Gerhard Tintner’s journal article develops a dynamic extension of Walrasian general equilibrium and illustrates it with a simplified model of American prices. Its central move is to make demand and supply depend on anticipated prices, with expectations formed by extrapolating current prices and their rates of change. Equilibrium then becomes a system of differential equations whose solutions can generate economic fluctuations. The article’s two numbered sections move from the mathematical construction to its statistical application: “simple” identifies a deliberately restrictive model intended to connect market interdependence, expectations, and cyclical movements.
The introduction situates this construction within a progression of theories of expectation. Walras makes demand and supply functions of existing prices; Evans and Roos introduce anticipated prices with determinate values. Tintner then distinguishes risk, represented by a single probability distribution over possible prices, from uncertainty, represented by several possible distributions with prior probabilities. Although he compares the latter framework to classical Bayesian probability, the model developed here does not estimate such distributions. It instead gives a parsimonious answer to the question of how expectations are formed, taking past experience as their basis.
Nous allons supposer que les anticipations des prix dépendent des prix existants eux-mêmes et des dérivées des prix. Ainsi admettons-nous que les individus extrapolent le prix et le changement du prix au cours du temps pour former leurs anticipations 8.
English translation: We shall suppose that price expectations depend on existing prices themselves and on the derivatives of prices. We thus assume that individuals extrapolate the price and the change in the price over time to form their expectations 8.
This assumption makes expectations operational without introducing a separate psychological or probabilistic model. The rate of price change carries information about the future into present demand and supply. Because each market can respond to the prices and price derivatives of all goods and services, the construction preserves the interdependence central to general equilibrium. Its dynamics arise within the simultaneous market relationships, rather than from an independently specified sequence of business-cycle phases.
Tintner’s second simplifying move is to make demand and supply linear in those variables, with constant coefficients. He explicitly qualifies the economic plausibility of this assumption:
Pour obtenir des conclusions complètes, il est également nécessaire de supposer, comme premières approximations, que les fonctions de la demande et de l'offre sont linéaires. Naturellement, il ne s'agit pas là d'une hypothèse très réaliste.
English translation: To obtain complete conclusions, it is also necessary to suppose, as first approximations, that the demand and supply functions are linear. Naturally, this is not a very realistic assumption.
The qualification defines the model’s scope: tractability permits a complete account of its possible motions, but does not establish that actual markets obey these functions. Equating demand and supply yields a first-order linear differential system. Tintner separates constant equilibrium prices from deviations around them, obtaining a homogeneous system whose solutions are combinations of exponential terms. A characteristic equation determines the exponents; its roots therefore connect the market coefficients to the temporal behavior of prices. Distinct roots give individual modes of motion, while repeated roots introduce polynomial factors in time.
The decisive distinction is between real and complex roots. Complex conjugate roots combine into sinusoidal terms, allowing a system defined by equilibrium conditions to produce periodic price movements.
Si les racines sont purement imaginaires, les fluctuations auront une amplitude constante. Si les racines sont des nombres complexes, les fluctuations vont augmenter ou diminuer avec le temps.
English translation: If the roots are purely imaginary, the fluctuations will have a constant amplitude. If the roots are complex numbers, the fluctuations will increase or decrease over time.
Tintner subsequently specifies that positive real parts produce increasing amplitudes and negative real parts produce decreasing ones. Cyclicality and stability are thus separate properties: a periodic component may persist, grow, or decay. He also states that symmetry conditions on both the price coefficients and the derivative coefficients ensure real roots and exclude periodic fluctuations. The former are identified with Hotelling’s symmetry conditions; the latter concern the structure of expectations. Within his presentation, this makes expectations consequential not merely for the speed of adjustment but for the possibility of oscillation.
Section II applies the framework to three annual American price indices: stocks, agricultural products, and non-agricultural products. The observations cover 1920–1942, with 1926 as the base year. After statistical transformations, Tintner reports a three-equation system linking each index’s derivative to all three indices. Its characteristic roots comprise a complex conjugate pair, approximately −0.0510 ± 0.4901i, and a positive real root of 0.042. The pair yields a damped periodic component, while the real root produces an exponential secular movement. Consequently, decay of the cyclical component does not mean that the entire price trajectory converges to a stationary level.
Les mouvements périodiques des trois prix ont une période de 12,82 années.
English translation: The periodic movements of the three prices have a period of 12.82 years.
Tintner compares this common model-derived period with harmonic analyses of the observed series. The reported periodogram peaks include twelve and fifteen years for stock prices and thirteen years for both agricultural and non-agricultural prices, alongside shorter periods. He judges the correspondence a reasonably good approximation and presents figures for the observed series, periodograms, and theoretical oscillations. The evidence offered is therefore a comparison of periodic structure, not a demonstration that the model reproduces every movement in the data.
The article’s relevance lies in its compact bridge between equilibrium theory and empirical fluctuation analysis. Expectations convert a static price system into a dynamic one; characteristic roots distinguish secular movement from oscillation and determine the latter’s stability. Its accomplishment remains bounded by linearity, constant coefficients, a three-variable illustration, and a brief account of estimation. Tintner offers a tractable mechanism and a suggestive empirical comparison, rather than an exhaustive explanation of economic cycles.
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