CHRISTIAN BIDARD

The Hicksian Traverse

Christian Bidard

Résumé

Nous considérons les perturbations dues à l'introduction d'une nouvelle machine dans une économie en croissance régulière. Hicks nomme traverse la trajectoire intertemporelle conduisant de l'ancien à un nouveau sentier régulier. La dynamique dépend des caractéristiques des deux techniques comparées. Nous simplifions et généralisons l'analyse de Hicks, qui repose sur un modèle néo-autrichien, et montrons que les conditions d'existence d'une traverse de plein emploi sont restrictives.

Mot(s) clé(s)

Modèle autrichien, changement technique, emploi, traverse

The Wage-Maximisation Property

Christian Bidard

Résumé

Pour les modèles linéaires de production simple, la technique concurrentielle de long terme est celle qui, à taux de profit donné, maximise le salaire,. Cette propriété est étendue aux modèles de production jointe qui satisfont une hypothèse additionnelle dénommée robustesse. En particulier, la propriété de non-substitution implique que les prix concurrentiels en termes de salaire sont minimaux. Le résultat est appliqué à plusieurs types de modèles, y compris ceux de production avec capital fixe. Sous l'hypothèse de robustesse, la maximisation du salaire peut être vue comme la contrepartie en termes de valeur de la règle d'or.

Mot(s) clé(s)

Non-substitution, Maximisation du salaire, règle d'or, capital fixe, Sraffa

An oddity property for cross-dual games

Christian Bidard

Résumé

The parametric Lemke algorithm is used to show the existence of an odd number of solutions of a generalized bimatrix game in a certain domain. These solutions are classified into two types according to the relative sign of two determinants. The British economist David Ricardo made an implicit use of that algorithm at the beginning of the nineteenth century.

Mot(s) clé(s)

Complementarity problems, Generalized bimatrix game, Oddity, Parametric Lemke algorithm, Ricardo.

The Wage Curve in Austrian Models

Christian Bidard

Résumé

We fully characterise, in terms of their local or global properties, the wage curves associated with Austrian models of production. When these properties are met, the degrees of freedom in the choice of parameters allow us to build an Austrian model which admits a given wage curve and satis…es other requirements.

Mot(s) clé(s)

Austrian model, long run, trade-o¤property, wage curve.

The Ricardian rent theory two centuries after

Christian Bidard

Résumé

We propose to re-read Ricardo's theory of rent and its modern versions. Ricardo's dynamic approach follows the transformations of a long-term equilibrium with demand. Sraffa adopted the same framework while substituting a value criterion for a physical criterion to determine the incoming marginal method, but he did not state the law of succession of methods explicitly. This prevented him to realize that his critique opens the door to all complications of capital the ory, with the consequence that the Ricardian dynamics fail when a divergence appears between profitability and productivity. Contemporary studies have cast doubts on the validity of some of Ricardo's and Sraffa's over-optimistic conclusions, but the abandonment of the dynamic approach does not allow them to explain the ultimate reason of the phenomena they have pointed at. Ricardo's method has been recently rediscovered by mathematicians.

Mot(s) clé(s)

Classical theory, land, rent, Ricardo, Sraffa.

Disequilibrium, reproduction and money: a Classical approach

Carlo Benetti, Christian Bidard, Edith Klimovsky, Antoine Rebeyrol

Résumé

We consider a bisector reproduction model in which money is introduced as a pure means of exchange issued by a bank at the producers' requests. Each capitalist aims at maximising accumulation in his own sector. Their plans are based on available quantities and expected prices. Effective prices are determined by a market-clearing mechanism. Temporary disequilibria occur in both physical and monetary terms. The settlement of the monetary balances is operated by means of a transfer of capital goods. Final allocations and effective productions are thus determined. The dynamics of the economy are those of a sequence of temporary disequilibria and let appear several possibilities (local or global stability, cycles) depending on the values of the parameters.

Mot(s) clé(s)

Classical Reproduction, Monetary prices, Disequilibrium, Growth, Cycle

GETTING RID OF RENT?

Christian Bidard

Résumé

In order to extend the theory of value and the trade-off property to economic systems with lands, Ricardo reduced their study to that of productive systems without lands by considering the marginal agricultural methods. Sraffa generalised the analysis to prices of production and rejected the notion of order of cultivation. The strategy works sometimes for extensive cultivation, fails in most cases of intensive cultivation, and always when the net product of agriculture is increased by making use of corn saving methods in industry.

