wheat market in the United States.- 2 Potato market in the United States.- 2.3 Is the spatial distribution of prices Gaussian?.- 1 ?2 test versus cumulant tests.- 2 The spatial distribution of prices.- 3 The reduction in spatial price differentials and its implications.- 3.1 Evidence of long term price convergence.- 1 How to measure spatial price dispersion?.- 2 Spatial price convergence.- 3.2 The relationship between price convergence and decrease in price volatility.- 3.3 The relationship between price convergence and trade development.- 1 Trade development at the level of single commodities.- 2 Trade development at the macroeconomic level.- 4 Estimation of the Enke-Samuelson trade model.- 4.1 Methodology.- 4.2 Results.- A Appendix A: Dispersion measures for spatial distributions.- A.1 The mean difference.- 1 Existence.- 2 Relation with Gini's coefficient.- 3 Sampling properties.- A.2 The range of the sample.- 1 The limiting distributions.- 2 Sampling properties 156 B Appendix B: Trade and wheat differentials between England and Prussia 1828-1859.- C Appendix C: Conversion tables for volumes, weights and currencies.- 5 Grain markets and demographic phenomena.- 1 The green-belt model for city-size distributions.- 1.1 The finite Pareto distribution.- 1 Cumulated distribution of the finite Pareto distribution.- 2 Expectation of the finite Pareto distribution.- 3 Concentration of a finite Pareto distribution.- 1.2 Evolution of urban systems in the Pareto plane.- 1 The transportation constraint in the green-belt model.- 2 Graphical representation in the Pareto plane: possible trajectories.- 1.3 Confr…