Mot(s) clé(s)

Land, rent, Ricardo, Sraffa, trade-off

RICARDO AND LEMKE

Christian Bidard

Résumé

We study the economic mechanism which sustains the substitution of a marginal method for another when demand increases, in the presence of scarce resources. In those Ricardian dynamics, it is shown that the outgoing method is determined by the quantity side of the problem, the incoming method by the value side. That discrepancy explains both the possible failure of the dynamics and the possible occurrence of multiple equilibria. Conditions for existence, uniqueness and the working of the dynamics are stated. A parallel is drawn with the parametric Lemke algorithm used to solve linear complementarity problems.

Mot(s) clé(s)

Dynamics, Lemke, rent, Ricardo, scarce resources

The Frail Grounds of the Ricardian Dynamics

Christian Bidard

Résumé

The Ricardian dynamics study the evolution of distribution when demand increases. The successive marginal methods in agriculture are determined by means of a rule which has never been stated explicitly by Ricardo's commentators. But the rule also allows us to point at two limits of Ricardo's construction, first in his attempt to get rid of rent in the analysis of distribution, second in the working of the dynamics themselves. Similarly, the identification of a productivity and a profitability criterion is at the basis of Sraffa's mistake in his reconstruction of the theory of rent, whereas post-Sraffian formalizations have abandoned Ricardo's dynamic approach.

Mot(s) clé(s)

Rent; Ricardian dynamics; Ricardo; Sraffa

The Ricardo-Lemke parametric algorithm on oddity and uniqueness

Christian Bidard

Résumé

The parametric Lemke algorithm finds an odd number of solutions to the linear complementarity problem LCP (q, M), for a matrix M with zero blocks on the diagonal and vector q within a certain domain. A criterion for monotonicity and uniqueness is given. The algorithm applies to the determination of a long-run equilibrium in the presence of scarce resources, and its first description can be traced back to the nineteenth century economist David Ricardo.

Mot(s) clé(s)

Oddity; parametric Lemke algorithm; Ricardo; uniqueness.

The Ricardian Dynamics Revisited

Christian Bidard

Résumé

The Ricardian dynamics describe the substitution of a new marginal method for an outgoing marginal method when demand increases. The process of extension or intensi…cation of cultivation allows for spasmodic changes in prices and rents but is smooth on the physical side. We criticize the notion of extension of cultivation and show the existence of non-Ricardian equilibria, when some good is not produced by a marginal method. The working of the dynamics requires that the incoming method satisfies a productivity condition which is expressed in algebraic terms. A parallel is drawn between Ricardo's views on dynamics and the working of a Lemke algorithm for linear complementarity problems.

Mot(s) clé(s)

Dynamics, Lemke, Linear Complementarity Problem, Rent, Ricardo

Reproduction and temporary disequilibrium: a Classical approach

Carlo Benetti, Christian Bidard, Edith Klimovsky, Antoine Rebeyrol

Résumé

We build a bisector reproduction model with classical features in which the capitalists aim at maximizing accumulation of their profits. At variance with gravitation models, it is assumed that they invest their profits in their own industry. Their plans are based on actual productions and expected prices. Effective prices and effective allocations of resources are determined by a market-clearing mechanism. A simple law on the formation of expectations allows us to define the dynamics of disequilibria, which let appear endogenous self-sustained fluctuations, around a long-run path. The long-run rate of growth and the amplitude of the fluctuations depend on the initial conditions.

Mot(s) clé(s)

Classical Reproduction, Market prices, Disequilibrium, Growth, Cycle

Complementarity Problems and General Equilibrium

Christian Bidard

Résumé

A general equilibrium technique is used to show the existence of a solution to a nonlinear complementarity problem involving a copositive function.

Mot(s) clé(s)

Nonlinear complementarity problem; general equilibrium; copositivity.

The Dynamics of Intensive Cultivation

Christian Bidard

Résumé

An increase in the demand for agricultural goods leads to the use of more intensive cultivation methods. Though Ricardo sees no difficulties in the intensification process, their existence is revealed by the possible occurrence of multiple equilibria. A general theory of intensive rent is based on a formal parallel with single-product systems without land.

Mot(s) clé(s)

intensive cultivation, land, rent, Ricardo